Research ArticleModel-Based Optimization of Velocity Strategy forLightweight Electric Racing Cars

MirosBaw Targosz Wojciech Skarka and Piotr PrzystaBka

Silesian University of Technology Institute of Fundamentals of Machinery Design 18A Konarskiego Street 44-100 Gliwice Poland

Correspondence should be addressed to Wojciech Skarka WojciechSkarkapolslpl

Received 17 December 2017 Revised 24 April 2018 Accepted 10 May 2018 Published 7 June 2018

Academic Editor Sara Moridpour

Copyright copy 2018 Mirosław Targosz et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The article presents amethod for optimizing driving strategies aimed atminimizing energy consumptionwhile drivingThemethodwas developed for the needs of an electric powered racing vehicle built for the purposes of the Shell Eco-marathon (SEM) the mostfamous and largest race of energy efficient vehicles Model-based optimization was used to determine the driving strategy Thenumerical model was elaborated in Simulink environment which includes both the electric vehicle model and the environmentie the race track as well as the vehicle environment and the atmospheric conditions The vehicle model itself includes vehicledynamic model numerical model describing issues concerning resistance of rolling tire resistance of the propulsion systemaerodynamic phenomena model of the electric motor and control system For the purpose of identifying design and functionalfeatures of individual subassemblies and components numerical and stand tests were carried outThemodel itself was tested on theresearch tracks to tune the model and determine the calculation parameters The evolutionary algorithms which are available intheMATLAB Global Optimization Toolbox were used for optimization In the race conditions the model was verified during SEMraces in Rotterdam where the race vehicle scored the result consistent with the results of simulation calculations In the followingyears the experience gathered by the team gave us the vice Championship in the SEM 2016 in London

1 Introduction

The issue of energy saving in road transport is getting moreand more important It is especially significant in the contextof electric drives in vehicles becomingwidespread Reductionof energy consumption togetherwith the development of newenergy sources of greater capacity is seen as a method ofovercoming the main limitation of electric vehicles which isrange Shell Eco-marathon car race is the testing ground fornew solutions in designing energy saving vehicles A teamof scientists and students from the Silesian University ofTechnology has been taking part in it since 2012 in energysaving vehicles with electric drives which are designedand built by them in the following categories PrototypeUrbanConceptwith Battery Electric andUrbanConceptwithHydrogen Fuel Cell Stack Significant reduction in energyconsumption is achieved by the usage of twomethods [1]Thefirst one includes design changes which result in lower energyconsumptionwhereas the latter one introduces new strategies

of driving and drive steering which allows minimalizingthe energy consumption on a given route By means of thismethod it is possible to reduce considerably the energyconsumption in vehicles and in particular in electric vehiclesCurrently electric vehicles (city cars segment B) can reachthe result of about 5kmkWh of energy whereas respectivevehicles of UrbanConcept Battery Electric category reachup to 200 kmkWh in simulated conditions of driving in acity However prototype battery electric vehicles which aredifferent type as far as their structure is concerned reach theresult of 1000 kmkWh It shows the potential of the designsolutions and the strategy of driving In both categoriesnumerical simulation vehicle models are used which allowdetermining the direction of designing changes as well asplanning the proper strategy of drivingThesemodels are alsoused for optimization based on Model-Based Optimizationmethodology (MBO) This proprietary methodology usedfor vehicles development and planning the driving strategyhas been described in this paper Vehicles modelling and in

HindawiJournal of Advanced TransportationVolume 2018 Article ID 3614025 20 pageshttpsdoiorg10115520183614025

2 Journal of Advanced Transportation

particular electric vehicles modelling are widely known andbecome of an increased interest to research in particularwith hybrid drive or power source The necessity to modelphenomena and objects is commonly known and createssubstantial branch of science and engineering activities Theresearch and analysis of mechanical systems technologicalprocesses and other phenomena in real world are possi-ble thanks to the use of proper mathematical apparatuswhich is based on previously assumed mathematical modelsof these processes [2] According to this by means ofmathematical model one should understand mathematicaldescription of an object process or phenomenon which itrepresents

Compared to cars with internal combustion engineselectric cars have a relatively simpler drive system howeverin order to achieve a significant reduction in energy con-sumption in the electric cars drive system additional systemssuch as the energy recovery system additional mechatronicsubsystems and advanced control systems are integratedresulting in a continuous increase in the complexity of theelectric drive systems currently used The complexity of thetechnical means influences the complexity of the mathemati-cal model of the vehicle Among the models describing thedynamics of vehicles which are used in the analysis andoptimization of energy consumption two approaches aregenerally observed due to the type of model used and thefollowing models are distinguished

(i) Analytical ones in which the model response to thesignal is recorded as a motion equation

(ii) Models in the black box concept where the model isbased on experimental data

The created vehicle simulation model can be a com-bination of two model types To some extent the math-ematical description of a given phenomenon is based onknown dependencies while another fragment of the modelis created in the concept of a black box Taking into accountthe direction of information processing in the model thefollowing models [3] are distinguished

(i) Simple where the calculations made by the modelstart with the engine energy is transferred to thewheels of the vehicle and vehicle behaviour can beanalyzed

(ii) Reverse in which the behaviour of the body of thevehicle is modelled eg the speed and on this basisthe required torque and the speed of rotation of themotor shaft are determined

The choice of model type is mainly determined by theneed for which the model is to be used For modelling ofdynamics of electric vehicles many computer programs areused among them noteworthy is the ADVISOR (AdvancedVehicle Simulator) platform [4ndash6] written as a program inthe MATLAB-Simulink package The program in its librariesgives you the opportunity to analyze many of the solutionsof the power system drive system or vehicle body Anotherplatform running in the MATLAB-Simulink environment is

PSAT (The Powertrain System Analysis Toolkit) which sim-ulates many predefined solutions for conventional electricand other vehicles [7]The evolution of PSAT isAutonomy [8]available onLMS ImagineLab In addition to these simulationenvironments where models are abstract and which takeinto account the mechatronic nature of the electric vehiclespropulsion system there are many specialized dynamicanalysis programs utilizing the multibody formalism suchas the LS-Dyna Adams orMotionSolve software Simulationmodels designed to analyze and optimize energy consump-tion should allow for less time consuming calculationsThis is especially important in optimization tasks wheresimulation is performed many times (often over several tensof thousands of times) You can say that the faster the modelis themore abstract it is In paper [9] this is demonstrated bythe synchronous motor written in MATLAB and SimplorerIn order to reduce the computational time the model shouldbe written in a low-level language eg C as given in[10] and the simulation time can be reduced by up to 20times compared to a program written in MATLABs ownlanguage

2 Research Methodology

In order to optimize the control strategy for a light electricracing vehicle the general methodology described below ispresented which explains the basic ideas and above all thedefinitions of the key concepts from energy consumptiondomain The general functional structure of the drive systemwith particular attention to drive control and the optimiza-tion scheme are also presented below

Energy Consumption E of the Movement Movement ofthe vehicle is a consequence of the longitudinal force whichovercoming the force of inertia and resistance against themovement performs work on a particular road section [12]The energy that is associated with this work is called energyintensity and in the case of wheeled vehicles it can beexpressed as

119864 = int1198631198880

119865119873 (119904) 119889119904 (1)

where F119873 is driving force and D119862 is travelled distanceEnergy consumption of the movement determines the

amount of energy supplied to the drive wheels and doesnot depend on the nature of the drive unit and thetransmission

Total Energy Consumption E119888 It determines total energyexpenditure In the case of an internal combustion engineunit expressed as the product of the fuel and its calorific valueor in the case of an electrical unit the energy is taken from anelectric source Total energy consumption E119888 is the sum of theenergy consumptionE and the power losses in themotorΔE119898and in the transmission system ΔE119879119878 [12]

119864119862 = 119864 + Δ119864119898 + Δ119864119879119878 (2)The losses from (2) are usually taken into account in efficiency120578

120578 = 119864119864119862 (3)

Journal of Advanced Transportation 3

Master Control System Motor Control System Motor Mechanical System Measuring SystemＲ３４ Ｒ３４

ＲＧ ＲＧ

ＲＬ ＲＬ ＲＬ

Figure 1 Functional diagram of the electric vehicle drive system

The overall efficiency of the drive system is the product ofthe motor efficiency 120578119898 and the efficiency of the transmission120578119879119878

120578 = 120578119898120578119879119878 (4)

The total energy consumption E119888 of the process whichis defined as driving of the given distance D119862 is influencedby many factors the vehicles structural parameters theenergy losses generated when generating and transmittingthe driving torque and the control method A functiondescribing the speed of a vehicle along a certain route isthe so-called speed profile [12 13] The speed profile isusually determined by the driver of the vehicle by means ofappropriate accelerator pedal control and shift gear selectionor by electronic control A cruise control system controls thepower delivered to the drive wheels in order to maintain acertain speed

If the vehicle is equipped with one drive system it can bepresented in the functional diagram as shown in Figure 1

Specific blocks describe the performance of the individualvehicle systems

(i) master control system a speed profile generatorusually the driver by adjusting the accelerator pedaldeciding on the profile and depending on the roadconditions

(ii) motor control system generator of appropriatemotorcontrol values (current voltage)

(iii) motor a machine that transforms the energy of asource into mechanical energy

(iv) mechanical systemof the vehicle torque transmissionfrom the motor shaft to the wheels of the vehicle(clutches gears etc)

(v) measurement system acting as feedback to provideinformation on the current position and speed of thevehicle

The optimization task can be reduced to the following(i) Optimization of design parameters p119896 and settings p119899

eg power of the drive TS ratio ie optimizing thecharacteristics of the vehicle describing the mechan-ical system and current controller The design of thesystem and its mathematical description in the formof the model are decisive for the optimization of theseparameters

(ii) Optimizing the control strategy ie searching for theoptimum speed V119878119864119879 profile or directing the controlsignal to the current controller 119880SET

(iii) Simultaneous optimization of control parameters andstrategy

You can use the Model-Based Optimization method tosolve the optimization task The scheme of the optimizationis shown in Figure 2

In this method decision variables whose value is deter-mined by the optimization algorithm are input variables forthe simulation model Numerical simulation of driving andobtained results during the simulation allows determiningthe result of the objective function Repeating the simulationresults for the subsequent driving parameters controlled bythe optimization algorithm allows the calculation of succes-sive results of the objective function Frequently repeatedresults are aimed at finding the minimum of the target func-tion and thus the optimal solution Stopping the optimizationalgorithm loop depends on the type of the algorithm usedThis usually occurs after a predetermined number of loopsafter a lack of change in the value of the criterion function orother constraints

3 Building the Model of the Electric Vehicle

To study the total energy consumption E119888 of an electricvehicle it is necessary to build amodel to analyze the transferof energy from the source of energy to the drive wheels of thevehicle Figure 3 shows the functional diagram of the electricvehicle drive system This diagram is the starting point forcreating a simulation model

According to the definition the total energy consumptiondepends on the energy consumption of the movement Ethat is on the work generated by the driving force andthe energy losses generated by the motor ΔE119898 as well ason the energy loss of the transmission ΔE119879119878 Accordinglya mathematical model of the vehicle should be createddescribing the phenomenon of resistance and loss of energyin transmission system The mathematical model of theelectric vehicle is shown in this section The model is basedon equations of motion of a wheeled vehicle biaxial withfront axle steering and rear wheel drive The focus is onthe representation of the driving forces and the resistance ofmovement acting in the direction of the longitudinal axis of

4 Journal of Advanced Transportation

Simulation

Simulationmodel

Inputvariables

Simulationresults

Optimization

Optimizationalgorithm

Stopcondition

Objective function Optimizationparameters

NO

OptimizationresultsYES

START

Figure 2 Schematic diagram of the optimization using model [11]

Vehicle

Driving wheels５Ｌ

＝

Motor control system２

ΔＧ

MotorＧ(P)

Transmission systemTS (P)

ΔTS

０ＧＧ＝Ｂ ０TS

Ｇ＝Ｂ

ＲＬ ＲＬ ＲＬ

Figure 3 Functional diagram of an electric vehicle

the vehicleThemodel described here is sufficient to simulateand optimize the parameters of an object that affect the totalenergy consumption E119888 of an object There was no need todetermine the values of forces and displacements affectingindividual vehicle components as in the case of for examplestrength analyses These issues are not the subject of thisstudy so the forces acting in the directions of the otheraxes of the vehicle are not dealt with except for the forceswhich as a result of their impact affect the total energyconsumption

31 Mathematical Model of the Vehicle The theory of vehiclemotion is widely published and has been presented manytimes in the scientific works [14 15] The following sectionprovides formulas and symbols used to build the vehiclemodel A detailed description of the presented issues shouldbe sought among others in the above-mentioned bibliogra-phy Figure 4 shows the forces acting on the vehicle movingalong the path of the inclination angle 120572

The following designations were used F119873 driving forcewhich is the quotient of the driving torque and the dynamicradius of the wheel 1198651198791 and 1198651198792 of the rolling resistance ofthe wheels of front and rear axles respectively Q119898 vehiclegravity force F119875 force of air resistance F119882 =119876119898 sin(120572) uphillresistance F119861 inertia force Z1 and Z2 ground reactions to thefront and rear axle wheelsm119911 =m120575119911 reduced mass

The equation of motion of the vehicle in the drivingdirection can be written as the sum of the driving forces anddrag forces parallel to the road surface as

119898119885 = 119865119873 minus 119865119879 minus 119865119882 minus 119865119875 (5)

The following simplifications were adopted The drivetorque applied to the rear wheel does not affect the pressuredistribution Z1 and Z2 In fact in vehicles with rear wheeldrive the rear is downforced whereas the front axle isrelieved The reaction values Z1 and Z2 were statisticallydeterminedThe coefficients of rolling resistance of all wheelsare identical

Journal of Advanced Transportation 5

2

1

４2

４1

１

１ＭＣＨ

v

C

１＝Ｉ

Ｍ

０

Figure 4 The system of forces acting on the vehicle

Resistance forces depend on many factors and parame-ters many of them are highly nonlinear Modelling of wheelrolling resistance is the subject of separate research and themodel used is very complex so in practice a simplifiedmodelis often used

The rolling resistance of a single wheel is as follows

119865119879119894 = 119888119903119903119885119894 (6)

c119903119903 is the coefficient of rolling resistance that dependson the type of road surface the type of tire or the pressurein the tire This factor also depends on the speed of traveland increases with its growth this is related to the increasein tire deformation The value of the rolling resistancecoefficient is usually given by the tire manufacturer andexemplary values and empirical models on the dependenceof this coefficient on the speed function can be found in theliterature [16] For low travel speeds (lt40kmh) the value ofthe rolling resistance coefficient is assumed to be constantindependent of speed In linear motion the total rollingresistance is the sum of the rolling resistance of all vehiclewheels

If an identical rolling resistance coefficient for eachwheel is assumed which is often justified given the similarconstruction of the front and rear axle wheels and identicaltires and the same pressure operation the sum of the rollingresistance shall be written as

119865119879 = 119888119903119903119876119898 cos120572 (7)

The total wheel resistance should take into account thetire rolling resistance bearing losses and so forth

The essence of resistance in bearings is identical to the tirerolling resistance described previously The bearing torqueis proportional to the bearing load friction coefficient andbearing radius Bearing friction is generally neglected as thebearing resistance value is small compared to the tire rollingresistance [16]

Similarly to the value of rolling resistance the turningresistance can be expressed as the product of the weight ofthe car and the coefficient of turning although according to

literature at low speeds it plays negligibly smaller role thanthe rolling resistance [16]

119865119904 = mg119891119911 (8)

f 119904 is the coefficient of turning anddepends on the pressureforce on the axles tires and so-called intensity of turningin other words ratio of centrifugal and vertical accelerationV2119877119892

The value of air resistance 119865119875 can be determined from

119865119875 = 120574V11990411990611989822 119860119888119909 (9)

where 120574 is the density of air v119904119906119898 [ms] is the total air velocityresulting from the linear velocity of the vehicle v119901 and windspeed v119908 and is the vector sum A is the vehicle front area[m2] and c119909 is the aerodynamic drag coefficient

In this study a TS based on a constant gear ratio was usedPM BLDC (Permanent Magnet Brushless Direct Current)motors are very often used in electric power systems [17]The mathematical description of all phenomena related tomagnetism electrical thermal or mechanical phenomenacan lead to a considerable complexity of the model sosimplifiedmodels are oftenusedThe electrical part ofmotorrsquosmodel can be found in work [9] The electromagnetic torquegenerated by the motor is proportional to the flowing currentand the so-called the motor torque constant K119898 and is givenby [17]

119872119890 = 2119870119898119894119911 (10)

In steady state the electromagnetic torque M119890 is equalto the torque on the motor shaft which is the sum of theload torque and the torque of the losses The efficiency of anelectric motor is defined as

120578119898 = 119875119898119890119888ℎ119898119875119890119897119890119888119905 (11)

119875119898119890119888ℎ119898 is the mechanical output power on the motor shaftand P119890119897119890119888119905 is the electrical power input Relations describing

6 Journal of Advanced Transportation

D [m]

S []Ｃ

RＣ

SＣ

S1

L1 Li

Figure 5 Driving path and its inclination profile

the phenomenon of loss can be found in professional litera-ture [10]

Themotor torque is transmitted to the drive wheel via theTS transmission The mechanical power on the drive wheeldepends on the efficiency of the TS

119875119898119890119888ℎ119901 = 120578119879119878119875119898119890119888ℎ119898 = 120578119879119878120578119898119875119890119897119890119888119905 (12)The efficiency 120578119879119878 is a function of many factors ie it

depends on the powertrain design the transmitted powerand quality of the system For TS based on tension transmis-sion efficiency can be approx 90 The efficiency of the tielink transmission is a function of inter alia transmission ratioi119879119878 interaxial distance belt angle tension force rotationalspeed or torque [18ndash20] In the case of lightweight vehiclesin the TS design it is often not necessary to use variable geartransmissions Speed and torque control is achieved by thecontrol system On the one hand it is an advantage becausethe TS is smaller in weight and less complicated but on theother hand it forces the electric drive to operate in a widerange of torque and rotational speed which affects the motorenergy efficiency

32 Building the Model of the Driving Route The parametersof the path that the vehicle travels on have a significant effecton the resistance values shown in Section 31 In the paper thepath of ride is determined by the exact path of the vehicle ona designated route It is assumed that the best path is knownand it is determined based on the teamrsquos experience (it meansthat the quickest best path along the track is not calculatedby the optimization method) The difference between thepath and the track is as follows A track is a system ofphysically existing roads between points A and B and whenthe path does not exist physically it is the trace that leavesthe selected point of the vehicle (eg center of gravity) onthe route surface With this in mind the journey along theroute can take place on a number of pathsThe route is only alimitation

Figure 5 shows a schematic drawing of one path andits elevation profile The description of the path is formedby its discretization ie the division into finite numbers ofelementary sections of O119905119894 119894 isin 1 2 119899 Each elementarysegment is described by a parameter vector

O119905119894 = [119871 119905119894 119877119905119894 119878119905119894 119864119905119894] where 119871 119905119894[m] is the length of thepath119877119905119894[m] is the radius of curvature 119878119905119894[] is the inclinationof the path and 119864119905119894 represents the type and condition of thepath The length of the path is the sum of the lengths of the119871 119905119894 sections

These basic data are essential for the correct determina-tion of motion resistance on each segment It is assumed thatany change in the inclination or radius of curvature makes itnecessary to define further vector O119905119894

Bearing in mind that vehicles usually move in the openair a suitablemodel should be created describing the externalconditions For this purpose the O119905119894 vector describing thenature of the path should include additional columns suchas velocity and direction of the wind V119908119894 and V119896119894 atmosphericpressure 119901119886119905119898119894 and air temperature t119886119905119898119894 In this situation thevector describing the path and external conditions takes theform O119905119894 = [119871 119905119894 119877119905119894 119878119905119894 119864119905119894 V119908119894 V119896119894 119901119886119905119898119894 t119886119905119898119894] The speedand direction of the wind have a significant effect on the valueof air resistance Determining the wind speed is relativelydifficult and not precise Temporary windsmay have differentdirections and a much higher amplitude than the averagePreliminary investigations have been carried out consideringthe uncertainty of weather conditions During optimizationwhere optimal control strategies were sought the wind speedwas randomly changedThe concept of optimizing the controlstrategy from taking into account the changing weatherconditions was to design a family of strategies It would bepossible to select one optimal strategy or part of it in thereal world because of the existing and changing weatherconditions

33 Control System Design Twomodes of the control systemare taken into consideration in this study They reflect thephysical implementations of the control system used in thebuilt-in electric race vehicles of Prototype class [21] andUrbanConcept class [22] Figures 6 and 7 represent blockdiagrams of the drive system of the vehicle for differentcontrol strategies The control scheme A (Figure 6) is usedin a case when a driver is able to control an acceleration ofthe vehicle by means of a binary signal In this case the goalof the optimization task is to find the control strategy takinginto account two criteria ie the determined travel time aswell as the minimal power consumption of the vehicle Thecontrol strategy is used to specify in which parts of the routethe driver should press or release the acceleration treadleWhen the setpoint signal 119880SET isin 0 1 is assumed then theoptimization task is to search for logic values of the controlsignal as the function corresponding to the position of thevehicle x(t)119880SET = f (x(t)) The supervisory role of the driveris included in the functional scheme as a decision moduleIn this study the behaviour of the driver is not modelled inthe simulation It means that heshe realises the strategy in

Journal of Advanced Transportation 7

Mechanical systemHigh-level control system Motor controller

Transmissionsystem

Currentcontroller

Angularvelocity

measuringsystem

Positionmeasuring

system

MotorDecisionmodule

Driverrsquos decision

Binary control

signal U (x)SET

USET ISET５ＬＲＧ ＲＬ ＲＬ ＲＬ

intint

Figure 6 Drive system diagram control scheme A

High-level control system

Decisionmodule

Velocitycontroller

Mechanical systemMotor controller

Transmissionsystem

Currentcontroller

Angular velocitymeasuring

system

Positionmeasuring system

Motor

Linear velocitymeasuring system

-

Driverrsquos decision

Velocity profileV (x)SET

VSET evＲＧ

Ｒm

USET Ur ISET ＲＬ ＲＬint int

ＲＬ

Figure 7 Drive system diagram control scheme B

the exact way The input control signal U119903 is always differentfrom the signal 119880SET in real conditions It means that thesignal 119880SET is mainly employed by the driver to know whenthe acceleration treadle should be used

In the case of the control scheme B (Figure 7) the generalgoal of the optimization task is the same as in the previouscase However the formal definition of the problem is quitedifferent because in this case the optimal form of the velocitysignal is searched according to the position of the vehicle onthe routeV119878119864119879 = f (x(t))The velocity controller compares thesetpoint signalV119878119864119879 with themeasured velocity of the vehicleand for certain controller setting as well as for control errore119907 it generates the control signal 119880SET As in the previouscase the supervisory role of the driver is included in thedecision module However the main difference is that in theoptimization process the setpoint signal V119878119864119879 can be limitedin the direct way

According to control schemes A and B the input controlsignal U119903 is used by the motor control unit where theemended current regulator normally outputs the correspond-ing signals to the motor terminals The driving torque of themotor shaft is transmitted through the transmission systemto the wheels of the vehicle

4 Evolutionary Optimization of theVelocity Strategy

41 Formulation of the Optimization Problem One of theways to define and to solve the dynamic optimization taskof the velocity strategy of the vehicle is to reduce sucha problem to the static optimization task through the so-called discretization of the independent variable If oneassumes that the independent variable is the position ofthe vehicle (a travelled distance) x(t) then the velocitystrategy st can be represented by a vector of instanta-neous values 119880SET or V119878119864119879 for discrete parts of the routeFigure 8 illustrates the idea of dividing the route into seg-ments

The path is divided into n segments O119894 each of the lengthL119894 where the sum of the lengths of the segments is equal tothe length of the total path For each segment it is necessaryto determine the 119880119878119864119879119894 or 119881119878119864119879119894 setpoint The task is to findthe optimal velocity strategy for control scheme A in thefollowing form

st119900119901119905U = [1198801198781198641198791 1198801198781198641198792 119880119878119864119879119899]119879 119880119878119864119879119894 isin 0 1 (13)

8 Journal of Advanced Transportation

D

L2L1 Ln

O2O1 On

Figure 8 Concept of discretization of the route

whereas in the second case for control scheme B

st119900119901119905V = [1198811198781198641198791 1198811198781198641198792 119881119878119864119879119899]119879 119881119878119864119879119894 isin 119881119898119894119899 119881119898119886119909

(14)

where119881min and119881max can be determined in different ways egbased on the minimummaximum vehicle speed or based onthe simple calculation corresponding to guidelines of the racecompetition

Evolutionary algorithms can be used to solve this prob-lem In the case of the search for strategy st119900119901119905119880 it is preferableto use a classical genetic algorithm In this instance the genesin a chromosome of the individual can be encoded directlyas the binary values of the control signal 119880119878119864119879119894 Thereforethe length of the chromosome N119888ℎ is equal to the number ofsections of the route

In accordance with the control scheme B the velocityprofile is determined as the vector including setpoint valuesof the velocity st119900119901119905119881 The components of the st119900119901119905119881 vectorare floating point values hence it is possible to use anevolutionary strategy proposed in [23] Each of the genes inthe chromosomeof the individual corresponds to the setpointvalue of the velocity during a part of the route

42 Chromosome Codding for Different Velocity StrategiesFor a vehicle that is equipped with a binary control systemof the motor the chromosome can be represented as theoptimal vector of the control signal in the following formst119900119901119905119880 = [1198801198781198641198791 1198801198781198641198792 119880119878119864119879119899]119879 119880119878119864119879119894 isin0 1 for eachsegment O119894 of the route (for control scheme A) or the

optimal vector of the control signal in the second form st119900119901119905119881= [1198811198781198641198791 1198811198781198641198792 119881119878119864119879119899]119879 119881119878119864119879119894 isin [119881min 119881max] for eachsegment O119894 of the route (for control scheme B)

In this optimization task the total distance of the roadD119862is composed of SEM race laps N119905119900 isin1 2 119873 The divisionof the whole route on a finite number of segments O119894 is notrecommended because it can lead to unnecessary increase inthe length of the vector st If the route consists of a minimumof four laps it is possible to limit the search of vector st toonly three types of laps

(i) the initial lap marked by 119874119894119904(ii) the middle laps marked by 119874119894119898(iii) the last lap marked as 119874119894119891Such assumption can be proven for at least three reasons(1) In the practical implementation of velocity strategies

the driver should not implement different control rules foreach lap The master control unit informs the driver aboutthe current velocity strategy but despite all the driver shouldremember this strategy to some extent

(2)The limitation of the velocity strategy only to the threetypes of laps reduces the length of the vector st In this waythe number of elements of the vector st corresponds to thenumber of decision variables of the optimization task

(3) Such division is reasonable by the nature of the laps Inthe initial lap it is necessary to accelerate the vehicle Withinthe middle laps the velocity profile of the vehicle should bethe same During the last lap the previously acquired kineticenergy E119896 is utilized

The task of finding the optimal vector st119900119901119905 can be solvedusing two types of evolutionary algorithms

(i) Classical genetic algorithm for control without avelocity regulator (according to control scheme A presentedin Figure 6)

(ii) Evolutionary strategy for the control system of thevehicle with a velocity regulator (according to control schemeB shown in Figure 7)

Theusage of two algorithms forces the appropriate codingof the velocity strategy which is described in the next twoparagraphs

421 Chromosome Coding For Control Scheme A The phe-notype of each individual determines the control vector st119906that means each gene of the individual of the population isthe value of the control signal 119880119878119864119879119894 for each section of thesegment O119894 of the route Assuming that we are looking for avelocity strategy of only three types of laps the phenotype canbe written as (for short form U equiv 119880SET)

st119880 = [ 1198801119904 1198802119904 119880119899119904 1198801119898 1198802119898 119880119899119904 1198801119891 1198802119891 119880119899119891 ]119879 (15)

where 119880119894119904 119880119894119898 119880119894119891 are the control signals for the initial lapmiddle laps and the last lap

422 Chromosome Coding for Control Scheme B In thiscase the elements in the vector 119881119878119864119879119894 change over a wide

Journal of Advanced Transportation 9

range and can assign real number values In the evolutionarystrategy the phenotype of each individual takes the followingformst119881

= [ 1198811119904 1198812119904 119881119899119904 1198811119898 1198812119898 119881119899119904 1198811119891 1198812119891 119881119899119891 ]119879 (16)

119881119894119904 119881119894119898 119881119894119891 are the setting values of velocity for the initiallap middle laps and the last lap

In the control mode according to scheme B the controlsignal is generated by the velocity controller based on thecontrol error

e119881 = 119881119878119864119879 minus 119881119904119894119898 (17)

where

U119878119864119879 = 1 for e119881 ge 10 otherwise

(18)

The coding for control scheme B in comparison withthe coding for control scheme A has undoubtedly oneadvantage namely the possibility of introducing a velocitylimit during the simulation of the passage of a given sectionof the route A velocity limitation is of great practicalimportance In many situations it is necessary to reducethe velocity of the vehicle during certain parts of theroute for example during cornering Accordingly in caseof control scheme B two velocity vectors are designated asfollows

(i) st11988115 for 119881119878119864119879119894 = [0 15] ms although it is formallylimited to 15ms it can never be achieved because themaximum vehicle speed (based on maximum enginespeed) is approximately 15ms

(ii) st11988110 for 119881119878119864119879119894 = [0 10] ms

43 The Fitness Functions In the case of evolutionary opti-mization the fitness function f 119907119886119897 has to be designed Thissection describes the formulas used to calculate the fitnessfunction of an individual that is needed for solving a task ofevolutionary optimization Each chromosome is a potentialsolution Each control strategy st is used during numericalsimulation The value of the fitness function f 119907119886119897 can becalculated based on the outcomes of the simulation suchas

(i) the total energy consumption r119904119894119898 [kmkWh](ii) the simulation time t119904119894119898(iii) the distance x119904119894119898

and limitations such as

(i) the maximum travel time T119898119886119909(ii) the total distance of the vehicle D119862The value of the function is also used to evaluate the

velocity strategy of the vehicle In the preliminary studies[24] the following fitness function f 119907119886119897 was used

Fitness Function 1

119891V1198861198971 = 11990811198911 + 11990821198912 + 11990831198913 (19)

where

1198911 = [1 + 1199031205821119904119894119898]1205821 (20)

1198912 = [119867 (119863119888 minus 119909119904119894119898) 1003816100381610038161003816119863119888 minus 1199091199041198941198981003816100381610038161003816119863119888 ]1205822 (21)

1198913 = [119867 (119905119904119894119898 minus 119879max)1003816100381610038161003816119879max minus 1199051199041198941198981003816100381610038161003816119879max

]1205822 (22)

where the weights w1 = 050E05 w2 = w3 = 025 andcoefficients 1205821 = minus2 1205822 = 1 were chosen experimentally Thepenalty functions f 2 and f 3 were introduced The Heavisidestep functionH() is used to penalize individuals representingunacceptable solutions [25 26] eg those that exceed themaximum time of the simulation H(t119904119894119898 minus T119898119886119909) or do notreach the specified distance H(D119888 minus x119904119894119898)

Fitness Function 2 In this study the authors have proposedthe fitness function which would lead to the convergenceof the evolutionary algorithm without searching for optimalvalues of weights Such a function is shown and describedbelow

119891V1198861198972 = 1 + 1198914 + 1198915119891111989121198913 (23)

1198911 = 119903119904119894119898 (24)

1198912 = cos(1003816100381610038161003816119863119888 minus 1198891199041198941198981003816100381610038161003816119863119888 ) (25)

1198913 = cos(1003816100381610038161003816119879max minus 1199051199041198941198981003816100381610038161003816119879max) (26)

1198914 = 120594 sdot 119867 (119863119888 minus 119889119904119894119898) (27)

1198915 = 120594 sdot 119867 (119879max minus 119905119904119894119898) (28)

where f 1 is a measure related to the simulated energyconsumption of the vehicle f 2 and f 3 correspond to thelimitations such as the maximum travel time and the totaldistance of the vehicle f 4 and f 5 also correspond to the limi-tations but these play strong penalty role and 120594 is arbitrarilylarge value eg significantly higher than maximal valuesf 2=f 3 =1 In this variant of the fitness function death penalty[26] is applied for unacceptable individuals in the form offactors f 4 and f 5 Individuals who do not reach a specifieddistance or exceed the time limit are eliminated These twocriteria act as a constraint and correspond to the limitationsformulated in the guidelines of the race competition On theother hand the criteria f 2 and f 3 have continuous nature andplay very important role in the fitness functionThey are veryneeded to evaluate continuously the individuals that are veryclose to and very far from the extremum

The argument of cos() function is not related to anangle However the usage of the cos() function is needed to

10 Journal of Advanced Transportation

Table 1 Research object main parameters

Type of the motor PM BLDCTransmission unit Toothed synchronous beltThe minimum turning radius 8 [m]The battery type and capacity Lithium-ion polymer 2100[mAh]Mass of the vehicle 42 [kg]Mass with the driver min 92 [kg]Diameter of wheels 0478 [m]Moment of inertia of the front wheel 119868119896119875 0023 [kgm2]Moment of inertia of the rear wheel 119868119896119879 0023[kgm2]Drag coefficient cx (see Table 2) 022 ndash 023Frontal area A [m2] (see Table 2) 0275 - 0297The total rolling coefficient crr (see Table 4) 00035 ndash 00058

eliminate the possibility of dividing by zero In addition theform of the cos() function is preferred At the initial stage ofoptimization when the simulation time t119904119894119898 and the distancex119904119894119898 differ significantly from the maximum time T119898119886119909 andthe specified distance D119888 a small change will have a greatereffect on the value of the fitness function At the final stageof optimization the function 119891V1198861198972 is more dependent on thesimulated energy consumption of the vehicle related to thefactor f 1 and thanks to the cos() function it is less dependentto the factors f 2 and f 3 The proposed function does notrequire the introduction of weights and therefore it is easierto use this function in other applications eg to find optimalvelocity strategies for different routes

It should be noted that fitness functions 119891val have beenwritten in such a way as to ensure that the optimizationalgorithm will look for a minimum of these functions

5 Case Study

As described in Sections 3 and 4 process of modelling andoptimization was applied and verified using a prototypeelectric vehicle on street race circuit in Rotterdam Themethodology was also carried out on the experimental ridestrack of the Fiat ChryslerAutomobiles Poland factory locatedin Tychy Based on (5)-(12) the simulation model was cre-ated in the MATLABSimulink environment Optimizationwas also carried out in MATLAB using the evolutionaryalgorithms available in the Global Optimization Toolbox Thelibrary of functions for simulating optimizing analyzingand presenting results has been developed

51 Research Object Light electric vehicle was a researchobject The vehicle shown in Figure 9 is a three-wheeledself-supporting structure The vehicle fuselage is made ofcomposites based on epoxy resin and woven of carbon andaramid fibre [21]

The dimensions of the vehicle and basic data are shownin Figure 10 and in Table 1

Identification of parameters for the mathematicalmodel of a research object was carried out by numericalsimulations tests on specially designed test bench [27]

Figure 9 Research object prototype electric vehicle ldquoMuSHELLkardquo(photo by M Wylezoł 2012)

and during conducted experiments in real environment[28]

The vehicle can be driven by two types of drive unit(i) DT1 drive unit based on PM BLDC motors and belt

transmission Drive wheel is equippedwith a one-wayclutch

(ii) DT2 a high-torque PMBLDCmotor mounted insidethe drive wheel The torque generated by the motor isdirectly transmitted to the rear drive wheel

The catalogue data can be used for creating the mathematicalmodel of the DT1 motor but for identifying the exactparameters it was necessary to carry out experimental testsThe manufacturer of the DT2 motor does not provide muchinformation so it was necessary to test the drive unit aswell DT1 drivetrain efficiencywas estimated using aBG75x50motor with toothed synchronous belt transmission ( z1= 28teeth z2 = 200 teeth i119879119878 = 714) The map of the efficiencywas shown on Figure 11(a) The same test was carried out forDT2 drive unit with a motor directly mounted on the drivewheel (Figure 11(b)) The obtained efficiency maps were usedto build the simulationmodel of the tested drivetrain systems

52 Determination of Air Drag Coefficient The air dragcoefficient c119909 was estimated as a result of CFD analysis usingANSYS software [24] and it was also verified by the researchin wind tunnel at the Institute of Aviation inWarsaw Frontalarea of vehicle A was determined from a three-dimensionalmodel in CAD environment Catia V5 The values of dragcoefficient c119909 and frontal area A are shown in Table 2

Journal of Advanced Transportation 11

623

972

1600

2605

Figure 10 Dimensions of the vehicle

(a) DT1 (b) DT2

Figure 11 Maps of the efficiency of tested drivetrain systems

Table 2 The air drag coefficient and frontal area

cx numericalsimulation

cx experimentalresearch Frontal area A [m2]

023 022 0275 0297

53 Determination of Rolling Resistance According to for-mula (7) the rolling resistance depends on the weight of thevehicle (Table 1) the tires rolling resistance coefficient andthe resistance of the bearings Depending on the drive unit(DT1 DT2) used in the vehicle additional resistance has to beadded In theDT1 system there is a one-way clutchwhich alsogenerates some resistance torque The DT2 system cannot bemechanically disconnected and therefore has a higher rollingresistance As a result of the coast down test the total rollingresistance of the vehicle has been identified for the four typesof tiresThe test was performed only with theDT1 system iethe systemwith the clutch Table 3 shows the basic parametersof the tires used in the experiments

The prototype vehicle can be equipped with speciallymanufactured Michelin tires with a low rolling resistantcoefficient of c119903119903 = 00014

In addition to the specialMichelin tires three other typesof tires were tested The identification of rolling resistance

coefficients was also estimated using a coast down test Themeasurements were made as follows

(i) The driver accelerated the vehicle to a fixed speed(ii) At themoment of crossing themarked gate the driver

pressed the marker button to save the flag in theacquired data

(iii) The run continued until free braking after which thedriver switched off the measuring system

(iv) The measurements were made at both directions ofthe road to minimize influence of the wind

(v) Before the attempts wind velocity temperature andatmospheric pressure were measured

(vi) The distance of the road was measured using ameasurement system mounted on the vehicle and itwas also verified using distance measuring wheel

On the basis of the experimental data the total rolling resis-tance coefficient of the vehicle was determined Table 4 showsthe coefficients of rolling resistance of the vehicle dependingon the tire used during the test Total resistance includesthe tire rolling coefficient the bearings resistance and theresistance of the clutch Verification of the data derived fromthe simulation and the experiment was conducted using

12 Journal of Advanced Transportation

Table 3 The types of tires used in the prototype vehicle

Tiresmarker Name of the tire Tirersquos

symbol Shape Type of tread Workingpressure

W1

Michelin ShellEco-marathon 4575R16 Rectangular Slick max500 [kPa]

W2

SchwalbeUl-Termo 23-406 Round Slick 600-1100 [kPa]

W3

Continental SportContact 28-406 Round Slick 600 [kPa]

W4

SchwalbeMarathon 40-406 Round Symmetrical 400-700 [kPa]

Table 4 The total rolling coefficient depending on the tires

Tiresmarker Name of the tire The total rolling coefficient crr mMAPE []

W1 Michelin ShellEco-marathon 00035 784W2 Schwalbe Ultermo 00043 1103W3 Continental SportContact 00058 1252W4 Schwalbe Marathon 00053 445

0

1

2

3

4

5

6

7

8

V [m

s]

100 200 300 400 500 6000x [m]

W1rW1simW2rW2sim

W3rW3simW4rW4sim

Figure 12 Velocity of the vehicle during coast down test

mMAPE (modifiable Mean Absolute Percentage Error) Forvelocity simulationmMAPE can be determined by

119898119872119860119875119864 = 1001119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119881119903 minus 119881119904119894119898119881119898119886119909 minus 119881119898119894119899

10038161003816100381610038161003816100381610038161003816 (29)

Figure 12 shows the experimental data obtained in a coastdown test compared with the results obtained during thecomputer simulation

54 Model of the Race Circuit In accordance with themethodology presented in Section 32 three routes have beendescribed

(i) Route 1 a street race circuit at the Shell Eco-marathoncompetition in Rotterdam

Figure 13 Plan view of the path of the drive on route 1 in Rotterdam

(ii) Routes 2 and 3 on the experimental rides track of theFiat Chrysler Automobiles Poland factory located inTychy in the south of Poland

The Shell Eco-marathon competition is held on a streetcircuit in Rotterdam One lap is 1630 meters long Vehicleshave to cover ten laps in no longer than 39 minutes so suchrequirements impose an averageminimum speed of 25 kmh

The trajectory of the vehicle path was developed usingsatellite images The vehicle trajectory was determined usingthe maximum curvature possible that could be obtained onthe existing roads

Movement of the vehicle in a curved motion causesthe centrifugal force Centrifugal force creates additionalresistance This resistance is inversely proportional to theradius of the path (8) so it is justified to select the largestradius In addition if the centrifugal force exceeds thelimit value it could provide to the side slip of the vehicleAccording to drawings in AutoCAD Civil 3D the lengths ofstraight sections and the lengths and the radius of arcs wereobtained Figure 13 shows a plan view of the path of the drive

Driving the prototype vehicle on public roads is prohib-ited and can be dangerous Vehicle testing was also carried

Journal of Advanced Transportation 13

Table 5 Travel times and total lengths of the routes

Route Length of the lap D [m] The numberof laps The total length of the route Dc [m] Travel time Tmax [s]

Route 1Rotterdam 1630 10 16 300 2340

Route 2Tychy 640 5 3200 460

Route 3Tychy 1000 5 5000 720

Figure 14 Plan view of the path of the drive on route 3 in Tychy

out on the experimental rides track of the Fiat ChryslerAutomobiles Poland factory

For the track in Tychy geodetic measurements weretaken using theDGPS (Differential Global Positioning System)technology The measuring points were collected along theaxis of the road with the distance between points amountingto 10 meters If on the measured route direction or elevationwere changed the frequency of measurement was increasedGeodetic coordinates were also imported intoAutoCADCivil3D and were used to prepare data concerning the route thatwas imported into the simulation environment MATLAB-Simulink Figures 14 and 15 show the path and elevationprofile respectively

Selected routes 2 and 3 have significant differences com-pared to route 1 especially in the height profile This set ofroutes was selected to verify the effect of the route profile onthe achieved results and to verify the proposed optimizationmethods for various road conditions The routes in Tychyare located in an open area there are no large buildingswhich guarantees stability of wind conditions The technicalcondition of the surface on routes 2 and 3 is much worsethan on route 1 which has a significant influence on therolling resistance Rolling resistance was also identified andintroduced into the simulation model For route 2 the c119903119903coefficient was 00056 and for route 3 was 00068

55 Verification of the Simulation Model In order to verifythe compatibility of the identified simulation model a seriesof numerical simulations and experimental tests were per-formed The first experiment consisted of running 300 [m]with a control strategy of 50 [m] with the workingmotor andafter that the vehicle was moving freely for the next 50 [m]The motor is turned on three times Figures 16(a) and 16(b)show the velocity of the vehicle and the power of the motorin function of the distance determined during the experiment

(red curves) and during the numerical simulations (greencurves)

Verification of the data derived from the simulation andthe experimentwas conducted usingmMAPE (29) Formotorpower simulationmMAPE can be determined by

119898119872119860119875119864119875 = 1001119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119875119903 minus 119875119904119894119898119875119898119886119909 minus 119875119898119894119899

10038161003816100381610038161003816100381610038161003816 (30)

where P119903 is the motor power measured during experimentand P119904119894119898 is the motor power conducted in simulation

As a result of the model validation tests estimationerror of the velocity was on level between 235 and 534However the motor power error level was greater It wasbetween 802 and 998

56 Determination of the Optimal Control Strategy Thelength of route 1 and the number of laps are determined bythe organizers of the Shell Eco-marathon competition Thelength of routes 2 and 3 is derived from the existing road planwhere it was possible to carry out trials in real conditionsThenumber of laps for routes 2 and 3 was assumed arbitrarily

The travel time for route 1 is based on the rules of therace which determine the minimum average speed of thevehicle Based on the average speed and the length of routes 2and 3 the travel times for these routes were determined Themaximum travel times and the total length of the route aswell as the number and length of one lap D are summarizedin Table 5

Evolutionary algorithms which are available in theMAT-LAB Global Optimization Toolbox were used From theMATLAB workspace the algorithm ran a simulation modelin a Simulink environment During optimization while usingevolutionary algorithms the maximum number of fitnessfunction evaluations 119873119891V119886119897

is the product of the populationsize 119873119901119900119901 and number of generations 119873119892119890119899

It was assumed that the total number of fitness functionevaluations was equal to 104 therefore should this value beexceeded the calculation would be cancelled Therefore thetotal number of generations 119873119892119890119899 is dependent on the valueof population size 119873119901119900119901

As part of this work phase the vectors st119880 st119881 15 andst119881 10 of the optimum control strategy for an electric vehiclefor routes 1 2 and 3 were determined During evolutionaryoptimization the heuristic method of crossing was usedand the probability of crossing was established on the basisof previous studies at the level of 08 [24 29] At the

14 Journal of Advanced Transportation

0+000

106410

minus164 minus492minus166 minus012 minus018 minus082 minus035 059 031

811

0+100 0+200 0+300 0+400 0+500 0+600 0+700 0+800 0+900 1+000

Figure 15 Profile of the path on route 3 in Tychy

50 100 150 200 250 3000X [m]

0

2

4

6

8

10

V [m

s]

(a) DT1

0

100

200

300

400

500

P [W

]50 100 150 200 250 3000

X [m]

(b) DT1

Figure 16 The velocity and the power determined with used DT1 drive unit

stage of reproduction the elitist succession method wasapplied where the best adapted two individuals in the currentpopulation passed to the next population An adaptivemethod of mutation was used The remaining parameters ofthe algorithm remain the default for the MATLAB GlobalOptimization Toolbox

The first case was the search st119880 vector for route 1Figures 17(a)ndash17(c) show the vehicle velocity V119904119894119898 obtainedby computer simulation The graph of the st119880 control signalis graphically displayed Figure 17 shows the results wherethe optimal control strategy st119880119900119901119905 was used and populationwas 119873119901119900119901=100 and 119873119892119890119899=100 The total energy consumptionwas estimated as r119904119894119898=527633 [km kWh] Figure 17(a) showsthe vehicle speed and control signal st119880 during the first lapwhile Figure 17(b) shows center laps and Figure 17(c) showsthe last lap Figure 17(d) shows the curves of the mean valuesof the fitness functions f 119907119886119897 depending on the number ofcalculations of these functions during the optimization ofthe control strategy There are eight curves in the graph(Figure 17(d)) for each of the 119873119901119900119901 parameters used in thealgorithm

When analyzing the vehicle velocity chart on the last lapof route 1 (Figure 17(c)) it can be seen that according tothe determined control strategy the propulsion system of thevehicle should no longer be used The vehicle should use thestored kinetic energy

The analysis of vehicle velocity V119904119894119898 during the last lapindicates that at the moment of reaching the given distancethe speed was still about 2 [ms] This demonstrates thatthe simulated vehicle has kinetic energy that would haveto be dispersed by the braking system or recovered by the

electric motor Having such a speed does not mean that thereis still possibility for improvement Lower speed at the endof the route has to cause higher speed of the earlier partsof the route This speed is the optimum speed due to thechosen criterion From the analysis of the shape of the fitnessfunction (Figure 17(d)) it can be seen that for route 1 itis preferable to use a smaller population of 119873119901119900119901=25 andincrease the number of 119873119892119890119899=400 The curve shape for thiscase is steep and it falls to the minimum value of the fitnessfunction which may indicate that the algorithm has reacheda convergence

Results of the optimization where B type of coding wasused were analyzed The results obtained as the mean of ther119904119894119898 result together with the standard deviation from all thetests were summarized in Table 6

By analyzing the results in Table 6 it can be seen thatfor route 1 better results were obtained (reduced simulatedtotal energy consumption) using A coding compared to Bespecially for st119881 15 whose results are characterized by thehighest standard deviation For routes 2 and 3 the same as forroute 1 the procedure was followed Optimization strategieshave been optimized for all variants of control vector st119880st119881 15 st10

The results using the control strategy st119881 10 are shownin Figures 18(a)ndash18(c) (119873119901119900119901=100 where r119904119894119898=351795 [km kWh]) Figure 18(d) illustrates the graph of the value of thefitness function

The results obtained for route 2 are presented in Table 7For route 2 compared to route 1 the best results were

achieved using the stV10 vector When using vectors st119880 andstV15 the results were slightly worse Having analyzed the size

Journal of Advanced Transportation 15

0

2

4

6

8

10V

[ms

]

VsimstU

500 1000 15000X [m]

(a) Lap 1

0

2

4

6

8

10

V [m

s]

2500 30002000X [m]

VsimstU

(b) Laps 2-9

0

2

4

6

8

10

V [m

s]

155 1615X [m]

Vsimstu

times104

(c) Lap 10

times10minus3

Npop=25Npop=50Npop=75Npop=100

Npop=125Npop=150Npop=175Npop=200

15

2

25

3

35

4f va

l

2000 4000 6000 8000 100000Nfval

(d) Mean values of the fitness functions

Figure 17 Vehicle speed and control signal st119880 for route 1

Table 6 The results for route 1

The type of coding A The type of coding Bst119880 st11988115 st11988110119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 52465 1459 42845 1741 51569 5477550 52579 10053 44431 22486 51492 3409475 52497 39913 43842 28173 51256 80682100 52589 18128 42232 1797 51166 49379125 52625 13862 42733 39616 51341 70765150 5243 2979 4435 47701 51486 27086175 52513 2511 41428 27299 51838 19358200 52579 19666 42337 25776 51204 78357

16 Journal of Advanced Transportation

100 200 300 400 500 6000X [m]

0

2

4

6

8

10V

[ms

]

VsimstV10

USET

(a) Lap 1

0

2

4

6

8

10

V [m

s]

800 900 1000 1100 1200700X [m]

VsimstV10

USET

(b) Laps 2-4

0

2

4

6

8

10

V [m

s]

2700 2800 2900 3000 3100 32002600X [m]

VsimstV10

USET

(c) Lap 5

times10minus3

Npop=25Npop=50Npop=75Npop=100

Npop=125Npop=150Npop=175Npop=200

275

28

285

29

295

3

305

f val

2000 4000 6000 8000 100000Nfval

(d) Mean values of the fitness functions

Figure 18 Vehicle speed and control signal st11988110 for route 2

of the population used in the optimization process it shouldbe noted that for route 2 it is preferable to use higher value of119873119901119900119901 For all the analyzed cases the best average results for119873119901119900119901=200 were obtained Table 8 summarizes the results forroute 3

For route 3 the average results were reported for a largerpopulation of119873119901119900119901 with B coding In the case of using vectorwith A type coding no characteristic change was notedAs expected comparing the standard deviation betweenalgorithms using B coding the standard deviation is less forthe less variance range

Evolutionary algorithms are not complete search algo-rithms therefore it is not possible to determine whetherthe solution found is best for the chosen criterion and theconstraints assumed

57 Applying the Optimal Control Strategy in Real ConditionsElectric vehicle energy consumption optimization was finallyverified in real conditions at the European edition of the ShellEco-marathon held on 16-18 May 2014 in Rotterdam

Optimal control strategy st119880was displayed by a prototypevisualization system Visualization unit is installed in the

Journal of Advanced Transportation 17

Table 7 The results for route 2

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 34138 66734 34294 23839 34873 5353250 34573 46359 35003 462 3506 3886275 34512 55134 34961 33476 35419 067858100 34836 45332 35253 26117 3544 19295125 34632 52704 35017 49039 35483 14756150 34552 63714 35326 14885 35343 071015175 35063 18728 35274 47141 35564 038022200 35073 14496 3540 13389 35569 14942

Table 8 The results for route 3

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 28071 10173 28643 7323 30994 277650 29346 6142 29581 7894 30874 439975 29711 5002 29217 7367 31141 1856100 29826 3231 29515 7022 30957 4049125 29781 2980 29866 12977 31168 3445150 29453 3346 30217 9623 31288 1249175 29234 2317 30621 6816 31481 1261200 29686 2337 30531 11737 31089 4880

Table 9 Comparison of simulation results with experimental tests

Number of attempts 119903119878119864ndash119898 119903119903 119903119904119894119898 119903119900119901119905 119890119898 119890119894 119890119904119905Attempt 1 3654 3608 - - 125 - -Attempt 2 4813 5082 5148 5265 558 129 36Attempt 3 4873 5127 5198 5265 521 139 269Attempt 4 Failed attempt damaged tires during 1st lap

steering wheel of the vehicle The visualization system showsthe basic data such as instantaneous speed average speedtravel time and distance In addition the visualization systemprovides information on which part of the track the drivershould press the acceleration button to execute the optimalcontrol strategy Measurement of the position on the track iscarried out by the odometrical measuring system Due to thepossibility of accumulating errors in the measurement of theroad the driver will reset the measuring system every timeheshe exceeds the lap line

Table 9 presents the results of all the measurementsconducted during the Shell Eco-marathonThe columns in theTable 9 contain

(i) r119878119864119898 [kmkWh] the result recorded during the raceby the measuring device provided by the organizerthe results are available on the Shell Eco-marathonofficial website

(ii) r119903 [kWkWh] the result based on the indications of aprototypemeasuring system permanently installed inthe vehicle

(iii) r119904119894119898 the result estimated by computer simulationusing recorded real control signal U119903

(iv) r119900119901119905 the result obtained by computer simulation usingthe optimal control strategy U119900119901119905

Table 9 also includes the following

(i) Measurement error

119890119898 = 1003816100381610038161003816119903119878119864119898 minus 1199031199031003816100381610038161003816119903119878119864119898 100 (31)

(ii) Identification error

119890119894 =1003816100381610038161003816119903119903 minus 1199031199041198941198981003816100381610038161003816119903119903 100 (32)

(iii) Strategy implementation error

119890119904119905 =10038161003816100381610038161003816119903119903 minus 11990311990011990111990510038161003816100381610038161003816119903119903 100 (33)

18 Journal of Advanced Transportation

There were four measurement trials available Duringrun 1 a much weaker result was obtained than estimated bysimulation The driver performed run 1 without a definedcontrol strategy As part of the experiment the driver andthe support team were asked to select the optimal tires forthe vehicle and to implement the proposed control strategyDuring run 1 only the travel time of individual laps waschecked According to the choice of the team in run 1 tiresW2 were selected (Table 4) During this test the worst resultwas obtained about 24 and 25 worse than in the othertrials In subsequent runs 2 and 3 the vehicle was equippedwith the best W1 tires (Table 4) The driver has implementedan algorithm-based optimal control strategy Strategy infor-mation was provided by the visualization system During run3 the best result was recorded This result was taken intoaccount in the classification of competitions where the teamplaced in 12 positions out of 28 classified teams Trials 4 dueto damage to the tires were not successful

Measurement error was from 125 to 558 dependingon the sample The measurement system installed perma-nently in the vehicle is a prototype system This systemhas been calibrated using available laboratory equipmentMeasurement errors indicate that other measuring devices ofthe higher accuracy class should be used

Based on the measurement data obtained during testdrives the model was tuned thus reducing the identificationerror The competition took place in stable weather thedivergence of results was small and was about 129 forsample 2 and 139 for sample 3

The difference between the results determined duringnumerical simulation and that obtained in the real run was36 for sample 2 and 269 for sample 3 The difference atthis level was considered to be small Searching for optimalcontrol strategy has not taken into account possible rdquoerrorsrdquowhich could be made by the driver and which result fromthe current situation on the route for example selecting thepath and using the route by other participants in the raceIncluding driver behaviour in the simulation model shouldbe the subject of further work

Figure 19 shows the vehicle velocity together with thecontrol signals recorded during run 2 The black curvesrepresent the real vehicle velocity V119903 and the control signalGreen curves are the optimum control strategy st119880 andthe optimal velocity V119900119901119905 determined by the simulationThe graph shows the entire distance travelled (10 laps) Theanalysis of the graph shows that the driver did not performthe exact planned strategy Errors in the implementationof the strategy are related to the disruptions During thecompetition the driver is not alone on the track in certainsituations the driver cannot overtake other participants andcannot take the optimal path In addition weather conditionsuch as wind has influence on the motion resistance In suchcases the driver has to modify the optimal control strategy

In Figure 20 the velocity recorded during the race V119903(black) and the velocity obtained by the computer simulationV119904119894119898 (red) were shown V119904119894119898 was determined by computersimulation by using real control signal The purpose of thissimulation was to investigate the correctness of identification

VrVopt

Ur Uopt

2000 4000 6000 8000 10000 12000 14000 16000 180000X [m]

05

10152025303540

V [k

mh

]

Figure 19 Comparison of speed and control signal during attempt2

2000 4000 6000 8000 10000 12000 14000 16000 180000x [m]

05

10152025303540

V [k

mh

]

Ur

VrVsim

Figure 20 Comparison of speed registered in real conditions withthe speed determined by computer simulation

of the simulation model and to identify the identificationerror

Compared to the Shell Eco-marathon competitions heldin 2012 and 2013 our performance has improved The resultsin these years were equal to 425 [km kWh] and 454[km kWh] respectively In 2012 and 2013 the controlstrategy was chosen on the basis of the simulation modelbut the model was not adequately identified and the controlstrategy had to be modified In previous editions of therace the implementation of optimal control strategy was notsupported by the visualization system which would informthe driver of the need to take specific actions (pressing orreleasing the accelerator button)

6 Conclusion

The presented method was developed and tested for aprototype electric racing car that has been designed for theShell Eco-marathon race As it was shown the results of thenumerical simulations were very similar to the outcomes ofthe real races in the context of the final result of energyconsumption and the profile of velocity of the car during therace The method has been developed and applied since 2012

Journal of Advanced Transportation 19

and led in 2014 to achieving the optimal result for this type ofthe vehicle

The optimization method was evaluated The resultsachieved during the race attempts where the optimal con-trol strategy was applied (4813 and 4873 kmkWh) werecompared to the result where the strategy was proposed bythe experts (3654 kmkWh) who already had contact withthe results of similar optimization models Optimal attemptswere better by over 30 despite errors in the implementationof the strategy by the driver In the case of experts who did nothave such experiences the differences were even greater

Further improvement of the control strategy is impossiblefor this type of a vehicle and the best way to reduce energyconsumption is by improving the mechanical design It wasthe reason to develop new racing cars for UrbanConceptBattery Electric and Hydrogen competitions The developedresearch methodology for vehicle optimization and controlstrategies has been developed and implemented in the ShellEco-marathon in 2015 which has improved the score to 504km kWhHowever the research has shown that the potentialfor improved performance of the MuSHELLka vehicle hasbeen exhausted No major structural changes in the vehiclecan significantly improve the result so in the followingyears the race was abandoned and the focus was on thedevelopment of the HydroGENIUS the electric vehicle ofUrbanConcept class with fuel cell stack as power sourcewhich eventually scored vice Championship in SEM 2016 Inthe further work it is planned to improve the optimizationresults by using the presented methodology in the case ofthe models of newly constructed vehicles The developmentof the optimization method should take into considerationthe uncertainty resulting from the given velocity strategyconsidering the real conditions of the race It is also possibleto use this method for controlling vehicles in traffic To dothis it is necessary to completely change the way of the routemodelling and the driving conditions modelling as well as todevelop a new optimization method for obtaining results inreal time

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] W Skarka ldquoReducing the Energy Consumption of ElectricVehiclesrdquo in Proceedings of the 22nd ISPE-Inc InternationalConference on Concurrent Engineering Location R Curran NWognumM Borsato et al Eds Advances in TransdisciplinaryEngineering pp 500ndash509 IOS Press Delft Netherlands 2015

[2] R Andrzejewski and J Awrejcewicz Nonlinear Dynamics of aWheeled Vehicle vol 10 Springer-Verlag New York NY USA2005

[3] D W Gao C Mi and A Emadi ldquoModeling and simulation ofelectric and hybrid vehiclesrdquo Proceedings of the IEEE vol 95 no4 pp 729ndash745 2007

[4] ldquoAdvisor documentationrdquo httpadv-vehiclesimsourceforgenet

[5] TMarkel A Brooker THendricks et al ldquoADVISORA systemsanalysis tool for advanced vehicle modelingrdquo Journal of PowerSources vol 110 no 1 pp 255ndash266 2002

[6] K B Wipke M R Cuddy and S D Burch ldquoADVISOR21 a user-friendly advanced powertrain simulation using acombined backwardforward approachrdquo IEEE Transactions onVehicular Technology vol 48 no 6 pp 1751ndash1761 1999

[7] ldquoWebsiterdquo 2014 httpwwwtransportationanlgovmodeling[8] ldquoWebsiterdquo 2014 httpwwwautonomienet[9] K Krykowski J Hetmanczyk Z Gałuszkiewicz and R Mik-

siewicz ldquoComputer analysis of high-speed PM BLDC motorpropertiesrdquo COMPEL - The International Journal for Computa-tion and Mathematics in Electrical and Electronic Engineeringvol 30 no 3 pp 941ndash956 2011

[10] M Vaillant M Eckert and F Gauterin ldquoEnergy managementstrategy to be used in design space exploration for electricpowertrain optimizationrdquo inProceedings of the 2014 9th Interna-tional Conference on Ecological Vehicles and Renewable EnergiesEVER 2014 mco March 2014

[11] A T Nguyen S Reiter and P Rigo ldquoA review on simulation-based optimization methods applied to building performanceanalysisrdquo Applied Energy vol 113 pp 1043ndash1058 2014

[12] W Silka and W Siłka Energy Intensity in the Car Traffic InPolish WNT Warszawa 1997

[13] T J Barlow S Latham I S Mrcrae and P Boulter A referencebook of driving cycles for use in the measurement of roadvehicle emissions TRL 2009 httpswwwgovukgovernmentuploadssystemdata

[14] R N Jazar Vehicle Dynamics Theory and Application SpringerUS Boston MA 2008

[15] MMeywerk ldquoVehicle Dynamicsrdquo inWest Sussex JohnWiley ampSons Lecture Notes to theMOOCVehicle Dynamics of iversity1st edition 2015

[16] MMitschke andHWallentowitzDynamik der KraftfahrzeugeSpringer Berlin Germany 1972

[17] T Stefanski and Ł Zawarczynski ldquoParametric identification ofPM motor mathematical modelsrdquo Przegląd Elektrotechnicznyvol 88 no 4 B pp 224ndash229 2012

[18] A Cameron ldquoMeasuring drive-train efficiencyrdquoHuman Powervol 46

[19] B Rohloff and P Greb ldquoEfficiency measurements of bicycletransmissions a neverending storyrdquo Human Power vol 55 p11 2004

[20] J B Spicer C J K Richardson M J Ehrlich J R BernsteinM Fukuda and M Terada ldquoEffects of frictional loss on bicyclechain drive efficiencyrdquo Journal of Mechanical Design vol 123no 4 pp 598ndash605 2001

[21] K Sternal A Cholewa W Skarka and M Targosz ldquoElec-tric vehicle for the studentsrsquo shell eco-marathon competitionDesign of the car and telemetry systemrdquo Communications inComputer and Information Science vol 329 pp 26ndash33 2012

[22] K Cichonski and W Skarka ldquoInnovative control system forhigh efficiency electric urban vehiclerdquo Communications inComputer and Information Science vol 531 pp 121ndash130 2015

[23] M J Er and R J Oentaryo ldquoComputational IntelligenceMethods andTechniques (Rutkowski L 2008) [BookReview]rdquoIEEE Computational Intelligence Magazine vol 6 no 4 pp 76ndash78 2011

[24] M Targosz M Szumowski W Skarka and P PrzystałkaldquoVelocity Planning of an Electric Vehicle Using an Evolutionary

Journal of Advanced Transportation 3

Master Control System Motor Control System Motor Mechanical System Measuring SystemＲ３４ Ｒ３４

ＲＧ ＲＧ

ＲＬ ＲＬ ＲＬ

Figure 1 Functional diagram of the electric vehicle drive system

The overall efficiency of the drive system is the product ofthe motor efficiency 120578119898 and the efficiency of the transmission120578119879119878

120578 = 120578119898120578119879119878 (4)

The total energy consumption E119888 of the process whichis defined as driving of the given distance D119862 is influencedby many factors the vehicles structural parameters theenergy losses generated when generating and transmittingthe driving torque and the control method A functiondescribing the speed of a vehicle along a certain route isthe so-called speed profile [12 13] The speed profile isusually determined by the driver of the vehicle by means ofappropriate accelerator pedal control and shift gear selectionor by electronic control A cruise control system controls thepower delivered to the drive wheels in order to maintain acertain speed

If the vehicle is equipped with one drive system it can bepresented in the functional diagram as shown in Figure 1

Specific blocks describe the performance of the individualvehicle systems

(i) master control system a speed profile generatorusually the driver by adjusting the accelerator pedaldeciding on the profile and depending on the roadconditions

(ii) motor control system generator of appropriatemotorcontrol values (current voltage)

(iii) motor a machine that transforms the energy of asource into mechanical energy

(iv) mechanical systemof the vehicle torque transmissionfrom the motor shaft to the wheels of the vehicle(clutches gears etc)

(v) measurement system acting as feedback to provideinformation on the current position and speed of thevehicle

The optimization task can be reduced to the following(i) Optimization of design parameters p119896 and settings p119899

eg power of the drive TS ratio ie optimizing thecharacteristics of the vehicle describing the mechan-ical system and current controller The design of thesystem and its mathematical description in the formof the model are decisive for the optimization of theseparameters

(ii) Optimizing the control strategy ie searching for theoptimum speed V119878119864119879 profile or directing the controlsignal to the current controller 119880SET

(iii) Simultaneous optimization of control parameters andstrategy

You can use the Model-Based Optimization method tosolve the optimization task The scheme of the optimizationis shown in Figure 2

In this method decision variables whose value is deter-mined by the optimization algorithm are input variables forthe simulation model Numerical simulation of driving andobtained results during the simulation allows determiningthe result of the objective function Repeating the simulationresults for the subsequent driving parameters controlled bythe optimization algorithm allows the calculation of succes-sive results of the objective function Frequently repeatedresults are aimed at finding the minimum of the target func-tion and thus the optimal solution Stopping the optimizationalgorithm loop depends on the type of the algorithm usedThis usually occurs after a predetermined number of loopsafter a lack of change in the value of the criterion function orother constraints

3 Building the Model of the Electric Vehicle

To study the total energy consumption E119888 of an electricvehicle it is necessary to build amodel to analyze the transferof energy from the source of energy to the drive wheels of thevehicle Figure 3 shows the functional diagram of the electricvehicle drive system This diagram is the starting point forcreating a simulation model

According to the definition the total energy consumptiondepends on the energy consumption of the movement Ethat is on the work generated by the driving force andthe energy losses generated by the motor ΔE119898 as well ason the energy loss of the transmission ΔE119879119878 Accordinglya mathematical model of the vehicle should be createddescribing the phenomenon of resistance and loss of energyin transmission system The mathematical model of theelectric vehicle is shown in this section The model is basedon equations of motion of a wheeled vehicle biaxial withfront axle steering and rear wheel drive The focus is onthe representation of the driving forces and the resistance ofmovement acting in the direction of the longitudinal axis of

4 Journal of Advanced Transportation

Simulation

Simulationmodel

Inputvariables

Simulationresults

Optimization

Optimizationalgorithm

Stopcondition

Objective function Optimizationparameters

NO

OptimizationresultsYES

START

Figure 2 Schematic diagram of the optimization using model [11]

Vehicle

Driving wheels５Ｌ

＝

Motor control system２

ΔＧ

MotorＧ(P)

Transmission systemTS (P)

ΔTS

０ＧＧ＝Ｂ ０TS

Ｇ＝Ｂ

ＲＬ ＲＬ ＲＬ

Figure 3 Functional diagram of an electric vehicle

the vehicleThemodel described here is sufficient to simulateand optimize the parameters of an object that affect the totalenergy consumption E119888 of an object There was no need todetermine the values of forces and displacements affectingindividual vehicle components as in the case of for examplestrength analyses These issues are not the subject of thisstudy so the forces acting in the directions of the otheraxes of the vehicle are not dealt with except for the forceswhich as a result of their impact affect the total energyconsumption

31 Mathematical Model of the Vehicle The theory of vehiclemotion is widely published and has been presented manytimes in the scientific works [14 15] The following sectionprovides formulas and symbols used to build the vehiclemodel A detailed description of the presented issues shouldbe sought among others in the above-mentioned bibliogra-phy Figure 4 shows the forces acting on the vehicle movingalong the path of the inclination angle 120572

The following designations were used F119873 driving forcewhich is the quotient of the driving torque and the dynamicradius of the wheel 1198651198791 and 1198651198792 of the rolling resistance ofthe wheels of front and rear axles respectively Q119898 vehiclegravity force F119875 force of air resistance F119882 =119876119898 sin(120572) uphillresistance F119861 inertia force Z1 and Z2 ground reactions to thefront and rear axle wheelsm119911 =m120575119911 reduced mass

The equation of motion of the vehicle in the drivingdirection can be written as the sum of the driving forces anddrag forces parallel to the road surface as

119898119885 = 119865119873 minus 119865119879 minus 119865119882 minus 119865119875 (5)

The following simplifications were adopted The drivetorque applied to the rear wheel does not affect the pressuredistribution Z1 and Z2 In fact in vehicles with rear wheeldrive the rear is downforced whereas the front axle isrelieved The reaction values Z1 and Z2 were statisticallydeterminedThe coefficients of rolling resistance of all wheelsare identical

Journal of Advanced Transportation 5

2

1

４2

４1

１

１ＭＣＨ

v

C

１＝Ｉ

Ｍ

０

Figure 4 The system of forces acting on the vehicle

Resistance forces depend on many factors and parame-ters many of them are highly nonlinear Modelling of wheelrolling resistance is the subject of separate research and themodel used is very complex so in practice a simplifiedmodelis often used

The rolling resistance of a single wheel is as follows

119865119879119894 = 119888119903119903119885119894 (6)

c119903119903 is the coefficient of rolling resistance that dependson the type of road surface the type of tire or the pressurein the tire This factor also depends on the speed of traveland increases with its growth this is related to the increasein tire deformation The value of the rolling resistancecoefficient is usually given by the tire manufacturer andexemplary values and empirical models on the dependenceof this coefficient on the speed function can be found in theliterature [16] For low travel speeds (lt40kmh) the value ofthe rolling resistance coefficient is assumed to be constantindependent of speed In linear motion the total rollingresistance is the sum of the rolling resistance of all vehiclewheels

If an identical rolling resistance coefficient for eachwheel is assumed which is often justified given the similarconstruction of the front and rear axle wheels and identicaltires and the same pressure operation the sum of the rollingresistance shall be written as

119865119879 = 119888119903119903119876119898 cos120572 (7)

The total wheel resistance should take into account thetire rolling resistance bearing losses and so forth

The essence of resistance in bearings is identical to the tirerolling resistance described previously The bearing torqueis proportional to the bearing load friction coefficient andbearing radius Bearing friction is generally neglected as thebearing resistance value is small compared to the tire rollingresistance [16]

Similarly to the value of rolling resistance the turningresistance can be expressed as the product of the weight ofthe car and the coefficient of turning although according to

literature at low speeds it plays negligibly smaller role thanthe rolling resistance [16]

119865119904 = mg119891119911 (8)

f 119904 is the coefficient of turning anddepends on the pressureforce on the axles tires and so-called intensity of turningin other words ratio of centrifugal and vertical accelerationV2119877119892

The value of air resistance 119865119875 can be determined from

119865119875 = 120574V11990411990611989822 119860119888119909 (9)

where 120574 is the density of air v119904119906119898 [ms] is the total air velocityresulting from the linear velocity of the vehicle v119901 and windspeed v119908 and is the vector sum A is the vehicle front area[m2] and c119909 is the aerodynamic drag coefficient

In this study a TS based on a constant gear ratio was usedPM BLDC (Permanent Magnet Brushless Direct Current)motors are very often used in electric power systems [17]The mathematical description of all phenomena related tomagnetism electrical thermal or mechanical phenomenacan lead to a considerable complexity of the model sosimplifiedmodels are oftenusedThe electrical part ofmotorrsquosmodel can be found in work [9] The electromagnetic torquegenerated by the motor is proportional to the flowing currentand the so-called the motor torque constant K119898 and is givenby [17]

119872119890 = 2119870119898119894119911 (10)

In steady state the electromagnetic torque M119890 is equalto the torque on the motor shaft which is the sum of theload torque and the torque of the losses The efficiency of anelectric motor is defined as

120578119898 = 119875119898119890119888ℎ119898119875119890119897119890119888119905 (11)

119875119898119890119888ℎ119898 is the mechanical output power on the motor shaftand P119890119897119890119888119905 is the electrical power input Relations describing

6 Journal of Advanced Transportation

D [m]

S []Ｃ

RＣ

SＣ

S1

L1 Li

Figure 5 Driving path and its inclination profile

the phenomenon of loss can be found in professional litera-ture [10]

Themotor torque is transmitted to the drive wheel via theTS transmission The mechanical power on the drive wheeldepends on the efficiency of the TS

119875119898119890119888ℎ119901 = 120578119879119878119875119898119890119888ℎ119898 = 120578119879119878120578119898119875119890119897119890119888119905 (12)The efficiency 120578119879119878 is a function of many factors ie it

depends on the powertrain design the transmitted powerand quality of the system For TS based on tension transmis-sion efficiency can be approx 90 The efficiency of the tielink transmission is a function of inter alia transmission ratioi119879119878 interaxial distance belt angle tension force rotationalspeed or torque [18ndash20] In the case of lightweight vehiclesin the TS design it is often not necessary to use variable geartransmissions Speed and torque control is achieved by thecontrol system On the one hand it is an advantage becausethe TS is smaller in weight and less complicated but on theother hand it forces the electric drive to operate in a widerange of torque and rotational speed which affects the motorenergy efficiency

32 Building the Model of the Driving Route The parametersof the path that the vehicle travels on have a significant effecton the resistance values shown in Section 31 In the paper thepath of ride is determined by the exact path of the vehicle ona designated route It is assumed that the best path is knownand it is determined based on the teamrsquos experience (it meansthat the quickest best path along the track is not calculatedby the optimization method) The difference between thepath and the track is as follows A track is a system ofphysically existing roads between points A and B and whenthe path does not exist physically it is the trace that leavesthe selected point of the vehicle (eg center of gravity) onthe route surface With this in mind the journey along theroute can take place on a number of pathsThe route is only alimitation

Figure 5 shows a schematic drawing of one path andits elevation profile The description of the path is formedby its discretization ie the division into finite numbers ofelementary sections of O119905119894 119894 isin 1 2 119899 Each elementarysegment is described by a parameter vector

O119905119894 = [119871 119905119894 119877119905119894 119878119905119894 119864119905119894] where 119871 119905119894[m] is the length of thepath119877119905119894[m] is the radius of curvature 119878119905119894[] is the inclinationof the path and 119864119905119894 represents the type and condition of thepath The length of the path is the sum of the lengths of the119871 119905119894 sections

These basic data are essential for the correct determina-tion of motion resistance on each segment It is assumed thatany change in the inclination or radius of curvature makes itnecessary to define further vector O119905119894

Bearing in mind that vehicles usually move in the openair a suitablemodel should be created describing the externalconditions For this purpose the O119905119894 vector describing thenature of the path should include additional columns suchas velocity and direction of the wind V119908119894 and V119896119894 atmosphericpressure 119901119886119905119898119894 and air temperature t119886119905119898119894 In this situation thevector describing the path and external conditions takes theform O119905119894 = [119871 119905119894 119877119905119894 119878119905119894 119864119905119894 V119908119894 V119896119894 119901119886119905119898119894 t119886119905119898119894] The speedand direction of the wind have a significant effect on the valueof air resistance Determining the wind speed is relativelydifficult and not precise Temporary windsmay have differentdirections and a much higher amplitude than the averagePreliminary investigations have been carried out consideringthe uncertainty of weather conditions During optimizationwhere optimal control strategies were sought the wind speedwas randomly changedThe concept of optimizing the controlstrategy from taking into account the changing weatherconditions was to design a family of strategies It would bepossible to select one optimal strategy or part of it in thereal world because of the existing and changing weatherconditions

33 Control System Design Twomodes of the control systemare taken into consideration in this study They reflect thephysical implementations of the control system used in thebuilt-in electric race vehicles of Prototype class [21] andUrbanConcept class [22] Figures 6 and 7 represent blockdiagrams of the drive system of the vehicle for differentcontrol strategies The control scheme A (Figure 6) is usedin a case when a driver is able to control an acceleration ofthe vehicle by means of a binary signal In this case the goalof the optimization task is to find the control strategy takinginto account two criteria ie the determined travel time aswell as the minimal power consumption of the vehicle Thecontrol strategy is used to specify in which parts of the routethe driver should press or release the acceleration treadleWhen the setpoint signal 119880SET isin 0 1 is assumed then theoptimization task is to search for logic values of the controlsignal as the function corresponding to the position of thevehicle x(t)119880SET = f (x(t)) The supervisory role of the driveris included in the functional scheme as a decision moduleIn this study the behaviour of the driver is not modelled inthe simulation It means that heshe realises the strategy in

Journal of Advanced Transportation 7

Mechanical systemHigh-level control system Motor controller

Transmissionsystem

Currentcontroller

Angularvelocity

measuringsystem

Positionmeasuring

system

MotorDecisionmodule

Driverrsquos decision

Binary control

signal U (x)SET

USET ISET５ＬＲＧ ＲＬ ＲＬ ＲＬ

intint

Figure 6 Drive system diagram control scheme A

High-level control system

Decisionmodule

Velocitycontroller

Mechanical systemMotor controller

Transmissionsystem

Currentcontroller

Angular velocitymeasuring

system

Positionmeasuring system

Motor

Linear velocitymeasuring system

-

Driverrsquos decision

Velocity profileV (x)SET

VSET evＲＧ

Ｒm

USET Ur ISET ＲＬ ＲＬint int

ＲＬ

Figure 7 Drive system diagram control scheme B

the exact way The input control signal U119903 is always differentfrom the signal 119880SET in real conditions It means that thesignal 119880SET is mainly employed by the driver to know whenthe acceleration treadle should be used

In the case of the control scheme B (Figure 7) the generalgoal of the optimization task is the same as in the previouscase However the formal definition of the problem is quitedifferent because in this case the optimal form of the velocitysignal is searched according to the position of the vehicle onthe routeV119878119864119879 = f (x(t))The velocity controller compares thesetpoint signalV119878119864119879 with themeasured velocity of the vehicleand for certain controller setting as well as for control errore119907 it generates the control signal 119880SET As in the previouscase the supervisory role of the driver is included in thedecision module However the main difference is that in theoptimization process the setpoint signal V119878119864119879 can be limitedin the direct way

According to control schemes A and B the input controlsignal U119903 is used by the motor control unit where theemended current regulator normally outputs the correspond-ing signals to the motor terminals The driving torque of themotor shaft is transmitted through the transmission systemto the wheels of the vehicle

4 Evolutionary Optimization of theVelocity Strategy

41 Formulation of the Optimization Problem One of theways to define and to solve the dynamic optimization taskof the velocity strategy of the vehicle is to reduce sucha problem to the static optimization task through the so-called discretization of the independent variable If oneassumes that the independent variable is the position ofthe vehicle (a travelled distance) x(t) then the velocitystrategy st can be represented by a vector of instanta-neous values 119880SET or V119878119864119879 for discrete parts of the routeFigure 8 illustrates the idea of dividing the route into seg-ments

The path is divided into n segments O119894 each of the lengthL119894 where the sum of the lengths of the segments is equal tothe length of the total path For each segment it is necessaryto determine the 119880119878119864119879119894 or 119881119878119864119879119894 setpoint The task is to findthe optimal velocity strategy for control scheme A in thefollowing form

st119900119901119905U = [1198801198781198641198791 1198801198781198641198792 119880119878119864119879119899]119879 119880119878119864119879119894 isin 0 1 (13)

8 Journal of Advanced Transportation

D

L2L1 Ln

O2O1 On

Figure 8 Concept of discretization of the route

whereas in the second case for control scheme B

st119900119901119905V = [1198811198781198641198791 1198811198781198641198792 119881119878119864119879119899]119879 119881119878119864119879119894 isin 119881119898119894119899 119881119898119886119909

(14)

where119881min and119881max can be determined in different ways egbased on the minimummaximum vehicle speed or based onthe simple calculation corresponding to guidelines of the racecompetition

Evolutionary algorithms can be used to solve this prob-lem In the case of the search for strategy st119900119901119905119880 it is preferableto use a classical genetic algorithm In this instance the genesin a chromosome of the individual can be encoded directlyas the binary values of the control signal 119880119878119864119879119894 Thereforethe length of the chromosome N119888ℎ is equal to the number ofsections of the route

In accordance with the control scheme B the velocityprofile is determined as the vector including setpoint valuesof the velocity st119900119901119905119881 The components of the st119900119901119905119881 vectorare floating point values hence it is possible to use anevolutionary strategy proposed in [23] Each of the genes inthe chromosomeof the individual corresponds to the setpointvalue of the velocity during a part of the route

42 Chromosome Codding for Different Velocity StrategiesFor a vehicle that is equipped with a binary control systemof the motor the chromosome can be represented as theoptimal vector of the control signal in the following formst119900119901119905119880 = [1198801198781198641198791 1198801198781198641198792 119880119878119864119879119899]119879 119880119878119864119879119894 isin0 1 for eachsegment O119894 of the route (for control scheme A) or the

optimal vector of the control signal in the second form st119900119901119905119881= [1198811198781198641198791 1198811198781198641198792 119881119878119864119879119899]119879 119881119878119864119879119894 isin [119881min 119881max] for eachsegment O119894 of the route (for control scheme B)

In this optimization task the total distance of the roadD119862is composed of SEM race laps N119905119900 isin1 2 119873 The divisionof the whole route on a finite number of segments O119894 is notrecommended because it can lead to unnecessary increase inthe length of the vector st If the route consists of a minimumof four laps it is possible to limit the search of vector st toonly three types of laps

(i) the initial lap marked by 119874119894119904(ii) the middle laps marked by 119874119894119898(iii) the last lap marked as 119874119894119891Such assumption can be proven for at least three reasons(1) In the practical implementation of velocity strategies

the driver should not implement different control rules foreach lap The master control unit informs the driver aboutthe current velocity strategy but despite all the driver shouldremember this strategy to some extent

(2)The limitation of the velocity strategy only to the threetypes of laps reduces the length of the vector st In this waythe number of elements of the vector st corresponds to thenumber of decision variables of the optimization task

(3) Such division is reasonable by the nature of the laps Inthe initial lap it is necessary to accelerate the vehicle Withinthe middle laps the velocity profile of the vehicle should bethe same During the last lap the previously acquired kineticenergy E119896 is utilized

The task of finding the optimal vector st119900119901119905 can be solvedusing two types of evolutionary algorithms

(i) Classical genetic algorithm for control without avelocity regulator (according to control scheme A presentedin Figure 6)

(ii) Evolutionary strategy for the control system of thevehicle with a velocity regulator (according to control schemeB shown in Figure 7)

Theusage of two algorithms forces the appropriate codingof the velocity strategy which is described in the next twoparagraphs

421 Chromosome Coding For Control Scheme A The phe-notype of each individual determines the control vector st119906that means each gene of the individual of the population isthe value of the control signal 119880119878119864119879119894 for each section of thesegment O119894 of the route Assuming that we are looking for avelocity strategy of only three types of laps the phenotype canbe written as (for short form U equiv 119880SET)

st119880 = [ 1198801119904 1198802119904 119880119899119904 1198801119898 1198802119898 119880119899119904 1198801119891 1198802119891 119880119899119891 ]119879 (15)

where 119880119894119904 119880119894119898 119880119894119891 are the control signals for the initial lapmiddle laps and the last lap

422 Chromosome Coding for Control Scheme B In thiscase the elements in the vector 119881119878119864119879119894 change over a wide

Journal of Advanced Transportation 9

range and can assign real number values In the evolutionarystrategy the phenotype of each individual takes the followingformst119881

= [ 1198811119904 1198812119904 119881119899119904 1198811119898 1198812119898 119881119899119904 1198811119891 1198812119891 119881119899119891 ]119879 (16)

119881119894119904 119881119894119898 119881119894119891 are the setting values of velocity for the initiallap middle laps and the last lap

In the control mode according to scheme B the controlsignal is generated by the velocity controller based on thecontrol error

e119881 = 119881119878119864119879 minus 119881119904119894119898 (17)

where

U119878119864119879 = 1 for e119881 ge 10 otherwise

(18)

The coding for control scheme B in comparison withthe coding for control scheme A has undoubtedly oneadvantage namely the possibility of introducing a velocitylimit during the simulation of the passage of a given sectionof the route A velocity limitation is of great practicalimportance In many situations it is necessary to reducethe velocity of the vehicle during certain parts of theroute for example during cornering Accordingly in caseof control scheme B two velocity vectors are designated asfollows

(i) st11988115 for 119881119878119864119879119894 = [0 15] ms although it is formallylimited to 15ms it can never be achieved because themaximum vehicle speed (based on maximum enginespeed) is approximately 15ms

(ii) st11988110 for 119881119878119864119879119894 = [0 10] ms

43 The Fitness Functions In the case of evolutionary opti-mization the fitness function f 119907119886119897 has to be designed Thissection describes the formulas used to calculate the fitnessfunction of an individual that is needed for solving a task ofevolutionary optimization Each chromosome is a potentialsolution Each control strategy st is used during numericalsimulation The value of the fitness function f 119907119886119897 can becalculated based on the outcomes of the simulation suchas

(i) the total energy consumption r119904119894119898 [kmkWh](ii) the simulation time t119904119894119898(iii) the distance x119904119894119898

and limitations such as

(i) the maximum travel time T119898119886119909(ii) the total distance of the vehicle D119862The value of the function is also used to evaluate the

velocity strategy of the vehicle In the preliminary studies[24] the following fitness function f 119907119886119897 was used

Fitness Function 1

119891V1198861198971 = 11990811198911 + 11990821198912 + 11990831198913 (19)

where

1198911 = [1 + 1199031205821119904119894119898]1205821 (20)

1198912 = [119867 (119863119888 minus 119909119904119894119898) 1003816100381610038161003816119863119888 minus 1199091199041198941198981003816100381610038161003816119863119888 ]1205822 (21)

1198913 = [119867 (119905119904119894119898 minus 119879max)1003816100381610038161003816119879max minus 1199051199041198941198981003816100381610038161003816119879max

]1205822 (22)

where the weights w1 = 050E05 w2 = w3 = 025 andcoefficients 1205821 = minus2 1205822 = 1 were chosen experimentally Thepenalty functions f 2 and f 3 were introduced The Heavisidestep functionH() is used to penalize individuals representingunacceptable solutions [25 26] eg those that exceed themaximum time of the simulation H(t119904119894119898 minus T119898119886119909) or do notreach the specified distance H(D119888 minus x119904119894119898)

Fitness Function 2 In this study the authors have proposedthe fitness function which would lead to the convergenceof the evolutionary algorithm without searching for optimalvalues of weights Such a function is shown and describedbelow

119891V1198861198972 = 1 + 1198914 + 1198915119891111989121198913 (23)

1198911 = 119903119904119894119898 (24)

1198912 = cos(1003816100381610038161003816119863119888 minus 1198891199041198941198981003816100381610038161003816119863119888 ) (25)

1198913 = cos(1003816100381610038161003816119879max minus 1199051199041198941198981003816100381610038161003816119879max) (26)

1198914 = 120594 sdot 119867 (119863119888 minus 119889119904119894119898) (27)

1198915 = 120594 sdot 119867 (119879max minus 119905119904119894119898) (28)

where f 1 is a measure related to the simulated energyconsumption of the vehicle f 2 and f 3 correspond to thelimitations such as the maximum travel time and the totaldistance of the vehicle f 4 and f 5 also correspond to the limi-tations but these play strong penalty role and 120594 is arbitrarilylarge value eg significantly higher than maximal valuesf 2=f 3 =1 In this variant of the fitness function death penalty[26] is applied for unacceptable individuals in the form offactors f 4 and f 5 Individuals who do not reach a specifieddistance or exceed the time limit are eliminated These twocriteria act as a constraint and correspond to the limitationsformulated in the guidelines of the race competition On theother hand the criteria f 2 and f 3 have continuous nature andplay very important role in the fitness functionThey are veryneeded to evaluate continuously the individuals that are veryclose to and very far from the extremum

The argument of cos() function is not related to anangle However the usage of the cos() function is needed to

10 Journal of Advanced Transportation

Table 1 Research object main parameters

Type of the motor PM BLDCTransmission unit Toothed synchronous beltThe minimum turning radius 8 [m]The battery type and capacity Lithium-ion polymer 2100[mAh]Mass of the vehicle 42 [kg]Mass with the driver min 92 [kg]Diameter of wheels 0478 [m]Moment of inertia of the front wheel 119868119896119875 0023 [kgm2]Moment of inertia of the rear wheel 119868119896119879 0023[kgm2]Drag coefficient cx (see Table 2) 022 ndash 023Frontal area A [m2] (see Table 2) 0275 - 0297The total rolling coefficient crr (see Table 4) 00035 ndash 00058

eliminate the possibility of dividing by zero In addition theform of the cos() function is preferred At the initial stage ofoptimization when the simulation time t119904119894119898 and the distancex119904119894119898 differ significantly from the maximum time T119898119886119909 andthe specified distance D119888 a small change will have a greatereffect on the value of the fitness function At the final stageof optimization the function 119891V1198861198972 is more dependent on thesimulated energy consumption of the vehicle related to thefactor f 1 and thanks to the cos() function it is less dependentto the factors f 2 and f 3 The proposed function does notrequire the introduction of weights and therefore it is easierto use this function in other applications eg to find optimalvelocity strategies for different routes

It should be noted that fitness functions 119891val have beenwritten in such a way as to ensure that the optimizationalgorithm will look for a minimum of these functions

5 Case Study

As described in Sections 3 and 4 process of modelling andoptimization was applied and verified using a prototypeelectric vehicle on street race circuit in Rotterdam Themethodology was also carried out on the experimental ridestrack of the Fiat ChryslerAutomobiles Poland factory locatedin Tychy Based on (5)-(12) the simulation model was cre-ated in the MATLABSimulink environment Optimizationwas also carried out in MATLAB using the evolutionaryalgorithms available in the Global Optimization Toolbox Thelibrary of functions for simulating optimizing analyzingand presenting results has been developed

51 Research Object Light electric vehicle was a researchobject The vehicle shown in Figure 9 is a three-wheeledself-supporting structure The vehicle fuselage is made ofcomposites based on epoxy resin and woven of carbon andaramid fibre [21]

The dimensions of the vehicle and basic data are shownin Figure 10 and in Table 1

Identification of parameters for the mathematicalmodel of a research object was carried out by numericalsimulations tests on specially designed test bench [27]

Figure 9 Research object prototype electric vehicle ldquoMuSHELLkardquo(photo by M Wylezoł 2012)

and during conducted experiments in real environment[28]

The vehicle can be driven by two types of drive unit(i) DT1 drive unit based on PM BLDC motors and belt

transmission Drive wheel is equippedwith a one-wayclutch

(ii) DT2 a high-torque PMBLDCmotor mounted insidethe drive wheel The torque generated by the motor isdirectly transmitted to the rear drive wheel

The catalogue data can be used for creating the mathematicalmodel of the DT1 motor but for identifying the exactparameters it was necessary to carry out experimental testsThe manufacturer of the DT2 motor does not provide muchinformation so it was necessary to test the drive unit aswell DT1 drivetrain efficiencywas estimated using aBG75x50motor with toothed synchronous belt transmission ( z1= 28teeth z2 = 200 teeth i119879119878 = 714) The map of the efficiencywas shown on Figure 11(a) The same test was carried out forDT2 drive unit with a motor directly mounted on the drivewheel (Figure 11(b)) The obtained efficiency maps were usedto build the simulationmodel of the tested drivetrain systems

52 Determination of Air Drag Coefficient The air dragcoefficient c119909 was estimated as a result of CFD analysis usingANSYS software [24] and it was also verified by the researchin wind tunnel at the Institute of Aviation inWarsaw Frontalarea of vehicle A was determined from a three-dimensionalmodel in CAD environment Catia V5 The values of dragcoefficient c119909 and frontal area A are shown in Table 2

Journal of Advanced Transportation 11

623

972

1600

2605

Figure 10 Dimensions of the vehicle

(a) DT1 (b) DT2

Figure 11 Maps of the efficiency of tested drivetrain systems

Table 2 The air drag coefficient and frontal area

cx numericalsimulation

cx experimentalresearch Frontal area A [m2]

023 022 0275 0297

53 Determination of Rolling Resistance According to for-mula (7) the rolling resistance depends on the weight of thevehicle (Table 1) the tires rolling resistance coefficient andthe resistance of the bearings Depending on the drive unit(DT1 DT2) used in the vehicle additional resistance has to beadded In theDT1 system there is a one-way clutchwhich alsogenerates some resistance torque The DT2 system cannot bemechanically disconnected and therefore has a higher rollingresistance As a result of the coast down test the total rollingresistance of the vehicle has been identified for the four typesof tiresThe test was performed only with theDT1 system iethe systemwith the clutch Table 3 shows the basic parametersof the tires used in the experiments

The prototype vehicle can be equipped with speciallymanufactured Michelin tires with a low rolling resistantcoefficient of c119903119903 = 00014

In addition to the specialMichelin tires three other typesof tires were tested The identification of rolling resistance

coefficients was also estimated using a coast down test Themeasurements were made as follows

(i) The driver accelerated the vehicle to a fixed speed(ii) At themoment of crossing themarked gate the driver

pressed the marker button to save the flag in theacquired data

(iii) The run continued until free braking after which thedriver switched off the measuring system

(iv) The measurements were made at both directions ofthe road to minimize influence of the wind

(v) Before the attempts wind velocity temperature andatmospheric pressure were measured

(vi) The distance of the road was measured using ameasurement system mounted on the vehicle and itwas also verified using distance measuring wheel

On the basis of the experimental data the total rolling resis-tance coefficient of the vehicle was determined Table 4 showsthe coefficients of rolling resistance of the vehicle dependingon the tire used during the test Total resistance includesthe tire rolling coefficient the bearings resistance and theresistance of the clutch Verification of the data derived fromthe simulation and the experiment was conducted using

12 Journal of Advanced Transportation

Table 3 The types of tires used in the prototype vehicle

Tiresmarker Name of the tire Tirersquos

symbol Shape Type of tread Workingpressure

W1

Michelin ShellEco-marathon 4575R16 Rectangular Slick max500 [kPa]

W2

SchwalbeUl-Termo 23-406 Round Slick 600-1100 [kPa]

W3

Continental SportContact 28-406 Round Slick 600 [kPa]

W4

SchwalbeMarathon 40-406 Round Symmetrical 400-700 [kPa]

Table 4 The total rolling coefficient depending on the tires

Tiresmarker Name of the tire The total rolling coefficient crr mMAPE []

W1 Michelin ShellEco-marathon 00035 784W2 Schwalbe Ultermo 00043 1103W3 Continental SportContact 00058 1252W4 Schwalbe Marathon 00053 445

0

1

2

3

4

5

6

7

8

V [m

s]

100 200 300 400 500 6000x [m]

W1rW1simW2rW2sim

W3rW3simW4rW4sim

Figure 12 Velocity of the vehicle during coast down test

mMAPE (modifiable Mean Absolute Percentage Error) Forvelocity simulationmMAPE can be determined by

119898119872119860119875119864 = 1001119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119881119903 minus 119881119904119894119898119881119898119886119909 minus 119881119898119894119899

10038161003816100381610038161003816100381610038161003816 (29)

Figure 12 shows the experimental data obtained in a coastdown test compared with the results obtained during thecomputer simulation

54 Model of the Race Circuit In accordance with themethodology presented in Section 32 three routes have beendescribed

(i) Route 1 a street race circuit at the Shell Eco-marathoncompetition in Rotterdam

Figure 13 Plan view of the path of the drive on route 1 in Rotterdam

(ii) Routes 2 and 3 on the experimental rides track of theFiat Chrysler Automobiles Poland factory located inTychy in the south of Poland

The Shell Eco-marathon competition is held on a streetcircuit in Rotterdam One lap is 1630 meters long Vehicleshave to cover ten laps in no longer than 39 minutes so suchrequirements impose an averageminimum speed of 25 kmh

The trajectory of the vehicle path was developed usingsatellite images The vehicle trajectory was determined usingthe maximum curvature possible that could be obtained onthe existing roads

Movement of the vehicle in a curved motion causesthe centrifugal force Centrifugal force creates additionalresistance This resistance is inversely proportional to theradius of the path (8) so it is justified to select the largestradius In addition if the centrifugal force exceeds thelimit value it could provide to the side slip of the vehicleAccording to drawings in AutoCAD Civil 3D the lengths ofstraight sections and the lengths and the radius of arcs wereobtained Figure 13 shows a plan view of the path of the drive

Driving the prototype vehicle on public roads is prohib-ited and can be dangerous Vehicle testing was also carried

Journal of Advanced Transportation 13

Table 5 Travel times and total lengths of the routes

Route Length of the lap D [m] The numberof laps The total length of the route Dc [m] Travel time Tmax [s]

Route 1Rotterdam 1630 10 16 300 2340

Route 2Tychy 640 5 3200 460

Route 3Tychy 1000 5 5000 720

Figure 14 Plan view of the path of the drive on route 3 in Tychy

out on the experimental rides track of the Fiat ChryslerAutomobiles Poland factory

For the track in Tychy geodetic measurements weretaken using theDGPS (Differential Global Positioning System)technology The measuring points were collected along theaxis of the road with the distance between points amountingto 10 meters If on the measured route direction or elevationwere changed the frequency of measurement was increasedGeodetic coordinates were also imported intoAutoCADCivil3D and were used to prepare data concerning the route thatwas imported into the simulation environment MATLAB-Simulink Figures 14 and 15 show the path and elevationprofile respectively

Selected routes 2 and 3 have significant differences com-pared to route 1 especially in the height profile This set ofroutes was selected to verify the effect of the route profile onthe achieved results and to verify the proposed optimizationmethods for various road conditions The routes in Tychyare located in an open area there are no large buildingswhich guarantees stability of wind conditions The technicalcondition of the surface on routes 2 and 3 is much worsethan on route 1 which has a significant influence on therolling resistance Rolling resistance was also identified andintroduced into the simulation model For route 2 the c119903119903coefficient was 00056 and for route 3 was 00068

55 Verification of the Simulation Model In order to verifythe compatibility of the identified simulation model a seriesof numerical simulations and experimental tests were per-formed The first experiment consisted of running 300 [m]with a control strategy of 50 [m] with the workingmotor andafter that the vehicle was moving freely for the next 50 [m]The motor is turned on three times Figures 16(a) and 16(b)show the velocity of the vehicle and the power of the motorin function of the distance determined during the experiment

(red curves) and during the numerical simulations (greencurves)

Verification of the data derived from the simulation andthe experimentwas conducted usingmMAPE (29) Formotorpower simulationmMAPE can be determined by

119898119872119860119875119864119875 = 1001119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119875119903 minus 119875119904119894119898119875119898119886119909 minus 119875119898119894119899

10038161003816100381610038161003816100381610038161003816 (30)

where P119903 is the motor power measured during experimentand P119904119894119898 is the motor power conducted in simulation

As a result of the model validation tests estimationerror of the velocity was on level between 235 and 534However the motor power error level was greater It wasbetween 802 and 998

56 Determination of the Optimal Control Strategy Thelength of route 1 and the number of laps are determined bythe organizers of the Shell Eco-marathon competition Thelength of routes 2 and 3 is derived from the existing road planwhere it was possible to carry out trials in real conditionsThenumber of laps for routes 2 and 3 was assumed arbitrarily

The travel time for route 1 is based on the rules of therace which determine the minimum average speed of thevehicle Based on the average speed and the length of routes 2and 3 the travel times for these routes were determined Themaximum travel times and the total length of the route aswell as the number and length of one lap D are summarizedin Table 5

Evolutionary algorithms which are available in theMAT-LAB Global Optimization Toolbox were used From theMATLAB workspace the algorithm ran a simulation modelin a Simulink environment During optimization while usingevolutionary algorithms the maximum number of fitnessfunction evaluations 119873119891V119886119897

is the product of the populationsize 119873119901119900119901 and number of generations 119873119892119890119899

It was assumed that the total number of fitness functionevaluations was equal to 104 therefore should this value beexceeded the calculation would be cancelled Therefore thetotal number of generations 119873119892119890119899 is dependent on the valueof population size 119873119901119900119901

As part of this work phase the vectors st119880 st119881 15 andst119881 10 of the optimum control strategy for an electric vehiclefor routes 1 2 and 3 were determined During evolutionaryoptimization the heuristic method of crossing was usedand the probability of crossing was established on the basisof previous studies at the level of 08 [24 29] At the

14 Journal of Advanced Transportation

0+000

106410

minus164 minus492minus166 minus012 minus018 minus082 minus035 059 031

811

0+100 0+200 0+300 0+400 0+500 0+600 0+700 0+800 0+900 1+000

Figure 15 Profile of the path on route 3 in Tychy

50 100 150 200 250 3000X [m]

0

2

4

6

8

10

V [m

s]

(a) DT1

0

100

200

300

400

500

P [W

]50 100 150 200 250 3000

X [m]

(b) DT1

Figure 16 The velocity and the power determined with used DT1 drive unit

stage of reproduction the elitist succession method wasapplied where the best adapted two individuals in the currentpopulation passed to the next population An adaptivemethod of mutation was used The remaining parameters ofthe algorithm remain the default for the MATLAB GlobalOptimization Toolbox

The first case was the search st119880 vector for route 1Figures 17(a)ndash17(c) show the vehicle velocity V119904119894119898 obtainedby computer simulation The graph of the st119880 control signalis graphically displayed Figure 17 shows the results wherethe optimal control strategy st119880119900119901119905 was used and populationwas 119873119901119900119901=100 and 119873119892119890119899=100 The total energy consumptionwas estimated as r119904119894119898=527633 [km kWh] Figure 17(a) showsthe vehicle speed and control signal st119880 during the first lapwhile Figure 17(b) shows center laps and Figure 17(c) showsthe last lap Figure 17(d) shows the curves of the mean valuesof the fitness functions f 119907119886119897 depending on the number ofcalculations of these functions during the optimization ofthe control strategy There are eight curves in the graph(Figure 17(d)) for each of the 119873119901119900119901 parameters used in thealgorithm

When analyzing the vehicle velocity chart on the last lapof route 1 (Figure 17(c)) it can be seen that according tothe determined control strategy the propulsion system of thevehicle should no longer be used The vehicle should use thestored kinetic energy

The analysis of vehicle velocity V119904119894119898 during the last lapindicates that at the moment of reaching the given distancethe speed was still about 2 [ms] This demonstrates thatthe simulated vehicle has kinetic energy that would haveto be dispersed by the braking system or recovered by the

electric motor Having such a speed does not mean that thereis still possibility for improvement Lower speed at the endof the route has to cause higher speed of the earlier partsof the route This speed is the optimum speed due to thechosen criterion From the analysis of the shape of the fitnessfunction (Figure 17(d)) it can be seen that for route 1 itis preferable to use a smaller population of 119873119901119900119901=25 andincrease the number of 119873119892119890119899=400 The curve shape for thiscase is steep and it falls to the minimum value of the fitnessfunction which may indicate that the algorithm has reacheda convergence

Results of the optimization where B type of coding wasused were analyzed The results obtained as the mean of ther119904119894119898 result together with the standard deviation from all thetests were summarized in Table 6

By analyzing the results in Table 6 it can be seen thatfor route 1 better results were obtained (reduced simulatedtotal energy consumption) using A coding compared to Bespecially for st119881 15 whose results are characterized by thehighest standard deviation For routes 2 and 3 the same as forroute 1 the procedure was followed Optimization strategieshave been optimized for all variants of control vector st119880st119881 15 st10

The results using the control strategy st119881 10 are shownin Figures 18(a)ndash18(c) (119873119901119900119901=100 where r119904119894119898=351795 [km kWh]) Figure 18(d) illustrates the graph of the value of thefitness function

The results obtained for route 2 are presented in Table 7For route 2 compared to route 1 the best results were

achieved using the stV10 vector When using vectors st119880 andstV15 the results were slightly worse Having analyzed the size

Journal of Advanced Transportation 15

0

2

4

6

8

10V

[ms

]

VsimstU

500 1000 15000X [m]

(a) Lap 1

0

2

4

6

8

10

V [m

s]

2500 30002000X [m]

VsimstU

(b) Laps 2-9

0

2

4

6

8

10

V [m

s]

155 1615X [m]

Vsimstu

times104

(c) Lap 10

times10minus3

Npop=25Npop=50Npop=75Npop=100

Npop=125Npop=150Npop=175Npop=200

15

2

25

3

35

4f va

l

2000 4000 6000 8000 100000Nfval

(d) Mean values of the fitness functions

Figure 17 Vehicle speed and control signal st119880 for route 1

Table 6 The results for route 1

The type of coding A The type of coding Bst119880 st11988115 st11988110119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 52465 1459 42845 1741 51569 5477550 52579 10053 44431 22486 51492 3409475 52497 39913 43842 28173 51256 80682100 52589 18128 42232 1797 51166 49379125 52625 13862 42733 39616 51341 70765150 5243 2979 4435 47701 51486 27086175 52513 2511 41428 27299 51838 19358200 52579 19666 42337 25776 51204 78357

16 Journal of Advanced Transportation

100 200 300 400 500 6000X [m]

0

2

4

6

8

10V

[ms

]

VsimstV10

USET

(a) Lap 1

0

2

4

6

8

10

V [m

s]

800 900 1000 1100 1200700X [m]

VsimstV10

USET

(b) Laps 2-4

0

2

4

6

8

10

V [m

s]

2700 2800 2900 3000 3100 32002600X [m]

VsimstV10

USET

(c) Lap 5

times10minus3

Npop=25Npop=50Npop=75Npop=100

Npop=125Npop=150Npop=175Npop=200

275

28

285

29

295

3

305

f val

2000 4000 6000 8000 100000Nfval

(d) Mean values of the fitness functions

Figure 18 Vehicle speed and control signal st11988110 for route 2

of the population used in the optimization process it shouldbe noted that for route 2 it is preferable to use higher value of119873119901119900119901 For all the analyzed cases the best average results for119873119901119900119901=200 were obtained Table 8 summarizes the results forroute 3

For route 3 the average results were reported for a largerpopulation of119873119901119900119901 with B coding In the case of using vectorwith A type coding no characteristic change was notedAs expected comparing the standard deviation betweenalgorithms using B coding the standard deviation is less forthe less variance range

Evolutionary algorithms are not complete search algo-rithms therefore it is not possible to determine whetherthe solution found is best for the chosen criterion and theconstraints assumed

57 Applying the Optimal Control Strategy in Real ConditionsElectric vehicle energy consumption optimization was finallyverified in real conditions at the European edition of the ShellEco-marathon held on 16-18 May 2014 in Rotterdam

Optimal control strategy st119880was displayed by a prototypevisualization system Visualization unit is installed in the

Journal of Advanced Transportation 17

Table 7 The results for route 2

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 34138 66734 34294 23839 34873 5353250 34573 46359 35003 462 3506 3886275 34512 55134 34961 33476 35419 067858100 34836 45332 35253 26117 3544 19295125 34632 52704 35017 49039 35483 14756150 34552 63714 35326 14885 35343 071015175 35063 18728 35274 47141 35564 038022200 35073 14496 3540 13389 35569 14942

Table 8 The results for route 3

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 28071 10173 28643 7323 30994 277650 29346 6142 29581 7894 30874 439975 29711 5002 29217 7367 31141 1856100 29826 3231 29515 7022 30957 4049125 29781 2980 29866 12977 31168 3445150 29453 3346 30217 9623 31288 1249175 29234 2317 30621 6816 31481 1261200 29686 2337 30531 11737 31089 4880

Table 9 Comparison of simulation results with experimental tests

Number of attempts 119903119878119864ndash119898 119903119903 119903119904119894119898 119903119900119901119905 119890119898 119890119894 119890119904119905Attempt 1 3654 3608 - - 125 - -Attempt 2 4813 5082 5148 5265 558 129 36Attempt 3 4873 5127 5198 5265 521 139 269Attempt 4 Failed attempt damaged tires during 1st lap

steering wheel of the vehicle The visualization system showsthe basic data such as instantaneous speed average speedtravel time and distance In addition the visualization systemprovides information on which part of the track the drivershould press the acceleration button to execute the optimalcontrol strategy Measurement of the position on the track iscarried out by the odometrical measuring system Due to thepossibility of accumulating errors in the measurement of theroad the driver will reset the measuring system every timeheshe exceeds the lap line

Table 9 presents the results of all the measurementsconducted during the Shell Eco-marathonThe columns in theTable 9 contain

(i) r119878119864119898 [kmkWh] the result recorded during the raceby the measuring device provided by the organizerthe results are available on the Shell Eco-marathonofficial website

(ii) r119903 [kWkWh] the result based on the indications of aprototypemeasuring system permanently installed inthe vehicle

(iii) r119904119894119898 the result estimated by computer simulationusing recorded real control signal U119903

(iv) r119900119901119905 the result obtained by computer simulation usingthe optimal control strategy U119900119901119905

Table 9 also includes the following

(i) Measurement error

119890119898 = 1003816100381610038161003816119903119878119864119898 minus 1199031199031003816100381610038161003816119903119878119864119898 100 (31)

(ii) Identification error

119890119894 =1003816100381610038161003816119903119903 minus 1199031199041198941198981003816100381610038161003816119903119903 100 (32)

(iii) Strategy implementation error

119890119904119905 =10038161003816100381610038161003816119903119903 minus 11990311990011990111990510038161003816100381610038161003816119903119903 100 (33)

18 Journal of Advanced Transportation

There were four measurement trials available Duringrun 1 a much weaker result was obtained than estimated bysimulation The driver performed run 1 without a definedcontrol strategy As part of the experiment the driver andthe support team were asked to select the optimal tires forthe vehicle and to implement the proposed control strategyDuring run 1 only the travel time of individual laps waschecked According to the choice of the team in run 1 tiresW2 were selected (Table 4) During this test the worst resultwas obtained about 24 and 25 worse than in the othertrials In subsequent runs 2 and 3 the vehicle was equippedwith the best W1 tires (Table 4) The driver has implementedan algorithm-based optimal control strategy Strategy infor-mation was provided by the visualization system During run3 the best result was recorded This result was taken intoaccount in the classification of competitions where the teamplaced in 12 positions out of 28 classified teams Trials 4 dueto damage to the tires were not successful

Measurement error was from 125 to 558 dependingon the sample The measurement system installed perma-nently in the vehicle is a prototype system This systemhas been calibrated using available laboratory equipmentMeasurement errors indicate that other measuring devices ofthe higher accuracy class should be used

Based on the measurement data obtained during testdrives the model was tuned thus reducing the identificationerror The competition took place in stable weather thedivergence of results was small and was about 129 forsample 2 and 139 for sample 3

The difference between the results determined duringnumerical simulation and that obtained in the real run was36 for sample 2 and 269 for sample 3 The difference atthis level was considered to be small Searching for optimalcontrol strategy has not taken into account possible rdquoerrorsrdquowhich could be made by the driver and which result fromthe current situation on the route for example selecting thepath and using the route by other participants in the raceIncluding driver behaviour in the simulation model shouldbe the subject of further work

Figure 19 shows the vehicle velocity together with thecontrol signals recorded during run 2 The black curvesrepresent the real vehicle velocity V119903 and the control signalGreen curves are the optimum control strategy st119880 andthe optimal velocity V119900119901119905 determined by the simulationThe graph shows the entire distance travelled (10 laps) Theanalysis of the graph shows that the driver did not performthe exact planned strategy Errors in the implementationof the strategy are related to the disruptions During thecompetition the driver is not alone on the track in certainsituations the driver cannot overtake other participants andcannot take the optimal path In addition weather conditionsuch as wind has influence on the motion resistance In suchcases the driver has to modify the optimal control strategy

In Figure 20 the velocity recorded during the race V119903(black) and the velocity obtained by the computer simulationV119904119894119898 (red) were shown V119904119894119898 was determined by computersimulation by using real control signal The purpose of thissimulation was to investigate the correctness of identification

VrVopt

Ur Uopt

2000 4000 6000 8000 10000 12000 14000 16000 180000X [m]

05

10152025303540

V [k

mh

]

Figure 19 Comparison of speed and control signal during attempt2

2000 4000 6000 8000 10000 12000 14000 16000 180000x [m]

05

10152025303540

V [k

mh

]

Ur

VrVsim

Figure 20 Comparison of speed registered in real conditions withthe speed determined by computer simulation

of the simulation model and to identify the identificationerror

Compared to the Shell Eco-marathon competitions heldin 2012 and 2013 our performance has improved The resultsin these years were equal to 425 [km kWh] and 454[km kWh] respectively In 2012 and 2013 the controlstrategy was chosen on the basis of the simulation modelbut the model was not adequately identified and the controlstrategy had to be modified In previous editions of therace the implementation of optimal control strategy was notsupported by the visualization system which would informthe driver of the need to take specific actions (pressing orreleasing the accelerator button)

6 Conclusion

The presented method was developed and tested for aprototype electric racing car that has been designed for theShell Eco-marathon race As it was shown the results of thenumerical simulations were very similar to the outcomes ofthe real races in the context of the final result of energyconsumption and the profile of velocity of the car during therace The method has been developed and applied since 2012

Journal of Advanced Transportation 19

and led in 2014 to achieving the optimal result for this type ofthe vehicle

The optimization method was evaluated The resultsachieved during the race attempts where the optimal con-trol strategy was applied (4813 and 4873 kmkWh) werecompared to the result where the strategy was proposed bythe experts (3654 kmkWh) who already had contact withthe results of similar optimization models Optimal attemptswere better by over 30 despite errors in the implementationof the strategy by the driver In the case of experts who did nothave such experiences the differences were even greater

Further improvement of the control strategy is impossiblefor this type of a vehicle and the best way to reduce energyconsumption is by improving the mechanical design It wasthe reason to develop new racing cars for UrbanConceptBattery Electric and Hydrogen competitions The developedresearch methodology for vehicle optimization and controlstrategies has been developed and implemented in the ShellEco-marathon in 2015 which has improved the score to 504km kWhHowever the research has shown that the potentialfor improved performance of the MuSHELLka vehicle hasbeen exhausted No major structural changes in the vehiclecan significantly improve the result so in the followingyears the race was abandoned and the focus was on thedevelopment of the HydroGENIUS the electric vehicle ofUrbanConcept class with fuel cell stack as power sourcewhich eventually scored vice Championship in SEM 2016 Inthe further work it is planned to improve the optimizationresults by using the presented methodology in the case ofthe models of newly constructed vehicles The developmentof the optimization method should take into considerationthe uncertainty resulting from the given velocity strategyconsidering the real conditions of the race It is also possibleto use this method for controlling vehicles in traffic To dothis it is necessary to completely change the way of the routemodelling and the driving conditions modelling as well as todevelop a new optimization method for obtaining results inreal time

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] W Skarka ldquoReducing the Energy Consumption of ElectricVehiclesrdquo in Proceedings of the 22nd ISPE-Inc InternationalConference on Concurrent Engineering Location R Curran NWognumM Borsato et al Eds Advances in TransdisciplinaryEngineering pp 500ndash509 IOS Press Delft Netherlands 2015

[2] R Andrzejewski and J Awrejcewicz Nonlinear Dynamics of aWheeled Vehicle vol 10 Springer-Verlag New York NY USA2005

[3] D W Gao C Mi and A Emadi ldquoModeling and simulation ofelectric and hybrid vehiclesrdquo Proceedings of the IEEE vol 95 no4 pp 729ndash745 2007

[4] ldquoAdvisor documentationrdquo httpadv-vehiclesimsourceforgenet

[5] TMarkel A Brooker THendricks et al ldquoADVISORA systemsanalysis tool for advanced vehicle modelingrdquo Journal of PowerSources vol 110 no 1 pp 255ndash266 2002

[6] K B Wipke M R Cuddy and S D Burch ldquoADVISOR21 a user-friendly advanced powertrain simulation using acombined backwardforward approachrdquo IEEE Transactions onVehicular Technology vol 48 no 6 pp 1751ndash1761 1999

[7] ldquoWebsiterdquo 2014 httpwwwtransportationanlgovmodeling[8] ldquoWebsiterdquo 2014 httpwwwautonomienet[9] K Krykowski J Hetmanczyk Z Gałuszkiewicz and R Mik-

siewicz ldquoComputer analysis of high-speed PM BLDC motorpropertiesrdquo COMPEL - The International Journal for Computa-tion and Mathematics in Electrical and Electronic Engineeringvol 30 no 3 pp 941ndash956 2011

[10] M Vaillant M Eckert and F Gauterin ldquoEnergy managementstrategy to be used in design space exploration for electricpowertrain optimizationrdquo inProceedings of the 2014 9th Interna-tional Conference on Ecological Vehicles and Renewable EnergiesEVER 2014 mco March 2014

[11] A T Nguyen S Reiter and P Rigo ldquoA review on simulation-based optimization methods applied to building performanceanalysisrdquo Applied Energy vol 113 pp 1043ndash1058 2014

[12] W Silka and W Siłka Energy Intensity in the Car Traffic InPolish WNT Warszawa 1997

[13] T J Barlow S Latham I S Mrcrae and P Boulter A referencebook of driving cycles for use in the measurement of roadvehicle emissions TRL 2009 httpswwwgovukgovernmentuploadssystemdata

[14] R N Jazar Vehicle Dynamics Theory and Application SpringerUS Boston MA 2008

[15] MMeywerk ldquoVehicle Dynamicsrdquo inWest Sussex JohnWiley ampSons Lecture Notes to theMOOCVehicle Dynamics of iversity1st edition 2015

[16] MMitschke andHWallentowitzDynamik der KraftfahrzeugeSpringer Berlin Germany 1972

[17] T Stefanski and Ł Zawarczynski ldquoParametric identification ofPM motor mathematical modelsrdquo Przegląd Elektrotechnicznyvol 88 no 4 B pp 224ndash229 2012

[18] A Cameron ldquoMeasuring drive-train efficiencyrdquoHuman Powervol 46

[19] B Rohloff and P Greb ldquoEfficiency measurements of bicycletransmissions a neverending storyrdquo Human Power vol 55 p11 2004

[20] J B Spicer C J K Richardson M J Ehrlich J R BernsteinM Fukuda and M Terada ldquoEffects of frictional loss on bicyclechain drive efficiencyrdquo Journal of Mechanical Design vol 123no 4 pp 598ndash605 2001

[21] K Sternal A Cholewa W Skarka and M Targosz ldquoElec-tric vehicle for the studentsrsquo shell eco-marathon competitionDesign of the car and telemetry systemrdquo Communications inComputer and Information Science vol 329 pp 26ndash33 2012

[22] K Cichonski and W Skarka ldquoInnovative control system forhigh efficiency electric urban vehiclerdquo Communications inComputer and Information Science vol 531 pp 121ndash130 2015

[23] M J Er and R J Oentaryo ldquoComputational IntelligenceMethods andTechniques (Rutkowski L 2008) [BookReview]rdquoIEEE Computational Intelligence Magazine vol 6 no 4 pp 76ndash78 2011

[24] M Targosz M Szumowski W Skarka and P PrzystałkaldquoVelocity Planning of an Electric Vehicle Using an Evolutionary

4 Journal of Advanced Transportation

Simulation

Simulationmodel

Inputvariables

Simulationresults

Optimization

Optimizationalgorithm

Stopcondition

Objective function Optimizationparameters

NO

OptimizationresultsYES

START

Figure 2 Schematic diagram of the optimization using model [11]

Vehicle

Driving wheels５Ｌ

＝

Motor control system２

ΔＧ

MotorＧ(P)

Transmission systemTS (P)

ΔTS

０ＧＧ＝Ｂ ０TS

Ｇ＝Ｂ

ＲＬ ＲＬ ＲＬ

Figure 3 Functional diagram of an electric vehicle

the vehicleThemodel described here is sufficient to simulateand optimize the parameters of an object that affect the totalenergy consumption E119888 of an object There was no need todetermine the values of forces and displacements affectingindividual vehicle components as in the case of for examplestrength analyses These issues are not the subject of thisstudy so the forces acting in the directions of the otheraxes of the vehicle are not dealt with except for the forceswhich as a result of their impact affect the total energyconsumption

31 Mathematical Model of the Vehicle The theory of vehiclemotion is widely published and has been presented manytimes in the scientific works [14 15] The following sectionprovides formulas and symbols used to build the vehiclemodel A detailed description of the presented issues shouldbe sought among others in the above-mentioned bibliogra-phy Figure 4 shows the forces acting on the vehicle movingalong the path of the inclination angle 120572

The following designations were used F119873 driving forcewhich is the quotient of the driving torque and the dynamicradius of the wheel 1198651198791 and 1198651198792 of the rolling resistance ofthe wheels of front and rear axles respectively Q119898 vehiclegravity force F119875 force of air resistance F119882 =119876119898 sin(120572) uphillresistance F119861 inertia force Z1 and Z2 ground reactions to thefront and rear axle wheelsm119911 =m120575119911 reduced mass

The equation of motion of the vehicle in the drivingdirection can be written as the sum of the driving forces anddrag forces parallel to the road surface as

119898119885 = 119865119873 minus 119865119879 minus 119865119882 minus 119865119875 (5)

The following simplifications were adopted The drivetorque applied to the rear wheel does not affect the pressuredistribution Z1 and Z2 In fact in vehicles with rear wheeldrive the rear is downforced whereas the front axle isrelieved The reaction values Z1 and Z2 were statisticallydeterminedThe coefficients of rolling resistance of all wheelsare identical

Journal of Advanced Transportation 5

2

1

４2

４1

１

１ＭＣＨ

v

C

１＝Ｉ

Ｍ

０

Figure 4 The system of forces acting on the vehicle

Resistance forces depend on many factors and parame-ters many of them are highly nonlinear Modelling of wheelrolling resistance is the subject of separate research and themodel used is very complex so in practice a simplifiedmodelis often used

The rolling resistance of a single wheel is as follows

119865119879119894 = 119888119903119903119885119894 (6)

c119903119903 is the coefficient of rolling resistance that dependson the type of road surface the type of tire or the pressurein the tire This factor also depends on the speed of traveland increases with its growth this is related to the increasein tire deformation The value of the rolling resistancecoefficient is usually given by the tire manufacturer andexemplary values and empirical models on the dependenceof this coefficient on the speed function can be found in theliterature [16] For low travel speeds (lt40kmh) the value ofthe rolling resistance coefficient is assumed to be constantindependent of speed In linear motion the total rollingresistance is the sum of the rolling resistance of all vehiclewheels

If an identical rolling resistance coefficient for eachwheel is assumed which is often justified given the similarconstruction of the front and rear axle wheels and identicaltires and the same pressure operation the sum of the rollingresistance shall be written as

119865119879 = 119888119903119903119876119898 cos120572 (7)

The total wheel resistance should take into account thetire rolling resistance bearing losses and so forth

The essence of resistance in bearings is identical to the tirerolling resistance described previously The bearing torqueis proportional to the bearing load friction coefficient andbearing radius Bearing friction is generally neglected as thebearing resistance value is small compared to the tire rollingresistance [16]

Similarly to the value of rolling resistance the turningresistance can be expressed as the product of the weight ofthe car and the coefficient of turning although according to

literature at low speeds it plays negligibly smaller role thanthe rolling resistance [16]

119865119904 = mg119891119911 (8)

f 119904 is the coefficient of turning anddepends on the pressureforce on the axles tires and so-called intensity of turningin other words ratio of centrifugal and vertical accelerationV2119877119892

The value of air resistance 119865119875 can be determined from

119865119875 = 120574V11990411990611989822 119860119888119909 (9)

where 120574 is the density of air v119904119906119898 [ms] is the total air velocityresulting from the linear velocity of the vehicle v119901 and windspeed v119908 and is the vector sum A is the vehicle front area[m2] and c119909 is the aerodynamic drag coefficient

In this study a TS based on a constant gear ratio was usedPM BLDC (Permanent Magnet Brushless Direct Current)motors are very often used in electric power systems [17]The mathematical description of all phenomena related tomagnetism electrical thermal or mechanical phenomenacan lead to a considerable complexity of the model sosimplifiedmodels are oftenusedThe electrical part ofmotorrsquosmodel can be found in work [9] The electromagnetic torquegenerated by the motor is proportional to the flowing currentand the so-called the motor torque constant K119898 and is givenby [17]

119872119890 = 2119870119898119894119911 (10)

In steady state the electromagnetic torque M119890 is equalto the torque on the motor shaft which is the sum of theload torque and the torque of the losses The efficiency of anelectric motor is defined as

120578119898 = 119875119898119890119888ℎ119898119875119890119897119890119888119905 (11)

119875119898119890119888ℎ119898 is the mechanical output power on the motor shaftand P119890119897119890119888119905 is the electrical power input Relations describing

6 Journal of Advanced Transportation

D [m]

S []Ｃ

RＣ

SＣ

S1

L1 Li

Figure 5 Driving path and its inclination profile

the phenomenon of loss can be found in professional litera-ture [10]

Themotor torque is transmitted to the drive wheel via theTS transmission The mechanical power on the drive wheeldepends on the efficiency of the TS

119875119898119890119888ℎ119901 = 120578119879119878119875119898119890119888ℎ119898 = 120578119879119878120578119898119875119890119897119890119888119905 (12)The efficiency 120578119879119878 is a function of many factors ie it

depends on the powertrain design the transmitted powerand quality of the system For TS based on tension transmis-sion efficiency can be approx 90 The efficiency of the tielink transmission is a function of inter alia transmission ratioi119879119878 interaxial distance belt angle tension force rotationalspeed or torque [18ndash20] In the case of lightweight vehiclesin the TS design it is often not necessary to use variable geartransmissions Speed and torque control is achieved by thecontrol system On the one hand it is an advantage becausethe TS is smaller in weight and less complicated but on theother hand it forces the electric drive to operate in a widerange of torque and rotational speed which affects the motorenergy efficiency

32 Building the Model of the Driving Route The parametersof the path that the vehicle travels on have a significant effecton the resistance values shown in Section 31 In the paper thepath of ride is determined by the exact path of the vehicle ona designated route It is assumed that the best path is knownand it is determined based on the teamrsquos experience (it meansthat the quickest best path along the track is not calculatedby the optimization method) The difference between thepath and the track is as follows A track is a system ofphysically existing roads between points A and B and whenthe path does not exist physically it is the trace that leavesthe selected point of the vehicle (eg center of gravity) onthe route surface With this in mind the journey along theroute can take place on a number of pathsThe route is only alimitation

Figure 5 shows a schematic drawing of one path andits elevation profile The description of the path is formedby its discretization ie the division into finite numbers ofelementary sections of O119905119894 119894 isin 1 2 119899 Each elementarysegment is described by a parameter vector

O119905119894 = [119871 119905119894 119877119905119894 119878119905119894 119864119905119894] where 119871 119905119894[m] is the length of thepath119877119905119894[m] is the radius of curvature 119878119905119894[] is the inclinationof the path and 119864119905119894 represents the type and condition of thepath The length of the path is the sum of the lengths of the119871 119905119894 sections

These basic data are essential for the correct determina-tion of motion resistance on each segment It is assumed thatany change in the inclination or radius of curvature makes itnecessary to define further vector O119905119894

Bearing in mind that vehicles usually move in the openair a suitablemodel should be created describing the externalconditions For this purpose the O119905119894 vector describing thenature of the path should include additional columns suchas velocity and direction of the wind V119908119894 and V119896119894 atmosphericpressure 119901119886119905119898119894 and air temperature t119886119905119898119894 In this situation thevector describing the path and external conditions takes theform O119905119894 = [119871 119905119894 119877119905119894 119878119905119894 119864119905119894 V119908119894 V119896119894 119901119886119905119898119894 t119886119905119898119894] The speedand direction of the wind have a significant effect on the valueof air resistance Determining the wind speed is relativelydifficult and not precise Temporary windsmay have differentdirections and a much higher amplitude than the averagePreliminary investigations have been carried out consideringthe uncertainty of weather conditions During optimizationwhere optimal control strategies were sought the wind speedwas randomly changedThe concept of optimizing the controlstrategy from taking into account the changing weatherconditions was to design a family of strategies It would bepossible to select one optimal strategy or part of it in thereal world because of the existing and changing weatherconditions

33 Control System Design Twomodes of the control systemare taken into consideration in this study They reflect thephysical implementations of the control system used in thebuilt-in electric race vehicles of Prototype class [21] andUrbanConcept class [22] Figures 6 and 7 represent blockdiagrams of the drive system of the vehicle for differentcontrol strategies The control scheme A (Figure 6) is usedin a case when a driver is able to control an acceleration ofthe vehicle by means of a binary signal In this case the goalof the optimization task is to find the control strategy takinginto account two criteria ie the determined travel time aswell as the minimal power consumption of the vehicle Thecontrol strategy is used to specify in which parts of the routethe driver should press or release the acceleration treadleWhen the setpoint signal 119880SET isin 0 1 is assumed then theoptimization task is to search for logic values of the controlsignal as the function corresponding to the position of thevehicle x(t)119880SET = f (x(t)) The supervisory role of the driveris included in the functional scheme as a decision moduleIn this study the behaviour of the driver is not modelled inthe simulation It means that heshe realises the strategy in

Journal of Advanced Transportation 7

Mechanical systemHigh-level control system Motor controller

Transmissionsystem

Currentcontroller

Angularvelocity

measuringsystem

Positionmeasuring

system

MotorDecisionmodule

Driverrsquos decision

Binary control

signal U (x)SET

USET ISET５ＬＲＧ ＲＬ ＲＬ ＲＬ

intint

Figure 6 Drive system diagram control scheme A

High-level control system

Decisionmodule

Velocitycontroller

Mechanical systemMotor controller

Transmissionsystem

Currentcontroller

Angular velocitymeasuring

system

Positionmeasuring system

Motor

Linear velocitymeasuring system

-

Driverrsquos decision

Velocity profileV (x)SET

VSET evＲＧ

Ｒm

USET Ur ISET ＲＬ ＲＬint int

ＲＬ

Figure 7 Drive system diagram control scheme B

the exact way The input control signal U119903 is always differentfrom the signal 119880SET in real conditions It means that thesignal 119880SET is mainly employed by the driver to know whenthe acceleration treadle should be used

In the case of the control scheme B (Figure 7) the generalgoal of the optimization task is the same as in the previouscase However the formal definition of the problem is quitedifferent because in this case the optimal form of the velocitysignal is searched according to the position of the vehicle onthe routeV119878119864119879 = f (x(t))The velocity controller compares thesetpoint signalV119878119864119879 with themeasured velocity of the vehicleand for certain controller setting as well as for control errore119907 it generates the control signal 119880SET As in the previouscase the supervisory role of the driver is included in thedecision module However the main difference is that in theoptimization process the setpoint signal V119878119864119879 can be limitedin the direct way

According to control schemes A and B the input controlsignal U119903 is used by the motor control unit where theemended current regulator normally outputs the correspond-ing signals to the motor terminals The driving torque of themotor shaft is transmitted through the transmission systemto the wheels of the vehicle

4 Evolutionary Optimization of theVelocity Strategy

41 Formulation of the Optimization Problem One of theways to define and to solve the dynamic optimization taskof the velocity strategy of the vehicle is to reduce sucha problem to the static optimization task through the so-called discretization of the independent variable If oneassumes that the independent variable is the position ofthe vehicle (a travelled distance) x(t) then the velocitystrategy st can be represented by a vector of instanta-neous values 119880SET or V119878119864119879 for discrete parts of the routeFigure 8 illustrates the idea of dividing the route into seg-ments

The path is divided into n segments O119894 each of the lengthL119894 where the sum of the lengths of the segments is equal tothe length of the total path For each segment it is necessaryto determine the 119880119878119864119879119894 or 119881119878119864119879119894 setpoint The task is to findthe optimal velocity strategy for control scheme A in thefollowing form

st119900119901119905U = [1198801198781198641198791 1198801198781198641198792 119880119878119864119879119899]119879 119880119878119864119879119894 isin 0 1 (13)

8 Journal of Advanced Transportation

D

L2L1 Ln

O2O1 On

Figure 8 Concept of discretization of the route

whereas in the second case for control scheme B

st119900119901119905V = [1198811198781198641198791 1198811198781198641198792 119881119878119864119879119899]119879 119881119878119864119879119894 isin 119881119898119894119899 119881119898119886119909

(14)

where119881min and119881max can be determined in different ways egbased on the minimummaximum vehicle speed or based onthe simple calculation corresponding to guidelines of the racecompetition

Evolutionary algorithms can be used to solve this prob-lem In the case of the search for strategy st119900119901119905119880 it is preferableto use a classical genetic algorithm In this instance the genesin a chromosome of the individual can be encoded directlyas the binary values of the control signal 119880119878119864119879119894 Thereforethe length of the chromosome N119888ℎ is equal to the number ofsections of the route

In accordance with the control scheme B the velocityprofile is determined as the vector including setpoint valuesof the velocity st119900119901119905119881 The components of the st119900119901119905119881 vectorare floating point values hence it is possible to use anevolutionary strategy proposed in [23] Each of the genes inthe chromosomeof the individual corresponds to the setpointvalue of the velocity during a part of the route

42 Chromosome Codding for Different Velocity StrategiesFor a vehicle that is equipped with a binary control systemof the motor the chromosome can be represented as theoptimal vector of the control signal in the following formst119900119901119905119880 = [1198801198781198641198791 1198801198781198641198792 119880119878119864119879119899]119879 119880119878119864119879119894 isin0 1 for eachsegment O119894 of the route (for control scheme A) or the

optimal vector of the control signal in the second form st119900119901119905119881= [1198811198781198641198791 1198811198781198641198792 119881119878119864119879119899]119879 119881119878119864119879119894 isin [119881min 119881max] for eachsegment O119894 of the route (for control scheme B)

In this optimization task the total distance of the roadD119862is composed of SEM race laps N119905119900 isin1 2 119873 The divisionof the whole route on a finite number of segments O119894 is notrecommended because it can lead to unnecessary increase inthe length of the vector st If the route consists of a minimumof four laps it is possible to limit the search of vector st toonly three types of laps

(i) the initial lap marked by 119874119894119904(ii) the middle laps marked by 119874119894119898(iii) the last lap marked as 119874119894119891Such assumption can be proven for at least three reasons(1) In the practical implementation of velocity strategies

the driver should not implement different control rules foreach lap The master control unit informs the driver aboutthe current velocity strategy but despite all the driver shouldremember this strategy to some extent

(2)The limitation of the velocity strategy only to the threetypes of laps reduces the length of the vector st In this waythe number of elements of the vector st corresponds to thenumber of decision variables of the optimization task

(3) Such division is reasonable by the nature of the laps Inthe initial lap it is necessary to accelerate the vehicle Withinthe middle laps the velocity profile of the vehicle should bethe same During the last lap the previously acquired kineticenergy E119896 is utilized

The task of finding the optimal vector st119900119901119905 can be solvedusing two types of evolutionary algorithms

(i) Classical genetic algorithm for control without avelocity regulator (according to control scheme A presentedin Figure 6)

(ii) Evolutionary strategy for the control system of thevehicle with a velocity regulator (according to control schemeB shown in Figure 7)

Theusage of two algorithms forces the appropriate codingof the velocity strategy which is described in the next twoparagraphs

421 Chromosome Coding For Control Scheme A The phe-notype of each individual determines the control vector st119906that means each gene of the individual of the population isthe value of the control signal 119880119878119864119879119894 for each section of thesegment O119894 of the route Assuming that we are looking for avelocity strategy of only three types of laps the phenotype canbe written as (for short form U equiv 119880SET)

st119880 = [ 1198801119904 1198802119904 119880119899119904 1198801119898 1198802119898 119880119899119904 1198801119891 1198802119891 119880119899119891 ]119879 (15)

where 119880119894119904 119880119894119898 119880119894119891 are the control signals for the initial lapmiddle laps and the last lap

422 Chromosome Coding for Control Scheme B In thiscase the elements in the vector 119881119878119864119879119894 change over a wide

Journal of Advanced Transportation 9

range and can assign real number values In the evolutionarystrategy the phenotype of each individual takes the followingformst119881

= [ 1198811119904 1198812119904 119881119899119904 1198811119898 1198812119898 119881119899119904 1198811119891 1198812119891 119881119899119891 ]119879 (16)

119881119894119904 119881119894119898 119881119894119891 are the setting values of velocity for the initiallap middle laps and the last lap

In the control mode according to scheme B the controlsignal is generated by the velocity controller based on thecontrol error

e119881 = 119881119878119864119879 minus 119881119904119894119898 (17)

where

U119878119864119879 = 1 for e119881 ge 10 otherwise

(18)

The coding for control scheme B in comparison withthe coding for control scheme A has undoubtedly oneadvantage namely the possibility of introducing a velocitylimit during the simulation of the passage of a given sectionof the route A velocity limitation is of great practicalimportance In many situations it is necessary to reducethe velocity of the vehicle during certain parts of theroute for example during cornering Accordingly in caseof control scheme B two velocity vectors are designated asfollows

(i) st11988115 for 119881119878119864119879119894 = [0 15] ms although it is formallylimited to 15ms it can never be achieved because themaximum vehicle speed (based on maximum enginespeed) is approximately 15ms

(ii) st11988110 for 119881119878119864119879119894 = [0 10] ms

43 The Fitness Functions In the case of evolutionary opti-mization the fitness function f 119907119886119897 has to be designed Thissection describes the formulas used to calculate the fitnessfunction of an individual that is needed for solving a task ofevolutionary optimization Each chromosome is a potentialsolution Each control strategy st is used during numericalsimulation The value of the fitness function f 119907119886119897 can becalculated based on the outcomes of the simulation suchas

(i) the total energy consumption r119904119894119898 [kmkWh](ii) the simulation time t119904119894119898(iii) the distance x119904119894119898

and limitations such as

(i) the maximum travel time T119898119886119909(ii) the total distance of the vehicle D119862The value of the function is also used to evaluate the

velocity strategy of the vehicle In the preliminary studies[24] the following fitness function f 119907119886119897 was used

Fitness Function 1

119891V1198861198971 = 11990811198911 + 11990821198912 + 11990831198913 (19)

where

1198911 = [1 + 1199031205821119904119894119898]1205821 (20)

1198912 = [119867 (119863119888 minus 119909119904119894119898) 1003816100381610038161003816119863119888 minus 1199091199041198941198981003816100381610038161003816119863119888 ]1205822 (21)

1198913 = [119867 (119905119904119894119898 minus 119879max)1003816100381610038161003816119879max minus 1199051199041198941198981003816100381610038161003816119879max

]1205822 (22)

where the weights w1 = 050E05 w2 = w3 = 025 andcoefficients 1205821 = minus2 1205822 = 1 were chosen experimentally Thepenalty functions f 2 and f 3 were introduced The Heavisidestep functionH() is used to penalize individuals representingunacceptable solutions [25 26] eg those that exceed themaximum time of the simulation H(t119904119894119898 minus T119898119886119909) or do notreach the specified distance H(D119888 minus x119904119894119898)

Fitness Function 2 In this study the authors have proposedthe fitness function which would lead to the convergenceof the evolutionary algorithm without searching for optimalvalues of weights Such a function is shown and describedbelow

119891V1198861198972 = 1 + 1198914 + 1198915119891111989121198913 (23)

1198911 = 119903119904119894119898 (24)

1198912 = cos(1003816100381610038161003816119863119888 minus 1198891199041198941198981003816100381610038161003816119863119888 ) (25)

1198913 = cos(1003816100381610038161003816119879max minus 1199051199041198941198981003816100381610038161003816119879max) (26)

1198914 = 120594 sdot 119867 (119863119888 minus 119889119904119894119898) (27)

1198915 = 120594 sdot 119867 (119879max minus 119905119904119894119898) (28)

where f 1 is a measure related to the simulated energyconsumption of the vehicle f 2 and f 3 correspond to thelimitations such as the maximum travel time and the totaldistance of the vehicle f 4 and f 5 also correspond to the limi-tations but these play strong penalty role and 120594 is arbitrarilylarge value eg significantly higher than maximal valuesf 2=f 3 =1 In this variant of the fitness function death penalty[26] is applied for unacceptable individuals in the form offactors f 4 and f 5 Individuals who do not reach a specifieddistance or exceed the time limit are eliminated These twocriteria act as a constraint and correspond to the limitationsformulated in the guidelines of the race competition On theother hand the criteria f 2 and f 3 have continuous nature andplay very important role in the fitness functionThey are veryneeded to evaluate continuously the individuals that are veryclose to and very far from the extremum

The argument of cos() function is not related to anangle However the usage of the cos() function is needed to

10 Journal of Advanced Transportation

Table 1 Research object main parameters

Type of the motor PM BLDCTransmission unit Toothed synchronous beltThe minimum turning radius 8 [m]The battery type and capacity Lithium-ion polymer 2100[mAh]Mass of the vehicle 42 [kg]Mass with the driver min 92 [kg]Diameter of wheels 0478 [m]Moment of inertia of the front wheel 119868119896119875 0023 [kgm2]Moment of inertia of the rear wheel 119868119896119879 0023[kgm2]Drag coefficient cx (see Table 2) 022 ndash 023Frontal area A [m2] (see Table 2) 0275 - 0297The total rolling coefficient crr (see Table 4) 00035 ndash 00058

eliminate the possibility of dividing by zero In addition theform of the cos() function is preferred At the initial stage ofoptimization when the simulation time t119904119894119898 and the distancex119904119894119898 differ significantly from the maximum time T119898119886119909 andthe specified distance D119888 a small change will have a greatereffect on the value of the fitness function At the final stageof optimization the function 119891V1198861198972 is more dependent on thesimulated energy consumption of the vehicle related to thefactor f 1 and thanks to the cos() function it is less dependentto the factors f 2 and f 3 The proposed function does notrequire the introduction of weights and therefore it is easierto use this function in other applications eg to find optimalvelocity strategies for different routes

It should be noted that fitness functions 119891val have beenwritten in such a way as to ensure that the optimizationalgorithm will look for a minimum of these functions

5 Case Study

As described in Sections 3 and 4 process of modelling andoptimization was applied and verified using a prototypeelectric vehicle on street race circuit in Rotterdam Themethodology was also carried out on the experimental ridestrack of the Fiat ChryslerAutomobiles Poland factory locatedin Tychy Based on (5)-(12) the simulation model was cre-ated in the MATLABSimulink environment Optimizationwas also carried out in MATLAB using the evolutionaryalgorithms available in the Global Optimization Toolbox Thelibrary of functions for simulating optimizing analyzingand presenting results has been developed

51 Research Object Light electric vehicle was a researchobject The vehicle shown in Figure 9 is a three-wheeledself-supporting structure The vehicle fuselage is made ofcomposites based on epoxy resin and woven of carbon andaramid fibre [21]

The dimensions of the vehicle and basic data are shownin Figure 10 and in Table 1

Identification of parameters for the mathematicalmodel of a research object was carried out by numericalsimulations tests on specially designed test bench [27]

Figure 9 Research object prototype electric vehicle ldquoMuSHELLkardquo(photo by M Wylezoł 2012)

and during conducted experiments in real environment[28]

The vehicle can be driven by two types of drive unit(i) DT1 drive unit based on PM BLDC motors and belt

transmission Drive wheel is equippedwith a one-wayclutch

(ii) DT2 a high-torque PMBLDCmotor mounted insidethe drive wheel The torque generated by the motor isdirectly transmitted to the rear drive wheel

The catalogue data can be used for creating the mathematicalmodel of the DT1 motor but for identifying the exactparameters it was necessary to carry out experimental testsThe manufacturer of the DT2 motor does not provide muchinformation so it was necessary to test the drive unit aswell DT1 drivetrain efficiencywas estimated using aBG75x50motor with toothed synchronous belt transmission ( z1= 28teeth z2 = 200 teeth i119879119878 = 714) The map of the efficiencywas shown on Figure 11(a) The same test was carried out forDT2 drive unit with a motor directly mounted on the drivewheel (Figure 11(b)) The obtained efficiency maps were usedto build the simulationmodel of the tested drivetrain systems

52 Determination of Air Drag Coefficient The air dragcoefficient c119909 was estimated as a result of CFD analysis usingANSYS software [24] and it was also verified by the researchin wind tunnel at the Institute of Aviation inWarsaw Frontalarea of vehicle A was determined from a three-dimensionalmodel in CAD environment Catia V5 The values of dragcoefficient c119909 and frontal area A are shown in Table 2

Journal of Advanced Transportation 11

623

972

1600

2605

Figure 10 Dimensions of the vehicle

(a) DT1 (b) DT2

Figure 11 Maps of the efficiency of tested drivetrain systems

Table 2 The air drag coefficient and frontal area

cx numericalsimulation

cx experimentalresearch Frontal area A [m2]

023 022 0275 0297

53 Determination of Rolling Resistance According to for-mula (7) the rolling resistance depends on the weight of thevehicle (Table 1) the tires rolling resistance coefficient andthe resistance of the bearings Depending on the drive unit(DT1 DT2) used in the vehicle additional resistance has to beadded In theDT1 system there is a one-way clutchwhich alsogenerates some resistance torque The DT2 system cannot bemechanically disconnected and therefore has a higher rollingresistance As a result of the coast down test the total rollingresistance of the vehicle has been identified for the four typesof tiresThe test was performed only with theDT1 system iethe systemwith the clutch Table 3 shows the basic parametersof the tires used in the experiments

The prototype vehicle can be equipped with speciallymanufactured Michelin tires with a low rolling resistantcoefficient of c119903119903 = 00014

In addition to the specialMichelin tires three other typesof tires were tested The identification of rolling resistance

coefficients was also estimated using a coast down test Themeasurements were made as follows

(i) The driver accelerated the vehicle to a fixed speed(ii) At themoment of crossing themarked gate the driver

pressed the marker button to save the flag in theacquired data

(iii) The run continued until free braking after which thedriver switched off the measuring system

(iv) The measurements were made at both directions ofthe road to minimize influence of the wind

(v) Before the attempts wind velocity temperature andatmospheric pressure were measured

(vi) The distance of the road was measured using ameasurement system mounted on the vehicle and itwas also verified using distance measuring wheel

On the basis of the experimental data the total rolling resis-tance coefficient of the vehicle was determined Table 4 showsthe coefficients of rolling resistance of the vehicle dependingon the tire used during the test Total resistance includesthe tire rolling coefficient the bearings resistance and theresistance of the clutch Verification of the data derived fromthe simulation and the experiment was conducted using

12 Journal of Advanced Transportation

Table 3 The types of tires used in the prototype vehicle

Tiresmarker Name of the tire Tirersquos

symbol Shape Type of tread Workingpressure

W1

Michelin ShellEco-marathon 4575R16 Rectangular Slick max500 [kPa]

W2

SchwalbeUl-Termo 23-406 Round Slick 600-1100 [kPa]

W3

Continental SportContact 28-406 Round Slick 600 [kPa]

W4

SchwalbeMarathon 40-406 Round Symmetrical 400-700 [kPa]

Table 4 The total rolling coefficient depending on the tires

Tiresmarker Name of the tire The total rolling coefficient crr mMAPE []

W1 Michelin ShellEco-marathon 00035 784W2 Schwalbe Ultermo 00043 1103W3 Continental SportContact 00058 1252W4 Schwalbe Marathon 00053 445

0

1

2

3

4

5

6

7

8

V [m

s]

100 200 300 400 500 6000x [m]

W1rW1simW2rW2sim

W3rW3simW4rW4sim

Figure 12 Velocity of the vehicle during coast down test

mMAPE (modifiable Mean Absolute Percentage Error) Forvelocity simulationmMAPE can be determined by

119898119872119860119875119864 = 1001119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119881119903 minus 119881119904119894119898119881119898119886119909 minus 119881119898119894119899

10038161003816100381610038161003816100381610038161003816 (29)

Figure 12 shows the experimental data obtained in a coastdown test compared with the results obtained during thecomputer simulation

54 Model of the Race Circuit In accordance with themethodology presented in Section 32 three routes have beendescribed

(i) Route 1 a street race circuit at the Shell Eco-marathoncompetition in Rotterdam

Figure 13 Plan view of the path of the drive on route 1 in Rotterdam

(ii) Routes 2 and 3 on the experimental rides track of theFiat Chrysler Automobiles Poland factory located inTychy in the south of Poland

The Shell Eco-marathon competition is held on a streetcircuit in Rotterdam One lap is 1630 meters long Vehicleshave to cover ten laps in no longer than 39 minutes so suchrequirements impose an averageminimum speed of 25 kmh

The trajectory of the vehicle path was developed usingsatellite images The vehicle trajectory was determined usingthe maximum curvature possible that could be obtained onthe existing roads

Movement of the vehicle in a curved motion causesthe centrifugal force Centrifugal force creates additionalresistance This resistance is inversely proportional to theradius of the path (8) so it is justified to select the largestradius In addition if the centrifugal force exceeds thelimit value it could provide to the side slip of the vehicleAccording to drawings in AutoCAD Civil 3D the lengths ofstraight sections and the lengths and the radius of arcs wereobtained Figure 13 shows a plan view of the path of the drive

Driving the prototype vehicle on public roads is prohib-ited and can be dangerous Vehicle testing was also carried

Journal of Advanced Transportation 13

Table 5 Travel times and total lengths of the routes

Route Length of the lap D [m] The numberof laps The total length of the route Dc [m] Travel time Tmax [s]

Route 1Rotterdam 1630 10 16 300 2340

Route 2Tychy 640 5 3200 460

Route 3Tychy 1000 5 5000 720

Figure 14 Plan view of the path of the drive on route 3 in Tychy

out on the experimental rides track of the Fiat ChryslerAutomobiles Poland factory

For the track in Tychy geodetic measurements weretaken using theDGPS (Differential Global Positioning System)technology The measuring points were collected along theaxis of the road with the distance between points amountingto 10 meters If on the measured route direction or elevationwere changed the frequency of measurement was increasedGeodetic coordinates were also imported intoAutoCADCivil3D and were used to prepare data concerning the route thatwas imported into the simulation environment MATLAB-Simulink Figures 14 and 15 show the path and elevationprofile respectively

Selected routes 2 and 3 have significant differences com-pared to route 1 especially in the height profile This set ofroutes was selected to verify the effect of the route profile onthe achieved results and to verify the proposed optimizationmethods for various road conditions The routes in Tychyare located in an open area there are no large buildingswhich guarantees stability of wind conditions The technicalcondition of the surface on routes 2 and 3 is much worsethan on route 1 which has a significant influence on therolling resistance Rolling resistance was also identified andintroduced into the simulation model For route 2 the c119903119903coefficient was 00056 and for route 3 was 00068

55 Verification of the Simulation Model In order to verifythe compatibility of the identified simulation model a seriesof numerical simulations and experimental tests were per-formed The first experiment consisted of running 300 [m]with a control strategy of 50 [m] with the workingmotor andafter that the vehicle was moving freely for the next 50 [m]The motor is turned on three times Figures 16(a) and 16(b)show the velocity of the vehicle and the power of the motorin function of the distance determined during the experiment

(red curves) and during the numerical simulations (greencurves)

Verification of the data derived from the simulation andthe experimentwas conducted usingmMAPE (29) Formotorpower simulationmMAPE can be determined by

119898119872119860119875119864119875 = 1001119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119875119903 minus 119875119904119894119898119875119898119886119909 minus 119875119898119894119899

10038161003816100381610038161003816100381610038161003816 (30)

where P119903 is the motor power measured during experimentand P119904119894119898 is the motor power conducted in simulation

As a result of the model validation tests estimationerror of the velocity was on level between 235 and 534However the motor power error level was greater It wasbetween 802 and 998

56 Determination of the Optimal Control Strategy Thelength of route 1 and the number of laps are determined bythe organizers of the Shell Eco-marathon competition Thelength of routes 2 and 3 is derived from the existing road planwhere it was possible to carry out trials in real conditionsThenumber of laps for routes 2 and 3 was assumed arbitrarily

The travel time for route 1 is based on the rules of therace which determine the minimum average speed of thevehicle Based on the average speed and the length of routes 2and 3 the travel times for these routes were determined Themaximum travel times and the total length of the route aswell as the number and length of one lap D are summarizedin Table 5

Evolutionary algorithms which are available in theMAT-LAB Global Optimization Toolbox were used From theMATLAB workspace the algorithm ran a simulation modelin a Simulink environment During optimization while usingevolutionary algorithms the maximum number of fitnessfunction evaluations 119873119891V119886119897

is the product of the populationsize 119873119901119900119901 and number of generations 119873119892119890119899

It was assumed that the total number of fitness functionevaluations was equal to 104 therefore should this value beexceeded the calculation would be cancelled Therefore thetotal number of generations 119873119892119890119899 is dependent on the valueof population size 119873119901119900119901

As part of this work phase the vectors st119880 st119881 15 andst119881 10 of the optimum control strategy for an electric vehiclefor routes 1 2 and 3 were determined During evolutionaryoptimization the heuristic method of crossing was usedand the probability of crossing was established on the basisof previous studies at the level of 08 [24 29] At the

14 Journal of Advanced Transportation

0+000

106410

minus164 minus492minus166 minus012 minus018 minus082 minus035 059 031

811

0+100 0+200 0+300 0+400 0+500 0+600 0+700 0+800 0+900 1+000

Figure 15 Profile of the path on route 3 in Tychy

50 100 150 200 250 3000X [m]

0

2

4

6

8

10

V [m

s]

(a) DT1

0

100

200

300

400

500

P [W

]50 100 150 200 250 3000

X [m]

(b) DT1

Figure 16 The velocity and the power determined with used DT1 drive unit

stage of reproduction the elitist succession method wasapplied where the best adapted two individuals in the currentpopulation passed to the next population An adaptivemethod of mutation was used The remaining parameters ofthe algorithm remain the default for the MATLAB GlobalOptimization Toolbox

The first case was the search st119880 vector for route 1Figures 17(a)ndash17(c) show the vehicle velocity V119904119894119898 obtainedby computer simulation The graph of the st119880 control signalis graphically displayed Figure 17 shows the results wherethe optimal control strategy st119880119900119901119905 was used and populationwas 119873119901119900119901=100 and 119873119892119890119899=100 The total energy consumptionwas estimated as r119904119894119898=527633 [km kWh] Figure 17(a) showsthe vehicle speed and control signal st119880 during the first lapwhile Figure 17(b) shows center laps and Figure 17(c) showsthe last lap Figure 17(d) shows the curves of the mean valuesof the fitness functions f 119907119886119897 depending on the number ofcalculations of these functions during the optimization ofthe control strategy There are eight curves in the graph(Figure 17(d)) for each of the 119873119901119900119901 parameters used in thealgorithm

When analyzing the vehicle velocity chart on the last lapof route 1 (Figure 17(c)) it can be seen that according tothe determined control strategy the propulsion system of thevehicle should no longer be used The vehicle should use thestored kinetic energy

The analysis of vehicle velocity V119904119894119898 during the last lapindicates that at the moment of reaching the given distancethe speed was still about 2 [ms] This demonstrates thatthe simulated vehicle has kinetic energy that would haveto be dispersed by the braking system or recovered by the

electric motor Having such a speed does not mean that thereis still possibility for improvement Lower speed at the endof the route has to cause higher speed of the earlier partsof the route This speed is the optimum speed due to thechosen criterion From the analysis of the shape of the fitnessfunction (Figure 17(d)) it can be seen that for route 1 itis preferable to use a smaller population of 119873119901119900119901=25 andincrease the number of 119873119892119890119899=400 The curve shape for thiscase is steep and it falls to the minimum value of the fitnessfunction which may indicate that the algorithm has reacheda convergence

Results of the optimization where B type of coding wasused were analyzed The results obtained as the mean of ther119904119894119898 result together with the standard deviation from all thetests were summarized in Table 6

By analyzing the results in Table 6 it can be seen thatfor route 1 better results were obtained (reduced simulatedtotal energy consumption) using A coding compared to Bespecially for st119881 15 whose results are characterized by thehighest standard deviation For routes 2 and 3 the same as forroute 1 the procedure was followed Optimization strategieshave been optimized for all variants of control vector st119880st119881 15 st10

The results using the control strategy st119881 10 are shownin Figures 18(a)ndash18(c) (119873119901119900119901=100 where r119904119894119898=351795 [km kWh]) Figure 18(d) illustrates the graph of the value of thefitness function

The results obtained for route 2 are presented in Table 7For route 2 compared to route 1 the best results were

achieved using the stV10 vector When using vectors st119880 andstV15 the results were slightly worse Having analyzed the size

Journal of Advanced Transportation 15

0

2

4

6

8

10V

[ms

]

VsimstU

500 1000 15000X [m]

(a) Lap 1

0

2

4

6

8

10

V [m

s]

2500 30002000X [m]

VsimstU

(b) Laps 2-9

0

2

4

6

8

10

V [m

s]

155 1615X [m]

Vsimstu

times104

(c) Lap 10

times10minus3

Npop=25Npop=50Npop=75Npop=100

Npop=125Npop=150Npop=175Npop=200

15

2

25

3

35

4f va

l

2000 4000 6000 8000 100000Nfval

(d) Mean values of the fitness functions

Figure 17 Vehicle speed and control signal st119880 for route 1

Table 6 The results for route 1

The type of coding A The type of coding Bst119880 st11988115 st11988110119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 52465 1459 42845 1741 51569 5477550 52579 10053 44431 22486 51492 3409475 52497 39913 43842 28173 51256 80682100 52589 18128 42232 1797 51166 49379125 52625 13862 42733 39616 51341 70765150 5243 2979 4435 47701 51486 27086175 52513 2511 41428 27299 51838 19358200 52579 19666 42337 25776 51204 78357

16 Journal of Advanced Transportation

100 200 300 400 500 6000X [m]

0

2

4

6

8

10V

[ms

]

VsimstV10

USET

(a) Lap 1

0

2

4

6

8

10

V [m

s]

800 900 1000 1100 1200700X [m]

VsimstV10

USET

(b) Laps 2-4

0

2

4

6

8

10

V [m

s]

2700 2800 2900 3000 3100 32002600X [m]

VsimstV10

USET

(c) Lap 5

times10minus3

Npop=25Npop=50Npop=75Npop=100

Npop=125Npop=150Npop=175Npop=200

275

28

285

29

295

3

305

f val

2000 4000 6000 8000 100000Nfval

(d) Mean values of the fitness functions

Figure 18 Vehicle speed and control signal st11988110 for route 2

of the population used in the optimization process it shouldbe noted that for route 2 it is preferable to use higher value of119873119901119900119901 For all the analyzed cases the best average results for119873119901119900119901=200 were obtained Table 8 summarizes the results forroute 3

For route 3 the average results were reported for a largerpopulation of119873119901119900119901 with B coding In the case of using vectorwith A type coding no characteristic change was notedAs expected comparing the standard deviation betweenalgorithms using B coding the standard deviation is less forthe less variance range

Evolutionary algorithms are not complete search algo-rithms therefore it is not possible to determine whetherthe solution found is best for the chosen criterion and theconstraints assumed

57 Applying the Optimal Control Strategy in Real ConditionsElectric vehicle energy consumption optimization was finallyverified in real conditions at the European edition of the ShellEco-marathon held on 16-18 May 2014 in Rotterdam

Optimal control strategy st119880was displayed by a prototypevisualization system Visualization unit is installed in the

Journal of Advanced Transportation 17

Table 7 The results for route 2

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 34138 66734 34294 23839 34873 5353250 34573 46359 35003 462 3506 3886275 34512 55134 34961 33476 35419 067858100 34836 45332 35253 26117 3544 19295125 34632 52704 35017 49039 35483 14756150 34552 63714 35326 14885 35343 071015175 35063 18728 35274 47141 35564 038022200 35073 14496 3540 13389 35569 14942

Table 8 The results for route 3

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 28071 10173 28643 7323 30994 277650 29346 6142 29581 7894 30874 439975 29711 5002 29217 7367 31141 1856100 29826 3231 29515 7022 30957 4049125 29781 2980 29866 12977 31168 3445150 29453 3346 30217 9623 31288 1249175 29234 2317 30621 6816 31481 1261200 29686 2337 30531 11737 31089 4880

Table 9 Comparison of simulation results with experimental tests

Number of attempts 119903119878119864ndash119898 119903119903 119903119904119894119898 119903119900119901119905 119890119898 119890119894 119890119904119905Attempt 1 3654 3608 - - 125 - -Attempt 2 4813 5082 5148 5265 558 129 36Attempt 3 4873 5127 5198 5265 521 139 269Attempt 4 Failed attempt damaged tires during 1st lap

steering wheel of the vehicle The visualization system showsthe basic data such as instantaneous speed average speedtravel time and distance In addition the visualization systemprovides information on which part of the track the drivershould press the acceleration button to execute the optimalcontrol strategy Measurement of the position on the track iscarried out by the odometrical measuring system Due to thepossibility of accumulating errors in the measurement of theroad the driver will reset the measuring system every timeheshe exceeds the lap line

Table 9 presents the results of all the measurementsconducted during the Shell Eco-marathonThe columns in theTable 9 contain

(i) r119878119864119898 [kmkWh] the result recorded during the raceby the measuring device provided by the organizerthe results are available on the Shell Eco-marathonofficial website

(ii) r119903 [kWkWh] the result based on the indications of aprototypemeasuring system permanently installed inthe vehicle

(iii) r119904119894119898 the result estimated by computer simulationusing recorded real control signal U119903

(iv) r119900119901119905 the result obtained by computer simulation usingthe optimal control strategy U119900119901119905

Table 9 also includes the following

(i) Measurement error

119890119898 = 1003816100381610038161003816119903119878119864119898 minus 1199031199031003816100381610038161003816119903119878119864119898 100 (31)

(ii) Identification error

119890119894 =1003816100381610038161003816119903119903 minus 1199031199041198941198981003816100381610038161003816119903119903 100 (32)

(iii) Strategy implementation error

119890119904119905 =10038161003816100381610038161003816119903119903 minus 11990311990011990111990510038161003816100381610038161003816119903119903 100 (33)

18 Journal of Advanced Transportation

There were four measurement trials available Duringrun 1 a much weaker result was obtained than estimated bysimulation The driver performed run 1 without a definedcontrol strategy As part of the experiment the driver andthe support team were asked to select the optimal tires forthe vehicle and to implement the proposed control strategyDuring run 1 only the travel time of individual laps waschecked According to the choice of the team in run 1 tiresW2 were selected (Table 4) During this test the worst resultwas obtained about 24 and 25 worse than in the othertrials In subsequent runs 2 and 3 the vehicle was equippedwith the best W1 tires (Table 4) The driver has implementedan algorithm-based optimal control strategy Strategy infor-mation was provided by the visualization system During run3 the best result was recorded This result was taken intoaccount in the classification of competitions where the teamplaced in 12 positions out of 28 classified teams Trials 4 dueto damage to the tires were not successful

Measurement error was from 125 to 558 dependingon the sample The measurement system installed perma-nently in the vehicle is a prototype system This systemhas been calibrated using available laboratory equipmentMeasurement errors indicate that other measuring devices ofthe higher accuracy class should be used

Based on the measurement data obtained during testdrives the model was tuned thus reducing the identificationerror The competition took place in stable weather thedivergence of results was small and was about 129 forsample 2 and 139 for sample 3

The difference between the results determined duringnumerical simulation and that obtained in the real run was36 for sample 2 and 269 for sample 3 The difference atthis level was considered to be small Searching for optimalcontrol strategy has not taken into account possible rdquoerrorsrdquowhich could be made by the driver and which result fromthe current situation on the route for example selecting thepath and using the route by other participants in the raceIncluding driver behaviour in the simulation model shouldbe the subject of further work

Figure 19 shows the vehicle velocity together with thecontrol signals recorded during run 2 The black curvesrepresent the real vehicle velocity V119903 and the control signalGreen curves are the optimum control strategy st119880 andthe optimal velocity V119900119901119905 determined by the simulationThe graph shows the entire distance travelled (10 laps) Theanalysis of the graph shows that the driver did not performthe exact planned strategy Errors in the implementationof the strategy are related to the disruptions During thecompetition the driver is not alone on the track in certainsituations the driver cannot overtake other participants andcannot take the optimal path In addition weather conditionsuch as wind has influence on the motion resistance In suchcases the driver has to modify the optimal control strategy

In Figure 20 the velocity recorded during the race V119903(black) and the velocity obtained by the computer simulationV119904119894119898 (red) were shown V119904119894119898 was determined by computersimulation by using real control signal The purpose of thissimulation was to investigate the correctness of identification

VrVopt

Ur Uopt

2000 4000 6000 8000 10000 12000 14000 16000 180000X [m]

05

10152025303540

V [k

mh

]

Figure 19 Comparison of speed and control signal during attempt2

2000 4000 6000 8000 10000 12000 14000 16000 180000x [m]

05

10152025303540

V [k

mh

]

Ur

VrVsim

Figure 20 Comparison of speed registered in real conditions withthe speed determined by computer simulation

of the simulation model and to identify the identificationerror

Compared to the Shell Eco-marathon competitions heldin 2012 and 2013 our performance has improved The resultsin these years were equal to 425 [km kWh] and 454[km kWh] respectively In 2012 and 2013 the controlstrategy was chosen on the basis of the simulation modelbut the model was not adequately identified and the controlstrategy had to be modified In previous editions of therace the implementation of optimal control strategy was notsupported by the visualization system which would informthe driver of the need to take specific actions (pressing orreleasing the accelerator button)

6 Conclusion

The presented method was developed and tested for aprototype electric racing car that has been designed for theShell Eco-marathon race As it was shown the results of thenumerical simulations were very similar to the outcomes ofthe real races in the context of the final result of energyconsumption and the profile of velocity of the car during therace The method has been developed and applied since 2012

Journal of Advanced Transportation 19

and led in 2014 to achieving the optimal result for this type ofthe vehicle

The optimization method was evaluated The resultsachieved during the race attempts where the optimal con-trol strategy was applied (4813 and 4873 kmkWh) werecompared to the result where the strategy was proposed bythe experts (3654 kmkWh) who already had contact withthe results of similar optimization models Optimal attemptswere better by over 30 despite errors in the implementationof the strategy by the driver In the case of experts who did nothave such experiences the differences were even greater

Further improvement of the control strategy is impossiblefor this type of a vehicle and the best way to reduce energyconsumption is by improving the mechanical design It wasthe reason to develop new racing cars for UrbanConceptBattery Electric and Hydrogen competitions The developedresearch methodology for vehicle optimization and controlstrategies has been developed and implemented in the ShellEco-marathon in 2015 which has improved the score to 504km kWhHowever the research has shown that the potentialfor improved performance of the MuSHELLka vehicle hasbeen exhausted No major structural changes in the vehiclecan significantly improve the result so in the followingyears the race was abandoned and the focus was on thedevelopment of the HydroGENIUS the electric vehicle ofUrbanConcept class with fuel cell stack as power sourcewhich eventually scored vice Championship in SEM 2016 Inthe further work it is planned to improve the optimizationresults by using the presented methodology in the case ofthe models of newly constructed vehicles The developmentof the optimization method should take into considerationthe uncertainty resulting from the given velocity strategyconsidering the real conditions of the race It is also possibleto use this method for controlling vehicles in traffic To dothis it is necessary to completely change the way of the routemodelling and the driving conditions modelling as well as todevelop a new optimization method for obtaining results inreal time

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] W Skarka ldquoReducing the Energy Consumption of ElectricVehiclesrdquo in Proceedings of the 22nd ISPE-Inc InternationalConference on Concurrent Engineering Location R Curran NWognumM Borsato et al Eds Advances in TransdisciplinaryEngineering pp 500ndash509 IOS Press Delft Netherlands 2015

[2] R Andrzejewski and J Awrejcewicz Nonlinear Dynamics of aWheeled Vehicle vol 10 Springer-Verlag New York NY USA2005

[3] D W Gao C Mi and A Emadi ldquoModeling and simulation ofelectric and hybrid vehiclesrdquo Proceedings of the IEEE vol 95 no4 pp 729ndash745 2007

[4] ldquoAdvisor documentationrdquo httpadv-vehiclesimsourceforgenet

[5] TMarkel A Brooker THendricks et al ldquoADVISORA systemsanalysis tool for advanced vehicle modelingrdquo Journal of PowerSources vol 110 no 1 pp 255ndash266 2002

[6] K B Wipke M R Cuddy and S D Burch ldquoADVISOR21 a user-friendly advanced powertrain simulation using acombined backwardforward approachrdquo IEEE Transactions onVehicular Technology vol 48 no 6 pp 1751ndash1761 1999

[7] ldquoWebsiterdquo 2014 httpwwwtransportationanlgovmodeling[8] ldquoWebsiterdquo 2014 httpwwwautonomienet[9] K Krykowski J Hetmanczyk Z Gałuszkiewicz and R Mik-

siewicz ldquoComputer analysis of high-speed PM BLDC motorpropertiesrdquo COMPEL - The International Journal for Computa-tion and Mathematics in Electrical and Electronic Engineeringvol 30 no 3 pp 941ndash956 2011

[10] M Vaillant M Eckert and F Gauterin ldquoEnergy managementstrategy to be used in design space exploration for electricpowertrain optimizationrdquo inProceedings of the 2014 9th Interna-tional Conference on Ecological Vehicles and Renewable EnergiesEVER 2014 mco March 2014

[11] A T Nguyen S Reiter and P Rigo ldquoA review on simulation-based optimization methods applied to building performanceanalysisrdquo Applied Energy vol 113 pp 1043ndash1058 2014

[12] W Silka and W Siłka Energy Intensity in the Car Traffic InPolish WNT Warszawa 1997

[13] T J Barlow S Latham I S Mrcrae and P Boulter A referencebook of driving cycles for use in the measurement of roadvehicle emissions TRL 2009 httpswwwgovukgovernmentuploadssystemdata

[14] R N Jazar Vehicle Dynamics Theory and Application SpringerUS Boston MA 2008

[15] MMeywerk ldquoVehicle Dynamicsrdquo inWest Sussex JohnWiley ampSons Lecture Notes to theMOOCVehicle Dynamics of iversity1st edition 2015

[16] MMitschke andHWallentowitzDynamik der KraftfahrzeugeSpringer Berlin Germany 1972

[17] T Stefanski and Ł Zawarczynski ldquoParametric identification ofPM motor mathematical modelsrdquo Przegląd Elektrotechnicznyvol 88 no 4 B pp 224ndash229 2012

[18] A Cameron ldquoMeasuring drive-train efficiencyrdquoHuman Powervol 46

[19] B Rohloff and P Greb ldquoEfficiency measurements of bicycletransmissions a neverending storyrdquo Human Power vol 55 p11 2004

[20] J B Spicer C J K Richardson M J Ehrlich J R BernsteinM Fukuda and M Terada ldquoEffects of frictional loss on bicyclechain drive efficiencyrdquo Journal of Mechanical Design vol 123no 4 pp 598ndash605 2001

[21] K Sternal A Cholewa W Skarka and M Targosz ldquoElec-tric vehicle for the studentsrsquo shell eco-marathon competitionDesign of the car and telemetry systemrdquo Communications inComputer and Information Science vol 329 pp 26ndash33 2012

[22] K Cichonski and W Skarka ldquoInnovative control system forhigh efficiency electric urban vehiclerdquo Communications inComputer and Information Science vol 531 pp 121ndash130 2015

[23] M J Er and R J Oentaryo ldquoComputational IntelligenceMethods andTechniques (Rutkowski L 2008) [BookReview]rdquoIEEE Computational Intelligence Magazine vol 6 no 4 pp 76ndash78 2011

[24] M Targosz M Szumowski W Skarka and P PrzystałkaldquoVelocity Planning of an Electric Vehicle Using an Evolutionary

Journal of Advanced Transportation 5

2

1

４2

４1

１

１ＭＣＨ

v

C

１＝Ｉ

Ｍ

０

Figure 4 The system of forces acting on the vehicle

Resistance forces depend on many factors and parame-ters many of them are highly nonlinear Modelling of wheelrolling resistance is the subject of separate research and themodel used is very complex so in practice a simplifiedmodelis often used

The rolling resistance of a single wheel is as follows

119865119879119894 = 119888119903119903119885119894 (6)

c119903119903 is the coefficient of rolling resistance that dependson the type of road surface the type of tire or the pressurein the tire This factor also depends on the speed of traveland increases with its growth this is related to the increasein tire deformation The value of the rolling resistancecoefficient is usually given by the tire manufacturer andexemplary values and empirical models on the dependenceof this coefficient on the speed function can be found in theliterature [16] For low travel speeds (lt40kmh) the value ofthe rolling resistance coefficient is assumed to be constantindependent of speed In linear motion the total rollingresistance is the sum of the rolling resistance of all vehiclewheels

If an identical rolling resistance coefficient for eachwheel is assumed which is often justified given the similarconstruction of the front and rear axle wheels and identicaltires and the same pressure operation the sum of the rollingresistance shall be written as

119865119879 = 119888119903119903119876119898 cos120572 (7)

The total wheel resistance should take into account thetire rolling resistance bearing losses and so forth

The essence of resistance in bearings is identical to the tirerolling resistance described previously The bearing torqueis proportional to the bearing load friction coefficient andbearing radius Bearing friction is generally neglected as thebearing resistance value is small compared to the tire rollingresistance [16]

Similarly to the value of rolling resistance the turningresistance can be expressed as the product of the weight ofthe car and the coefficient of turning although according to

literature at low speeds it plays negligibly smaller role thanthe rolling resistance [16]

119865119904 = mg119891119911 (8)

f 119904 is the coefficient of turning anddepends on the pressureforce on the axles tires and so-called intensity of turningin other words ratio of centrifugal and vertical accelerationV2119877119892

The value of air resistance 119865119875 can be determined from

119865119875 = 120574V11990411990611989822 119860119888119909 (9)

where 120574 is the density of air v119904119906119898 [ms] is the total air velocityresulting from the linear velocity of the vehicle v119901 and windspeed v119908 and is the vector sum A is the vehicle front area[m2] and c119909 is the aerodynamic drag coefficient

In this study a TS based on a constant gear ratio was usedPM BLDC (Permanent Magnet Brushless Direct Current)motors are very often used in electric power systems [17]The mathematical description of all phenomena related tomagnetism electrical thermal or mechanical phenomenacan lead to a considerable complexity of the model sosimplifiedmodels are oftenusedThe electrical part ofmotorrsquosmodel can be found in work [9] The electromagnetic torquegenerated by the motor is proportional to the flowing currentand the so-called the motor torque constant K119898 and is givenby [17]

119872119890 = 2119870119898119894119911 (10)

In steady state the electromagnetic torque M119890 is equalto the torque on the motor shaft which is the sum of theload torque and the torque of the losses The efficiency of anelectric motor is defined as

120578119898 = 119875119898119890119888ℎ119898119875119890119897119890119888119905 (11)

119875119898119890119888ℎ119898 is the mechanical output power on the motor shaftand P119890119897119890119888119905 is the electrical power input Relations describing

6 Journal of Advanced Transportation

D [m]

S []Ｃ

RＣ

SＣ

S1

L1 Li

Figure 5 Driving path and its inclination profile

the phenomenon of loss can be found in professional litera-ture [10]

Themotor torque is transmitted to the drive wheel via theTS transmission The mechanical power on the drive wheeldepends on the efficiency of the TS

119875119898119890119888ℎ119901 = 120578119879119878119875119898119890119888ℎ119898 = 120578119879119878120578119898119875119890119897119890119888119905 (12)The efficiency 120578119879119878 is a function of many factors ie it

depends on the powertrain design the transmitted powerand quality of the system For TS based on tension transmis-sion efficiency can be approx 90 The efficiency of the tielink transmission is a function of inter alia transmission ratioi119879119878 interaxial distance belt angle tension force rotationalspeed or torque [18ndash20] In the case of lightweight vehiclesin the TS design it is often not necessary to use variable geartransmissions Speed and torque control is achieved by thecontrol system On the one hand it is an advantage becausethe TS is smaller in weight and less complicated but on theother hand it forces the electric drive to operate in a widerange of torque and rotational speed which affects the motorenergy efficiency

32 Building the Model of the Driving Route The parametersof the path that the vehicle travels on have a significant effecton the resistance values shown in Section 31 In the paper thepath of ride is determined by the exact path of the vehicle ona designated route It is assumed that the best path is knownand it is determined based on the teamrsquos experience (it meansthat the quickest best path along the track is not calculatedby the optimization method) The difference between thepath and the track is as follows A track is a system ofphysically existing roads between points A and B and whenthe path does not exist physically it is the trace that leavesthe selected point of the vehicle (eg center of gravity) onthe route surface With this in mind the journey along theroute can take place on a number of pathsThe route is only alimitation

Figure 5 shows a schematic drawing of one path andits elevation profile The description of the path is formedby its discretization ie the division into finite numbers ofelementary sections of O119905119894 119894 isin 1 2 119899 Each elementarysegment is described by a parameter vector

O119905119894 = [119871 119905119894 119877119905119894 119878119905119894 119864119905119894] where 119871 119905119894[m] is the length of thepath119877119905119894[m] is the radius of curvature 119878119905119894[] is the inclinationof the path and 119864119905119894 represents the type and condition of thepath The length of the path is the sum of the lengths of the119871 119905119894 sections

These basic data are essential for the correct determina-tion of motion resistance on each segment It is assumed thatany change in the inclination or radius of curvature makes itnecessary to define further vector O119905119894

Bearing in mind that vehicles usually move in the openair a suitablemodel should be created describing the externalconditions For this purpose the O119905119894 vector describing thenature of the path should include additional columns suchas velocity and direction of the wind V119908119894 and V119896119894 atmosphericpressure 119901119886119905119898119894 and air temperature t119886119905119898119894 In this situation thevector describing the path and external conditions takes theform O119905119894 = [119871 119905119894 119877119905119894 119878119905119894 119864119905119894 V119908119894 V119896119894 119901119886119905119898119894 t119886119905119898119894] The speedand direction of the wind have a significant effect on the valueof air resistance Determining the wind speed is relativelydifficult and not precise Temporary windsmay have differentdirections and a much higher amplitude than the averagePreliminary investigations have been carried out consideringthe uncertainty of weather conditions During optimizationwhere optimal control strategies were sought the wind speedwas randomly changedThe concept of optimizing the controlstrategy from taking into account the changing weatherconditions was to design a family of strategies It would bepossible to select one optimal strategy or part of it in thereal world because of the existing and changing weatherconditions

33 Control System Design Twomodes of the control systemare taken into consideration in this study They reflect thephysical implementations of the control system used in thebuilt-in electric race vehicles of Prototype class [21] andUrbanConcept class [22] Figures 6 and 7 represent blockdiagrams of the drive system of the vehicle for differentcontrol strategies The control scheme A (Figure 6) is usedin a case when a driver is able to control an acceleration ofthe vehicle by means of a binary signal In this case the goalof the optimization task is to find the control strategy takinginto account two criteria ie the determined travel time aswell as the minimal power consumption of the vehicle Thecontrol strategy is used to specify in which parts of the routethe driver should press or release the acceleration treadleWhen the setpoint signal 119880SET isin 0 1 is assumed then theoptimization task is to search for logic values of the controlsignal as the function corresponding to the position of thevehicle x(t)119880SET = f (x(t)) The supervisory role of the driveris included in the functional scheme as a decision moduleIn this study the behaviour of the driver is not modelled inthe simulation It means that heshe realises the strategy in

Journal of Advanced Transportation 7

Mechanical systemHigh-level control system Motor controller

Transmissionsystem

Currentcontroller

Angularvelocity

measuringsystem

Positionmeasuring

system

MotorDecisionmodule

Driverrsquos decision

Binary control

signal U (x)SET

USET ISET５ＬＲＧ ＲＬ ＲＬ ＲＬ

intint

Figure 6 Drive system diagram control scheme A

High-level control system

Decisionmodule

Velocitycontroller

Mechanical systemMotor controller

Transmissionsystem

Currentcontroller

Angular velocitymeasuring

system

Positionmeasuring system

Motor

Linear velocitymeasuring system

-

Driverrsquos decision

Velocity profileV (x)SET

VSET evＲＧ

Ｒm

USET Ur ISET ＲＬ ＲＬint int

ＲＬ

Figure 7 Drive system diagram control scheme B

the exact way The input control signal U119903 is always differentfrom the signal 119880SET in real conditions It means that thesignal 119880SET is mainly employed by the driver to know whenthe acceleration treadle should be used

In the case of the control scheme B (Figure 7) the generalgoal of the optimization task is the same as in the previouscase However the formal definition of the problem is quitedifferent because in this case the optimal form of the velocitysignal is searched according to the position of the vehicle onthe routeV119878119864119879 = f (x(t))The velocity controller compares thesetpoint signalV119878119864119879 with themeasured velocity of the vehicleand for certain controller setting as well as for control errore119907 it generates the control signal 119880SET As in the previouscase the supervisory role of the driver is included in thedecision module However the main difference is that in theoptimization process the setpoint signal V119878119864119879 can be limitedin the direct way

According to control schemes A and B the input controlsignal U119903 is used by the motor control unit where theemended current regulator normally outputs the correspond-ing signals to the motor terminals The driving torque of themotor shaft is transmitted through the transmission systemto the wheels of the vehicle

4 Evolutionary Optimization of theVelocity Strategy

41 Formulation of the Optimization Problem One of theways to define and to solve the dynamic optimization taskof the velocity strategy of the vehicle is to reduce sucha problem to the static optimization task through the so-called discretization of the independent variable If oneassumes that the independent variable is the position ofthe vehicle (a travelled distance) x(t) then the velocitystrategy st can be represented by a vector of instanta-neous values 119880SET or V119878119864119879 for discrete parts of the routeFigure 8 illustrates the idea of dividing the route into seg-ments

The path is divided into n segments O119894 each of the lengthL119894 where the sum of the lengths of the segments is equal tothe length of the total path For each segment it is necessaryto determine the 119880119878119864119879119894 or 119881119878119864119879119894 setpoint The task is to findthe optimal velocity strategy for control scheme A in thefollowing form

st119900119901119905U = [1198801198781198641198791 1198801198781198641198792 119880119878119864119879119899]119879 119880119878119864119879119894 isin 0 1 (13)

8 Journal of Advanced Transportation

D

L2L1 Ln

O2O1 On

Figure 8 Concept of discretization of the route

whereas in the second case for control scheme B

st119900119901119905V = [1198811198781198641198791 1198811198781198641198792 119881119878119864119879119899]119879 119881119878119864119879119894 isin 119881119898119894119899 119881119898119886119909

(14)

where119881min and119881max can be determined in different ways egbased on the minimummaximum vehicle speed or based onthe simple calculation corresponding to guidelines of the racecompetition

Evolutionary algorithms can be used to solve this prob-lem In the case of the search for strategy st119900119901119905119880 it is preferableto use a classical genetic algorithm In this instance the genesin a chromosome of the individual can be encoded directlyas the binary values of the control signal 119880119878119864119879119894 Thereforethe length of the chromosome N119888ℎ is equal to the number ofsections of the route

In accordance with the control scheme B the velocityprofile is determined as the vector including setpoint valuesof the velocity st119900119901119905119881 The components of the st119900119901119905119881 vectorare floating point values hence it is possible to use anevolutionary strategy proposed in [23] Each of the genes inthe chromosomeof the individual corresponds to the setpointvalue of the velocity during a part of the route

42 Chromosome Codding for Different Velocity StrategiesFor a vehicle that is equipped with a binary control systemof the motor the chromosome can be represented as theoptimal vector of the control signal in the following formst119900119901119905119880 = [1198801198781198641198791 1198801198781198641198792 119880119878119864119879119899]119879 119880119878119864119879119894 isin0 1 for eachsegment O119894 of the route (for control scheme A) or the

optimal vector of the control signal in the second form st119900119901119905119881= [1198811198781198641198791 1198811198781198641198792 119881119878119864119879119899]119879 119881119878119864119879119894 isin [119881min 119881max] for eachsegment O119894 of the route (for control scheme B)

In this optimization task the total distance of the roadD119862is composed of SEM race laps N119905119900 isin1 2 119873 The divisionof the whole route on a finite number of segments O119894 is notrecommended because it can lead to unnecessary increase inthe length of the vector st If the route consists of a minimumof four laps it is possible to limit the search of vector st toonly three types of laps

(i) the initial lap marked by 119874119894119904(ii) the middle laps marked by 119874119894119898(iii) the last lap marked as 119874119894119891Such assumption can be proven for at least three reasons(1) In the practical implementation of velocity strategies

the driver should not implement different control rules foreach lap The master control unit informs the driver aboutthe current velocity strategy but despite all the driver shouldremember this strategy to some extent

(2)The limitation of the velocity strategy only to the threetypes of laps reduces the length of the vector st In this waythe number of elements of the vector st corresponds to thenumber of decision variables of the optimization task

(3) Such division is reasonable by the nature of the laps Inthe initial lap it is necessary to accelerate the vehicle Withinthe middle laps the velocity profile of the vehicle should bethe same During the last lap the previously acquired kineticenergy E119896 is utilized

The task of finding the optimal vector st119900119901119905 can be solvedusing two types of evolutionary algorithms

(i) Classical genetic algorithm for control without avelocity regulator (according to control scheme A presentedin Figure 6)

(ii) Evolutionary strategy for the control system of thevehicle with a velocity regulator (according to control schemeB shown in Figure 7)

Theusage of two algorithms forces the appropriate codingof the velocity strategy which is described in the next twoparagraphs

421 Chromosome Coding For Control Scheme A The phe-notype of each individual determines the control vector st119906that means each gene of the individual of the population isthe value of the control signal 119880119878119864119879119894 for each section of thesegment O119894 of the route Assuming that we are looking for avelocity strategy of only three types of laps the phenotype canbe written as (for short form U equiv 119880SET)

st119880 = [ 1198801119904 1198802119904 119880119899119904 1198801119898 1198802119898 119880119899119904 1198801119891 1198802119891 119880119899119891 ]119879 (15)

where 119880119894119904 119880119894119898 119880119894119891 are the control signals for the initial lapmiddle laps and the last lap

422 Chromosome Coding for Control Scheme B In thiscase the elements in the vector 119881119878119864119879119894 change over a wide

Journal of Advanced Transportation 9

range and can assign real number values In the evolutionarystrategy the phenotype of each individual takes the followingformst119881

= [ 1198811119904 1198812119904 119881119899119904 1198811119898 1198812119898 119881119899119904 1198811119891 1198812119891 119881119899119891 ]119879 (16)

119881119894119904 119881119894119898 119881119894119891 are the setting values of velocity for the initiallap middle laps and the last lap

In the control mode according to scheme B the controlsignal is generated by the velocity controller based on thecontrol error

e119881 = 119881119878119864119879 minus 119881119904119894119898 (17)

where

U119878119864119879 = 1 for e119881 ge 10 otherwise

(18)

The coding for control scheme B in comparison withthe coding for control scheme A has undoubtedly oneadvantage namely the possibility of introducing a velocitylimit during the simulation of the passage of a given sectionof the route A velocity limitation is of great practicalimportance In many situations it is necessary to reducethe velocity of the vehicle during certain parts of theroute for example during cornering Accordingly in caseof control scheme B two velocity vectors are designated asfollows

(i) st11988115 for 119881119878119864119879119894 = [0 15] ms although it is formallylimited to 15ms it can never be achieved because themaximum vehicle speed (based on maximum enginespeed) is approximately 15ms

(ii) st11988110 for 119881119878119864119879119894 = [0 10] ms

43 The Fitness Functions In the case of evolutionary opti-mization the fitness function f 119907119886119897 has to be designed Thissection describes the formulas used to calculate the fitnessfunction of an individual that is needed for solving a task ofevolutionary optimization Each chromosome is a potentialsolution Each control strategy st is used during numericalsimulation The value of the fitness function f 119907119886119897 can becalculated based on the outcomes of the simulation suchas

(i) the total energy consumption r119904119894119898 [kmkWh](ii) the simulation time t119904119894119898(iii) the distance x119904119894119898

and limitations such as

(i) the maximum travel time T119898119886119909(ii) the total distance of the vehicle D119862The value of the function is also used to evaluate the

velocity strategy of the vehicle In the preliminary studies[24] the following fitness function f 119907119886119897 was used

Fitness Function 1

119891V1198861198971 = 11990811198911 + 11990821198912 + 11990831198913 (19)

where

1198911 = [1 + 1199031205821119904119894119898]1205821 (20)

1198912 = [119867 (119863119888 minus 119909119904119894119898) 1003816100381610038161003816119863119888 minus 1199091199041198941198981003816100381610038161003816119863119888 ]1205822 (21)

1198913 = [119867 (119905119904119894119898 minus 119879max)1003816100381610038161003816119879max minus 1199051199041198941198981003816100381610038161003816119879max

]1205822 (22)

where the weights w1 = 050E05 w2 = w3 = 025 andcoefficients 1205821 = minus2 1205822 = 1 were chosen experimentally Thepenalty functions f 2 and f 3 were introduced The Heavisidestep functionH() is used to penalize individuals representingunacceptable solutions [25 26] eg those that exceed themaximum time of the simulation H(t119904119894119898 minus T119898119886119909) or do notreach the specified distance H(D119888 minus x119904119894119898)

Fitness Function 2 In this study the authors have proposedthe fitness function which would lead to the convergenceof the evolutionary algorithm without searching for optimalvalues of weights Such a function is shown and describedbelow

119891V1198861198972 = 1 + 1198914 + 1198915119891111989121198913 (23)

1198911 = 119903119904119894119898 (24)

1198912 = cos(1003816100381610038161003816119863119888 minus 1198891199041198941198981003816100381610038161003816119863119888 ) (25)

1198913 = cos(1003816100381610038161003816119879max minus 1199051199041198941198981003816100381610038161003816119879max) (26)

1198914 = 120594 sdot 119867 (119863119888 minus 119889119904119894119898) (27)

1198915 = 120594 sdot 119867 (119879max minus 119905119904119894119898) (28)

where f 1 is a measure related to the simulated energyconsumption of the vehicle f 2 and f 3 correspond to thelimitations such as the maximum travel time and the totaldistance of the vehicle f 4 and f 5 also correspond to the limi-tations but these play strong penalty role and 120594 is arbitrarilylarge value eg significantly higher than maximal valuesf 2=f 3 =1 In this variant of the fitness function death penalty[26] is applied for unacceptable individuals in the form offactors f 4 and f 5 Individuals who do not reach a specifieddistance or exceed the time limit are eliminated These twocriteria act as a constraint and correspond to the limitationsformulated in the guidelines of the race competition On theother hand the criteria f 2 and f 3 have continuous nature andplay very important role in the fitness functionThey are veryneeded to evaluate continuously the individuals that are veryclose to and very far from the extremum

The argument of cos() function is not related to anangle However the usage of the cos() function is needed to

10 Journal of Advanced Transportation

Table 1 Research object main parameters

Type of the motor PM BLDCTransmission unit Toothed synchronous beltThe minimum turning radius 8 [m]The battery type and capacity Lithium-ion polymer 2100[mAh]Mass of the vehicle 42 [kg]Mass with the driver min 92 [kg]Diameter of wheels 0478 [m]Moment of inertia of the front wheel 119868119896119875 0023 [kgm2]Moment of inertia of the rear wheel 119868119896119879 0023[kgm2]Drag coefficient cx (see Table 2) 022 ndash 023Frontal area A [m2] (see Table 2) 0275 - 0297The total rolling coefficient crr (see Table 4) 00035 ndash 00058

eliminate the possibility of dividing by zero In addition theform of the cos() function is preferred At the initial stage ofoptimization when the simulation time t119904119894119898 and the distancex119904119894119898 differ significantly from the maximum time T119898119886119909 andthe specified distance D119888 a small change will have a greatereffect on the value of the fitness function At the final stageof optimization the function 119891V1198861198972 is more dependent on thesimulated energy consumption of the vehicle related to thefactor f 1 and thanks to the cos() function it is less dependentto the factors f 2 and f 3 The proposed function does notrequire the introduction of weights and therefore it is easierto use this function in other applications eg to find optimalvelocity strategies for different routes

It should be noted that fitness functions 119891val have beenwritten in such a way as to ensure that the optimizationalgorithm will look for a minimum of these functions

5 Case Study

As described in Sections 3 and 4 process of modelling andoptimization was applied and verified using a prototypeelectric vehicle on street race circuit in Rotterdam Themethodology was also carried out on the experimental ridestrack of the Fiat ChryslerAutomobiles Poland factory locatedin Tychy Based on (5)-(12) the simulation model was cre-ated in the MATLABSimulink environment Optimizationwas also carried out in MATLAB using the evolutionaryalgorithms available in the Global Optimization Toolbox Thelibrary of functions for simulating optimizing analyzingand presenting results has been developed

51 Research Object Light electric vehicle was a researchobject The vehicle shown in Figure 9 is a three-wheeledself-supporting structure The vehicle fuselage is made ofcomposites based on epoxy resin and woven of carbon andaramid fibre [21]

The dimensions of the vehicle and basic data are shownin Figure 10 and in Table 1

Identification of parameters for the mathematicalmodel of a research object was carried out by numericalsimulations tests on specially designed test bench [27]

Figure 9 Research object prototype electric vehicle ldquoMuSHELLkardquo(photo by M Wylezoł 2012)

and during conducted experiments in real environment[28]

The vehicle can be driven by two types of drive unit(i) DT1 drive unit based on PM BLDC motors and belt

transmission Drive wheel is equippedwith a one-wayclutch

(ii) DT2 a high-torque PMBLDCmotor mounted insidethe drive wheel The torque generated by the motor isdirectly transmitted to the rear drive wheel

The catalogue data can be used for creating the mathematicalmodel of the DT1 motor but for identifying the exactparameters it was necessary to carry out experimental testsThe manufacturer of the DT2 motor does not provide muchinformation so it was necessary to test the drive unit aswell DT1 drivetrain efficiencywas estimated using aBG75x50motor with toothed synchronous belt transmission ( z1= 28teeth z2 = 200 teeth i119879119878 = 714) The map of the efficiencywas shown on Figure 11(a) The same test was carried out forDT2 drive unit with a motor directly mounted on the drivewheel (Figure 11(b)) The obtained efficiency maps were usedto build the simulationmodel of the tested drivetrain systems

52 Determination of Air Drag Coefficient The air dragcoefficient c119909 was estimated as a result of CFD analysis usingANSYS software [24] and it was also verified by the researchin wind tunnel at the Institute of Aviation inWarsaw Frontalarea of vehicle A was determined from a three-dimensionalmodel in CAD environment Catia V5 The values of dragcoefficient c119909 and frontal area A are shown in Table 2

Journal of Advanced Transportation 11

623

972

1600

2605

Figure 10 Dimensions of the vehicle

(a) DT1 (b) DT2

Figure 11 Maps of the efficiency of tested drivetrain systems

Table 2 The air drag coefficient and frontal area

cx numericalsimulation

cx experimentalresearch Frontal area A [m2]

023 022 0275 0297

53 Determination of Rolling Resistance According to for-mula (7) the rolling resistance depends on the weight of thevehicle (Table 1) the tires rolling resistance coefficient andthe resistance of the bearings Depending on the drive unit(DT1 DT2) used in the vehicle additional resistance has to beadded In theDT1 system there is a one-way clutchwhich alsogenerates some resistance torque The DT2 system cannot bemechanically disconnected and therefore has a higher rollingresistance As a result of the coast down test the total rollingresistance of the vehicle has been identified for the four typesof tiresThe test was performed only with theDT1 system iethe systemwith the clutch Table 3 shows the basic parametersof the tires used in the experiments

The prototype vehicle can be equipped with speciallymanufactured Michelin tires with a low rolling resistantcoefficient of c119903119903 = 00014

In addition to the specialMichelin tires three other typesof tires were tested The identification of rolling resistance

coefficients was also estimated using a coast down test Themeasurements were made as follows

(i) The driver accelerated the vehicle to a fixed speed(ii) At themoment of crossing themarked gate the driver

pressed the marker button to save the flag in theacquired data

(iii) The run continued until free braking after which thedriver switched off the measuring system

(iv) The measurements were made at both directions ofthe road to minimize influence of the wind

(v) Before the attempts wind velocity temperature andatmospheric pressure were measured

(vi) The distance of the road was measured using ameasurement system mounted on the vehicle and itwas also verified using distance measuring wheel

On the basis of the experimental data the total rolling resis-tance coefficient of the vehicle was determined Table 4 showsthe coefficients of rolling resistance of the vehicle dependingon the tire used during the test Total resistance includesthe tire rolling coefficient the bearings resistance and theresistance of the clutch Verification of the data derived fromthe simulation and the experiment was conducted using

12 Journal of Advanced Transportation

Table 3 The types of tires used in the prototype vehicle

Tiresmarker Name of the tire Tirersquos

symbol Shape Type of tread Workingpressure

W1

Michelin ShellEco-marathon 4575R16 Rectangular Slick max500 [kPa]

W2

SchwalbeUl-Termo 23-406 Round Slick 600-1100 [kPa]

W3

Continental SportContact 28-406 Round Slick 600 [kPa]

W4

SchwalbeMarathon 40-406 Round Symmetrical 400-700 [kPa]

Table 4 The total rolling coefficient depending on the tires

Tiresmarker Name of the tire The total rolling coefficient crr mMAPE []

W1 Michelin ShellEco-marathon 00035 784W2 Schwalbe Ultermo 00043 1103W3 Continental SportContact 00058 1252W4 Schwalbe Marathon 00053 445

0

1

2

3

4

5

6

7

8

V [m

s]

100 200 300 400 500 6000x [m]

W1rW1simW2rW2sim

W3rW3simW4rW4sim

Figure 12 Velocity of the vehicle during coast down test

mMAPE (modifiable Mean Absolute Percentage Error) Forvelocity simulationmMAPE can be determined by

119898119872119860119875119864 = 1001119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119881119903 minus 119881119904119894119898119881119898119886119909 minus 119881119898119894119899

10038161003816100381610038161003816100381610038161003816 (29)

Figure 12 shows the experimental data obtained in a coastdown test compared with the results obtained during thecomputer simulation

54 Model of the Race Circuit In accordance with themethodology presented in Section 32 three routes have beendescribed

(i) Route 1 a street race circuit at the Shell Eco-marathoncompetition in Rotterdam

Figure 13 Plan view of the path of the drive on route 1 in Rotterdam

(ii) Routes 2 and 3 on the experimental rides track of theFiat Chrysler Automobiles Poland factory located inTychy in the south of Poland

The Shell Eco-marathon competition is held on a streetcircuit in Rotterdam One lap is 1630 meters long Vehicleshave to cover ten laps in no longer than 39 minutes so suchrequirements impose an averageminimum speed of 25 kmh

The trajectory of the vehicle path was developed usingsatellite images The vehicle trajectory was determined usingthe maximum curvature possible that could be obtained onthe existing roads

Movement of the vehicle in a curved motion causesthe centrifugal force Centrifugal force creates additionalresistance This resistance is inversely proportional to theradius of the path (8) so it is justified to select the largestradius In addition if the centrifugal force exceeds thelimit value it could provide to the side slip of the vehicleAccording to drawings in AutoCAD Civil 3D the lengths ofstraight sections and the lengths and the radius of arcs wereobtained Figure 13 shows a plan view of the path of the drive

Driving the prototype vehicle on public roads is prohib-ited and can be dangerous Vehicle testing was also carried

Journal of Advanced Transportation 13

Table 5 Travel times and total lengths of the routes

Route Length of the lap D [m] The numberof laps The total length of the route Dc [m] Travel time Tmax [s]

Route 1Rotterdam 1630 10 16 300 2340

Route 2Tychy 640 5 3200 460

Route 3Tychy 1000 5 5000 720

Figure 14 Plan view of the path of the drive on route 3 in Tychy

out on the experimental rides track of the Fiat ChryslerAutomobiles Poland factory

For the track in Tychy geodetic measurements weretaken using theDGPS (Differential Global Positioning System)technology The measuring points were collected along theaxis of the road with the distance between points amountingto 10 meters If on the measured route direction or elevationwere changed the frequency of measurement was increasedGeodetic coordinates were also imported intoAutoCADCivil3D and were used to prepare data concerning the route thatwas imported into the simulation environment MATLAB-Simulink Figures 14 and 15 show the path and elevationprofile respectively

Selected routes 2 and 3 have significant differences com-pared to route 1 especially in the height profile This set ofroutes was selected to verify the effect of the route profile onthe achieved results and to verify the proposed optimizationmethods for various road conditions The routes in Tychyare located in an open area there are no large buildingswhich guarantees stability of wind conditions The technicalcondition of the surface on routes 2 and 3 is much worsethan on route 1 which has a significant influence on therolling resistance Rolling resistance was also identified andintroduced into the simulation model For route 2 the c119903119903coefficient was 00056 and for route 3 was 00068

55 Verification of the Simulation Model In order to verifythe compatibility of the identified simulation model a seriesof numerical simulations and experimental tests were per-formed The first experiment consisted of running 300 [m]with a control strategy of 50 [m] with the workingmotor andafter that the vehicle was moving freely for the next 50 [m]The motor is turned on three times Figures 16(a) and 16(b)show the velocity of the vehicle and the power of the motorin function of the distance determined during the experiment

(red curves) and during the numerical simulations (greencurves)

Verification of the data derived from the simulation andthe experimentwas conducted usingmMAPE (29) Formotorpower simulationmMAPE can be determined by

119898119872119860119875119864119875 = 1001119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119875119903 minus 119875119904119894119898119875119898119886119909 minus 119875119898119894119899

10038161003816100381610038161003816100381610038161003816 (30)

where P119903 is the motor power measured during experimentand P119904119894119898 is the motor power conducted in simulation

As a result of the model validation tests estimationerror of the velocity was on level between 235 and 534However the motor power error level was greater It wasbetween 802 and 998

56 Determination of the Optimal Control Strategy Thelength of route 1 and the number of laps are determined bythe organizers of the Shell Eco-marathon competition Thelength of routes 2 and 3 is derived from the existing road planwhere it was possible to carry out trials in real conditionsThenumber of laps for routes 2 and 3 was assumed arbitrarily

The travel time for route 1 is based on the rules of therace which determine the minimum average speed of thevehicle Based on the average speed and the length of routes 2and 3 the travel times for these routes were determined Themaximum travel times and the total length of the route aswell as the number and length of one lap D are summarizedin Table 5

Evolutionary algorithms which are available in theMAT-LAB Global Optimization Toolbox were used From theMATLAB workspace the algorithm ran a simulation modelin a Simulink environment During optimization while usingevolutionary algorithms the maximum number of fitnessfunction evaluations 119873119891V119886119897

is the product of the populationsize 119873119901119900119901 and number of generations 119873119892119890119899

It was assumed that the total number of fitness functionevaluations was equal to 104 therefore should this value beexceeded the calculation would be cancelled Therefore thetotal number of generations 119873119892119890119899 is dependent on the valueof population size 119873119901119900119901

As part of this work phase the vectors st119880 st119881 15 andst119881 10 of the optimum control strategy for an electric vehiclefor routes 1 2 and 3 were determined During evolutionaryoptimization the heuristic method of crossing was usedand the probability of crossing was established on the basisof previous studies at the level of 08 [24 29] At the

14 Journal of Advanced Transportation

0+000

106410

minus164 minus492minus166 minus012 minus018 minus082 minus035 059 031

811

0+100 0+200 0+300 0+400 0+500 0+600 0+700 0+800 0+900 1+000

Figure 15 Profile of the path on route 3 in Tychy

50 100 150 200 250 3000X [m]

0

2

4

6

8

10

V [m

s]

(a) DT1

0

100

200

300

400

500

P [W

]50 100 150 200 250 3000

X [m]

(b) DT1

Figure 16 The velocity and the power determined with used DT1 drive unit

stage of reproduction the elitist succession method wasapplied where the best adapted two individuals in the currentpopulation passed to the next population An adaptivemethod of mutation was used The remaining parameters ofthe algorithm remain the default for the MATLAB GlobalOptimization Toolbox

The first case was the search st119880 vector for route 1Figures 17(a)ndash17(c) show the vehicle velocity V119904119894119898 obtainedby computer simulation The graph of the st119880 control signalis graphically displayed Figure 17 shows the results wherethe optimal control strategy st119880119900119901119905 was used and populationwas 119873119901119900119901=100 and 119873119892119890119899=100 The total energy consumptionwas estimated as r119904119894119898=527633 [km kWh] Figure 17(a) showsthe vehicle speed and control signal st119880 during the first lapwhile Figure 17(b) shows center laps and Figure 17(c) showsthe last lap Figure 17(d) shows the curves of the mean valuesof the fitness functions f 119907119886119897 depending on the number ofcalculations of these functions during the optimization ofthe control strategy There are eight curves in the graph(Figure 17(d)) for each of the 119873119901119900119901 parameters used in thealgorithm

When analyzing the vehicle velocity chart on the last lapof route 1 (Figure 17(c)) it can be seen that according tothe determined control strategy the propulsion system of thevehicle should no longer be used The vehicle should use thestored kinetic energy

The analysis of vehicle velocity V119904119894119898 during the last lapindicates that at the moment of reaching the given distancethe speed was still about 2 [ms] This demonstrates thatthe simulated vehicle has kinetic energy that would haveto be dispersed by the braking system or recovered by the

electric motor Having such a speed does not mean that thereis still possibility for improvement Lower speed at the endof the route has to cause higher speed of the earlier partsof the route This speed is the optimum speed due to thechosen criterion From the analysis of the shape of the fitnessfunction (Figure 17(d)) it can be seen that for route 1 itis preferable to use a smaller population of 119873119901119900119901=25 andincrease the number of 119873119892119890119899=400 The curve shape for thiscase is steep and it falls to the minimum value of the fitnessfunction which may indicate that the algorithm has reacheda convergence

Results of the optimization where B type of coding wasused were analyzed The results obtained as the mean of ther119904119894119898 result together with the standard deviation from all thetests were summarized in Table 6

By analyzing the results in Table 6 it can be seen thatfor route 1 better results were obtained (reduced simulatedtotal energy consumption) using A coding compared to Bespecially for st119881 15 whose results are characterized by thehighest standard deviation For routes 2 and 3 the same as forroute 1 the procedure was followed Optimization strategieshave been optimized for all variants of control vector st119880st119881 15 st10

The results using the control strategy st119881 10 are shownin Figures 18(a)ndash18(c) (119873119901119900119901=100 where r119904119894119898=351795 [km kWh]) Figure 18(d) illustrates the graph of the value of thefitness function

The results obtained for route 2 are presented in Table 7For route 2 compared to route 1 the best results were

achieved using the stV10 vector When using vectors st119880 andstV15 the results were slightly worse Having analyzed the size

Journal of Advanced Transportation 15

0

2

4

6

8

10V

[ms

]

VsimstU

500 1000 15000X [m]

(a) Lap 1

0

2

4

6

8

10

V [m

s]

2500 30002000X [m]

VsimstU

(b) Laps 2-9

0

2

4

6

8

10

V [m

s]

155 1615X [m]

Vsimstu

times104

(c) Lap 10

times10minus3

Npop=25Npop=50Npop=75Npop=100

Npop=125Npop=150Npop=175Npop=200

15

2

25

3

35

4f va

l

2000 4000 6000 8000 100000Nfval

(d) Mean values of the fitness functions

Figure 17 Vehicle speed and control signal st119880 for route 1

Table 6 The results for route 1

The type of coding A The type of coding Bst119880 st11988115 st11988110119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 52465 1459 42845 1741 51569 5477550 52579 10053 44431 22486 51492 3409475 52497 39913 43842 28173 51256 80682100 52589 18128 42232 1797 51166 49379125 52625 13862 42733 39616 51341 70765150 5243 2979 4435 47701 51486 27086175 52513 2511 41428 27299 51838 19358200 52579 19666 42337 25776 51204 78357

16 Journal of Advanced Transportation

100 200 300 400 500 6000X [m]

0

2

4

6

8

10V

[ms

]

VsimstV10

USET

(a) Lap 1

0

2

4

6

8

10

V [m

s]

800 900 1000 1100 1200700X [m]

VsimstV10

USET

(b) Laps 2-4

0

2

4

6

8

10

V [m

s]

2700 2800 2900 3000 3100 32002600X [m]

VsimstV10

USET

(c) Lap 5

times10minus3

Npop=25Npop=50Npop=75Npop=100

Npop=125Npop=150Npop=175Npop=200

275

28

285

29

295

3

305

f val

2000 4000 6000 8000 100000Nfval

(d) Mean values of the fitness functions

Figure 18 Vehicle speed and control signal st11988110 for route 2

of the population used in the optimization process it shouldbe noted that for route 2 it is preferable to use higher value of119873119901119900119901 For all the analyzed cases the best average results for119873119901119900119901=200 were obtained Table 8 summarizes the results forroute 3

For route 3 the average results were reported for a largerpopulation of119873119901119900119901 with B coding In the case of using vectorwith A type coding no characteristic change was notedAs expected comparing the standard deviation betweenalgorithms using B coding the standard deviation is less forthe less variance range

Evolutionary algorithms are not complete search algo-rithms therefore it is not possible to determine whetherthe solution found is best for the chosen criterion and theconstraints assumed

57 Applying the Optimal Control Strategy in Real ConditionsElectric vehicle energy consumption optimization was finallyverified in real conditions at the European edition of the ShellEco-marathon held on 16-18 May 2014 in Rotterdam

Optimal control strategy st119880was displayed by a prototypevisualization system Visualization unit is installed in the

Journal of Advanced Transportation 17

Table 7 The results for route 2

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 34138 66734 34294 23839 34873 5353250 34573 46359 35003 462 3506 3886275 34512 55134 34961 33476 35419 067858100 34836 45332 35253 26117 3544 19295125 34632 52704 35017 49039 35483 14756150 34552 63714 35326 14885 35343 071015175 35063 18728 35274 47141 35564 038022200 35073 14496 3540 13389 35569 14942

Table 8 The results for route 3

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 28071 10173 28643 7323 30994 277650 29346 6142 29581 7894 30874 439975 29711 5002 29217 7367 31141 1856100 29826 3231 29515 7022 30957 4049125 29781 2980 29866 12977 31168 3445150 29453 3346 30217 9623 31288 1249175 29234 2317 30621 6816 31481 1261200 29686 2337 30531 11737 31089 4880

Table 9 Comparison of simulation results with experimental tests

Number of attempts 119903119878119864ndash119898 119903119903 119903119904119894119898 119903119900119901119905 119890119898 119890119894 119890119904119905Attempt 1 3654 3608 - - 125 - -Attempt 2 4813 5082 5148 5265 558 129 36Attempt 3 4873 5127 5198 5265 521 139 269Attempt 4 Failed attempt damaged tires during 1st lap

steering wheel of the vehicle The visualization system showsthe basic data such as instantaneous speed average speedtravel time and distance In addition the visualization systemprovides information on which part of the track the drivershould press the acceleration button to execute the optimalcontrol strategy Measurement of the position on the track iscarried out by the odometrical measuring system Due to thepossibility of accumulating errors in the measurement of theroad the driver will reset the measuring system every timeheshe exceeds the lap line

Table 9 presents the results of all the measurementsconducted during the Shell Eco-marathonThe columns in theTable 9 contain

(i) r119878119864119898 [kmkWh] the result recorded during the raceby the measuring device provided by the organizerthe results are available on the Shell Eco-marathonofficial website

(ii) r119903 [kWkWh] the result based on the indications of aprototypemeasuring system permanently installed inthe vehicle

(iii) r119904119894119898 the result estimated by computer simulationusing recorded real control signal U119903

(iv) r119900119901119905 the result obtained by computer simulation usingthe optimal control strategy U119900119901119905

Table 9 also includes the following

(i) Measurement error

119890119898 = 1003816100381610038161003816119903119878119864119898 minus 1199031199031003816100381610038161003816119903119878119864119898 100 (31)

(ii) Identification error

119890119894 =1003816100381610038161003816119903119903 minus 1199031199041198941198981003816100381610038161003816119903119903 100 (32)

(iii) Strategy implementation error

119890119904119905 =10038161003816100381610038161003816119903119903 minus 11990311990011990111990510038161003816100381610038161003816119903119903 100 (33)

18 Journal of Advanced Transportation

There were four measurement trials available Duringrun 1 a much weaker result was obtained than estimated bysimulation The driver performed run 1 without a definedcontrol strategy As part of the experiment the driver andthe support team were asked to select the optimal tires forthe vehicle and to implement the proposed control strategyDuring run 1 only the travel time of individual laps waschecked According to the choice of the team in run 1 tiresW2 were selected (Table 4) During this test the worst resultwas obtained about 24 and 25 worse than in the othertrials In subsequent runs 2 and 3 the vehicle was equippedwith the best W1 tires (Table 4) The driver has implementedan algorithm-based optimal control strategy Strategy infor-mation was provided by the visualization system During run3 the best result was recorded This result was taken intoaccount in the classification of competitions where the teamplaced in 12 positions out of 28 classified teams Trials 4 dueto damage to the tires were not successful

Measurement error was from 125 to 558 dependingon the sample The measurement system installed perma-nently in the vehicle is a prototype system This systemhas been calibrated using available laboratory equipmentMeasurement errors indicate that other measuring devices ofthe higher accuracy class should be used

Based on the measurement data obtained during testdrives the model was tuned thus reducing the identificationerror The competition took place in stable weather thedivergence of results was small and was about 129 forsample 2 and 139 for sample 3

The difference between the results determined duringnumerical simulation and that obtained in the real run was36 for sample 2 and 269 for sample 3 The difference atthis level was considered to be small Searching for optimalcontrol strategy has not taken into account possible rdquoerrorsrdquowhich could be made by the driver and which result fromthe current situation on the route for example selecting thepath and using the route by other participants in the raceIncluding driver behaviour in the simulation model shouldbe the subject of further work

Figure 19 shows the vehicle velocity together with thecontrol signals recorded during run 2 The black curvesrepresent the real vehicle velocity V119903 and the control signalGreen curves are the optimum control strategy st119880 andthe optimal velocity V119900119901119905 determined by the simulationThe graph shows the entire distance travelled (10 laps) Theanalysis of the graph shows that the driver did not performthe exact planned strategy Errors in the implementationof the strategy are related to the disruptions During thecompetition the driver is not alone on the track in certainsituations the driver cannot overtake other participants andcannot take the optimal path In addition weather conditionsuch as wind has influence on the motion resistance In suchcases the driver has to modify the optimal control strategy

In Figure 20 the velocity recorded during the race V119903(black) and the velocity obtained by the computer simulationV119904119894119898 (red) were shown V119904119894119898 was determined by computersimulation by using real control signal The purpose of thissimulation was to investigate the correctness of identification

VrVopt

Ur Uopt

2000 4000 6000 8000 10000 12000 14000 16000 180000X [m]

05

10152025303540

V [k

mh

]

Figure 19 Comparison of speed and control signal during attempt2

2000 4000 6000 8000 10000 12000 14000 16000 180000x [m]

05

10152025303540

V [k

mh

]

Ur

VrVsim

Figure 20 Comparison of speed registered in real conditions withthe speed determined by computer simulation

of the simulation model and to identify the identificationerror

Compared to the Shell Eco-marathon competitions heldin 2012 and 2013 our performance has improved The resultsin these years were equal to 425 [km kWh] and 454[km kWh] respectively In 2012 and 2013 the controlstrategy was chosen on the basis of the simulation modelbut the model was not adequately identified and the controlstrategy had to be modified In previous editions of therace the implementation of optimal control strategy was notsupported by the visualization system which would informthe driver of the need to take specific actions (pressing orreleasing the accelerator button)

6 Conclusion

The presented method was developed and tested for aprototype electric racing car that has been designed for theShell Eco-marathon race As it was shown the results of thenumerical simulations were very similar to the outcomes ofthe real races in the context of the final result of energyconsumption and the profile of velocity of the car during therace The method has been developed and applied since 2012

Journal of Advanced Transportation 19

and led in 2014 to achieving the optimal result for this type ofthe vehicle

The optimization method was evaluated The resultsachieved during the race attempts where the optimal con-trol strategy was applied (4813 and 4873 kmkWh) werecompared to the result where the strategy was proposed bythe experts (3654 kmkWh) who already had contact withthe results of similar optimization models Optimal attemptswere better by over 30 despite errors in the implementationof the strategy by the driver In the case of experts who did nothave such experiences the differences were even greater

Further improvement of the control strategy is impossiblefor this type of a vehicle and the best way to reduce energyconsumption is by improving the mechanical design It wasthe reason to develop new racing cars for UrbanConceptBattery Electric and Hydrogen competitions The developedresearch methodology for vehicle optimization and controlstrategies has been developed and implemented in the ShellEco-marathon in 2015 which has improved the score to 504km kWhHowever the research has shown that the potentialfor improved performance of the MuSHELLka vehicle hasbeen exhausted No major structural changes in the vehiclecan significantly improve the result so in the followingyears the race was abandoned and the focus was on thedevelopment of the HydroGENIUS the electric vehicle ofUrbanConcept class with fuel cell stack as power sourcewhich eventually scored vice Championship in SEM 2016 Inthe further work it is planned to improve the optimizationresults by using the presented methodology in the case ofthe models of newly constructed vehicles The developmentof the optimization method should take into considerationthe uncertainty resulting from the given velocity strategyconsidering the real conditions of the race It is also possibleto use this method for controlling vehicles in traffic To dothis it is necessary to completely change the way of the routemodelling and the driving conditions modelling as well as todevelop a new optimization method for obtaining results inreal time

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] W Skarka ldquoReducing the Energy Consumption of ElectricVehiclesrdquo in Proceedings of the 22nd ISPE-Inc InternationalConference on Concurrent Engineering Location R Curran NWognumM Borsato et al Eds Advances in TransdisciplinaryEngineering pp 500ndash509 IOS Press Delft Netherlands 2015

[2] R Andrzejewski and J Awrejcewicz Nonlinear Dynamics of aWheeled Vehicle vol 10 Springer-Verlag New York NY USA2005

[3] D W Gao C Mi and A Emadi ldquoModeling and simulation ofelectric and hybrid vehiclesrdquo Proceedings of the IEEE vol 95 no4 pp 729ndash745 2007

[4] ldquoAdvisor documentationrdquo httpadv-vehiclesimsourceforgenet

[5] TMarkel A Brooker THendricks et al ldquoADVISORA systemsanalysis tool for advanced vehicle modelingrdquo Journal of PowerSources vol 110 no 1 pp 255ndash266 2002

[6] K B Wipke M R Cuddy and S D Burch ldquoADVISOR21 a user-friendly advanced powertrain simulation using acombined backwardforward approachrdquo IEEE Transactions onVehicular Technology vol 48 no 6 pp 1751ndash1761 1999

[7] ldquoWebsiterdquo 2014 httpwwwtransportationanlgovmodeling[8] ldquoWebsiterdquo 2014 httpwwwautonomienet[9] K Krykowski J Hetmanczyk Z Gałuszkiewicz and R Mik-

siewicz ldquoComputer analysis of high-speed PM BLDC motorpropertiesrdquo COMPEL - The International Journal for Computa-tion and Mathematics in Electrical and Electronic Engineeringvol 30 no 3 pp 941ndash956 2011

[10] M Vaillant M Eckert and F Gauterin ldquoEnergy managementstrategy to be used in design space exploration for electricpowertrain optimizationrdquo inProceedings of the 2014 9th Interna-tional Conference on Ecological Vehicles and Renewable EnergiesEVER 2014 mco March 2014

[11] A T Nguyen S Reiter and P Rigo ldquoA review on simulation-based optimization methods applied to building performanceanalysisrdquo Applied Energy vol 113 pp 1043ndash1058 2014

[12] W Silka and W Siłka Energy Intensity in the Car Traffic InPolish WNT Warszawa 1997

[13] T J Barlow S Latham I S Mrcrae and P Boulter A referencebook of driving cycles for use in the measurement of roadvehicle emissions TRL 2009 httpswwwgovukgovernmentuploadssystemdata

[14] R N Jazar Vehicle Dynamics Theory and Application SpringerUS Boston MA 2008

[15] MMeywerk ldquoVehicle Dynamicsrdquo inWest Sussex JohnWiley ampSons Lecture Notes to theMOOCVehicle Dynamics of iversity1st edition 2015

[16] MMitschke andHWallentowitzDynamik der KraftfahrzeugeSpringer Berlin Germany 1972

[17] T Stefanski and Ł Zawarczynski ldquoParametric identification ofPM motor mathematical modelsrdquo Przegląd Elektrotechnicznyvol 88 no 4 B pp 224ndash229 2012

[18] A Cameron ldquoMeasuring drive-train efficiencyrdquoHuman Powervol 46

[19] B Rohloff and P Greb ldquoEfficiency measurements of bicycletransmissions a neverending storyrdquo Human Power vol 55 p11 2004

[20] J B Spicer C J K Richardson M J Ehrlich J R BernsteinM Fukuda and M Terada ldquoEffects of frictional loss on bicyclechain drive efficiencyrdquo Journal of Mechanical Design vol 123no 4 pp 598ndash605 2001

[21] K Sternal A Cholewa W Skarka and M Targosz ldquoElec-tric vehicle for the studentsrsquo shell eco-marathon competitionDesign of the car and telemetry systemrdquo Communications inComputer and Information Science vol 329 pp 26ndash33 2012

[22] K Cichonski and W Skarka ldquoInnovative control system forhigh efficiency electric urban vehiclerdquo Communications inComputer and Information Science vol 531 pp 121ndash130 2015

[23] M J Er and R J Oentaryo ldquoComputational IntelligenceMethods andTechniques (Rutkowski L 2008) [BookReview]rdquoIEEE Computational Intelligence Magazine vol 6 no 4 pp 76ndash78 2011

[24] M Targosz M Szumowski W Skarka and P PrzystałkaldquoVelocity Planning of an Electric Vehicle Using an Evolutionary

6 Journal of Advanced Transportation

D [m]

S []Ｃ

RＣ

SＣ

S1

L1 Li

Figure 5 Driving path and its inclination profile

the phenomenon of loss can be found in professional litera-ture [10]

Themotor torque is transmitted to the drive wheel via theTS transmission The mechanical power on the drive wheeldepends on the efficiency of the TS

119875119898119890119888ℎ119901 = 120578119879119878119875119898119890119888ℎ119898 = 120578119879119878120578119898119875119890119897119890119888119905 (12)The efficiency 120578119879119878 is a function of many factors ie it

depends on the powertrain design the transmitted powerand quality of the system For TS based on tension transmis-sion efficiency can be approx 90 The efficiency of the tielink transmission is a function of inter alia transmission ratioi119879119878 interaxial distance belt angle tension force rotationalspeed or torque [18ndash20] In the case of lightweight vehiclesin the TS design it is often not necessary to use variable geartransmissions Speed and torque control is achieved by thecontrol system On the one hand it is an advantage becausethe TS is smaller in weight and less complicated but on theother hand it forces the electric drive to operate in a widerange of torque and rotational speed which affects the motorenergy efficiency

32 Building the Model of the Driving Route The parametersof the path that the vehicle travels on have a significant effecton the resistance values shown in Section 31 In the paper thepath of ride is determined by the exact path of the vehicle ona designated route It is assumed that the best path is knownand it is determined based on the teamrsquos experience (it meansthat the quickest best path along the track is not calculatedby the optimization method) The difference between thepath and the track is as follows A track is a system ofphysically existing roads between points A and B and whenthe path does not exist physically it is the trace that leavesthe selected point of the vehicle (eg center of gravity) onthe route surface With this in mind the journey along theroute can take place on a number of pathsThe route is only alimitation

Figure 5 shows a schematic drawing of one path andits elevation profile The description of the path is formedby its discretization ie the division into finite numbers ofelementary sections of O119905119894 119894 isin 1 2 119899 Each elementarysegment is described by a parameter vector

O119905119894 = [119871 119905119894 119877119905119894 119878119905119894 119864119905119894] where 119871 119905119894[m] is the length of thepath119877119905119894[m] is the radius of curvature 119878119905119894[] is the inclinationof the path and 119864119905119894 represents the type and condition of thepath The length of the path is the sum of the lengths of the119871 119905119894 sections

These basic data are essential for the correct determina-tion of motion resistance on each segment It is assumed thatany change in the inclination or radius of curvature makes itnecessary to define further vector O119905119894

Bearing in mind that vehicles usually move in the openair a suitablemodel should be created describing the externalconditions For this purpose the O119905119894 vector describing thenature of the path should include additional columns suchas velocity and direction of the wind V119908119894 and V119896119894 atmosphericpressure 119901119886119905119898119894 and air temperature t119886119905119898119894 In this situation thevector describing the path and external conditions takes theform O119905119894 = [119871 119905119894 119877119905119894 119878119905119894 119864119905119894 V119908119894 V119896119894 119901119886119905119898119894 t119886119905119898119894] The speedand direction of the wind have a significant effect on the valueof air resistance Determining the wind speed is relativelydifficult and not precise Temporary windsmay have differentdirections and a much higher amplitude than the averagePreliminary investigations have been carried out consideringthe uncertainty of weather conditions During optimizationwhere optimal control strategies were sought the wind speedwas randomly changedThe concept of optimizing the controlstrategy from taking into account the changing weatherconditions was to design a family of strategies It would bepossible to select one optimal strategy or part of it in thereal world because of the existing and changing weatherconditions

33 Control System Design Twomodes of the control systemare taken into consideration in this study They reflect thephysical implementations of the control system used in thebuilt-in electric race vehicles of Prototype class [21] andUrbanConcept class [22] Figures 6 and 7 represent blockdiagrams of the drive system of the vehicle for differentcontrol strategies The control scheme A (Figure 6) is usedin a case when a driver is able to control an acceleration ofthe vehicle by means of a binary signal In this case the goalof the optimization task is to find the control strategy takinginto account two criteria ie the determined travel time aswell as the minimal power consumption of the vehicle Thecontrol strategy is used to specify in which parts of the routethe driver should press or release the acceleration treadleWhen the setpoint signal 119880SET isin 0 1 is assumed then theoptimization task is to search for logic values of the controlsignal as the function corresponding to the position of thevehicle x(t)119880SET = f (x(t)) The supervisory role of the driveris included in the functional scheme as a decision moduleIn this study the behaviour of the driver is not modelled inthe simulation It means that heshe realises the strategy in

Journal of Advanced Transportation 7

Mechanical systemHigh-level control system Motor controller

Transmissionsystem

Currentcontroller

Angularvelocity

measuringsystem

Positionmeasuring

system

MotorDecisionmodule

Driverrsquos decision

Binary control

signal U (x)SET

USET ISET５ＬＲＧ ＲＬ ＲＬ ＲＬ

intint

Figure 6 Drive system diagram control scheme A

High-level control system

Decisionmodule

Velocitycontroller

Mechanical systemMotor controller

Transmissionsystem

Currentcontroller

Angular velocitymeasuring

system

Positionmeasuring system

Motor

Linear velocitymeasuring system

-

Driverrsquos decision

Velocity profileV (x)SET

VSET evＲＧ

Ｒm

USET Ur ISET ＲＬ ＲＬint int

ＲＬ

Figure 7 Drive system diagram control scheme B

the exact way The input control signal U119903 is always differentfrom the signal 119880SET in real conditions It means that thesignal 119880SET is mainly employed by the driver to know whenthe acceleration treadle should be used

In the case of the control scheme B (Figure 7) the generalgoal of the optimization task is the same as in the previouscase However the formal definition of the problem is quitedifferent because in this case the optimal form of the velocitysignal is searched according to the position of the vehicle onthe routeV119878119864119879 = f (x(t))The velocity controller compares thesetpoint signalV119878119864119879 with themeasured velocity of the vehicleand for certain controller setting as well as for control errore119907 it generates the control signal 119880SET As in the previouscase the supervisory role of the driver is included in thedecision module However the main difference is that in theoptimization process the setpoint signal V119878119864119879 can be limitedin the direct way

According to control schemes A and B the input controlsignal U119903 is used by the motor control unit where theemended current regulator normally outputs the correspond-ing signals to the motor terminals The driving torque of themotor shaft is transmitted through the transmission systemto the wheels of the vehicle

4 Evolutionary Optimization of theVelocity Strategy

41 Formulation of the Optimization Problem One of theways to define and to solve the dynamic optimization taskof the velocity strategy of the vehicle is to reduce sucha problem to the static optimization task through the so-called discretization of the independent variable If oneassumes that the independent variable is the position ofthe vehicle (a travelled distance) x(t) then the velocitystrategy st can be represented by a vector of instanta-neous values 119880SET or V119878119864119879 for discrete parts of the routeFigure 8 illustrates the idea of dividing the route into seg-ments

The path is divided into n segments O119894 each of the lengthL119894 where the sum of the lengths of the segments is equal tothe length of the total path For each segment it is necessaryto determine the 119880119878119864119879119894 or 119881119878119864119879119894 setpoint The task is to findthe optimal velocity strategy for control scheme A in thefollowing form

st119900119901119905U = [1198801198781198641198791 1198801198781198641198792 119880119878119864119879119899]119879 119880119878119864119879119894 isin 0 1 (13)

8 Journal of Advanced Transportation

D

L2L1 Ln

O2O1 On

Figure 8 Concept of discretization of the route

whereas in the second case for control scheme B

st119900119901119905V = [1198811198781198641198791 1198811198781198641198792 119881119878119864119879119899]119879 119881119878119864119879119894 isin 119881119898119894119899 119881119898119886119909

(14)

where119881min and119881max can be determined in different ways egbased on the minimummaximum vehicle speed or based onthe simple calculation corresponding to guidelines of the racecompetition

Evolutionary algorithms can be used to solve this prob-lem In the case of the search for strategy st119900119901119905119880 it is preferableto use a classical genetic algorithm In this instance the genesin a chromosome of the individual can be encoded directlyas the binary values of the control signal 119880119878119864119879119894 Thereforethe length of the chromosome N119888ℎ is equal to the number ofsections of the route

In accordance with the control scheme B the velocityprofile is determined as the vector including setpoint valuesof the velocity st119900119901119905119881 The components of the st119900119901119905119881 vectorare floating point values hence it is possible to use anevolutionary strategy proposed in [23] Each of the genes inthe chromosomeof the individual corresponds to the setpointvalue of the velocity during a part of the route

42 Chromosome Codding for Different Velocity StrategiesFor a vehicle that is equipped with a binary control systemof the motor the chromosome can be represented as theoptimal vector of the control signal in the following formst119900119901119905119880 = [1198801198781198641198791 1198801198781198641198792 119880119878119864119879119899]119879 119880119878119864119879119894 isin0 1 for eachsegment O119894 of the route (for control scheme A) or the

optimal vector of the control signal in the second form st119900119901119905119881= [1198811198781198641198791 1198811198781198641198792 119881119878119864119879119899]119879 119881119878119864119879119894 isin [119881min 119881max] for eachsegment O119894 of the route (for control scheme B)

In this optimization task the total distance of the roadD119862is composed of SEM race laps N119905119900 isin1 2 119873 The divisionof the whole route on a finite number of segments O119894 is notrecommended because it can lead to unnecessary increase inthe length of the vector st If the route consists of a minimumof four laps it is possible to limit the search of vector st toonly three types of laps

(i) the initial lap marked by 119874119894119904(ii) the middle laps marked by 119874119894119898(iii) the last lap marked as 119874119894119891Such assumption can be proven for at least three reasons(1) In the practical implementation of velocity strategies

the driver should not implement different control rules foreach lap The master control unit informs the driver aboutthe current velocity strategy but despite all the driver shouldremember this strategy to some extent

(2)The limitation of the velocity strategy only to the threetypes of laps reduces the length of the vector st In this waythe number of elements of the vector st corresponds to thenumber of decision variables of the optimization task

(3) Such division is reasonable by the nature of the laps Inthe initial lap it is necessary to accelerate the vehicle Withinthe middle laps the velocity profile of the vehicle should bethe same During the last lap the previously acquired kineticenergy E119896 is utilized

The task of finding the optimal vector st119900119901119905 can be solvedusing two types of evolutionary algorithms

(i) Classical genetic algorithm for control without avelocity regulator (according to control scheme A presentedin Figure 6)

(ii) Evolutionary strategy for the control system of thevehicle with a velocity regulator (according to control schemeB shown in Figure 7)

Theusage of two algorithms forces the appropriate codingof the velocity strategy which is described in the next twoparagraphs

421 Chromosome Coding For Control Scheme A The phe-notype of each individual determines the control vector st119906that means each gene of the individual of the population isthe value of the control signal 119880119878119864119879119894 for each section of thesegment O119894 of the route Assuming that we are looking for avelocity strategy of only three types of laps the phenotype canbe written as (for short form U equiv 119880SET)

st119880 = [ 1198801119904 1198802119904 119880119899119904 1198801119898 1198802119898 119880119899119904 1198801119891 1198802119891 119880119899119891 ]119879 (15)

where 119880119894119904 119880119894119898 119880119894119891 are the control signals for the initial lapmiddle laps and the last lap

422 Chromosome Coding for Control Scheme B In thiscase the elements in the vector 119881119878119864119879119894 change over a wide

Journal of Advanced Transportation 9

range and can assign real number values In the evolutionarystrategy the phenotype of each individual takes the followingformst119881

= [ 1198811119904 1198812119904 119881119899119904 1198811119898 1198812119898 119881119899119904 1198811119891 1198812119891 119881119899119891 ]119879 (16)

119881119894119904 119881119894119898 119881119894119891 are the setting values of velocity for the initiallap middle laps and the last lap

In the control mode according to scheme B the controlsignal is generated by the velocity controller based on thecontrol error

e119881 = 119881119878119864119879 minus 119881119904119894119898 (17)

where

U119878119864119879 = 1 for e119881 ge 10 otherwise

(18)

The coding for control scheme B in comparison withthe coding for control scheme A has undoubtedly oneadvantage namely the possibility of introducing a velocitylimit during the simulation of the passage of a given sectionof the route A velocity limitation is of great practicalimportance In many situations it is necessary to reducethe velocity of the vehicle during certain parts of theroute for example during cornering Accordingly in caseof control scheme B two velocity vectors are designated asfollows

(i) st11988115 for 119881119878119864119879119894 = [0 15] ms although it is formallylimited to 15ms it can never be achieved because themaximum vehicle speed (based on maximum enginespeed) is approximately 15ms

(ii) st11988110 for 119881119878119864119879119894 = [0 10] ms

43 The Fitness Functions In the case of evolutionary opti-mization the fitness function f 119907119886119897 has to be designed Thissection describes the formulas used to calculate the fitnessfunction of an individual that is needed for solving a task ofevolutionary optimization Each chromosome is a potentialsolution Each control strategy st is used during numericalsimulation The value of the fitness function f 119907119886119897 can becalculated based on the outcomes of the simulation suchas

(i) the total energy consumption r119904119894119898 [kmkWh](ii) the simulation time t119904119894119898(iii) the distance x119904119894119898

and limitations such as

(i) the maximum travel time T119898119886119909(ii) the total distance of the vehicle D119862The value of the function is also used to evaluate the

velocity strategy of the vehicle In the preliminary studies[24] the following fitness function f 119907119886119897 was used

Fitness Function 1

119891V1198861198971 = 11990811198911 + 11990821198912 + 11990831198913 (19)

where

1198911 = [1 + 1199031205821119904119894119898]1205821 (20)

1198912 = [119867 (119863119888 minus 119909119904119894119898) 1003816100381610038161003816119863119888 minus 1199091199041198941198981003816100381610038161003816119863119888 ]1205822 (21)

1198913 = [119867 (119905119904119894119898 minus 119879max)1003816100381610038161003816119879max minus 1199051199041198941198981003816100381610038161003816119879max

]1205822 (22)

where the weights w1 = 050E05 w2 = w3 = 025 andcoefficients 1205821 = minus2 1205822 = 1 were chosen experimentally Thepenalty functions f 2 and f 3 were introduced The Heavisidestep functionH() is used to penalize individuals representingunacceptable solutions [25 26] eg those that exceed themaximum time of the simulation H(t119904119894119898 minus T119898119886119909) or do notreach the specified distance H(D119888 minus x119904119894119898)

Fitness Function 2 In this study the authors have proposedthe fitness function which would lead to the convergenceof the evolutionary algorithm without searching for optimalvalues of weights Such a function is shown and describedbelow

119891V1198861198972 = 1 + 1198914 + 1198915119891111989121198913 (23)

1198911 = 119903119904119894119898 (24)

1198912 = cos(1003816100381610038161003816119863119888 minus 1198891199041198941198981003816100381610038161003816119863119888 ) (25)

1198913 = cos(1003816100381610038161003816119879max minus 1199051199041198941198981003816100381610038161003816119879max) (26)

1198914 = 120594 sdot 119867 (119863119888 minus 119889119904119894119898) (27)

1198915 = 120594 sdot 119867 (119879max minus 119905119904119894119898) (28)

where f 1 is a measure related to the simulated energyconsumption of the vehicle f 2 and f 3 correspond to thelimitations such as the maximum travel time and the totaldistance of the vehicle f 4 and f 5 also correspond to the limi-tations but these play strong penalty role and 120594 is arbitrarilylarge value eg significantly higher than maximal valuesf 2=f 3 =1 In this variant of the fitness function death penalty[26] is applied for unacceptable individuals in the form offactors f 4 and f 5 Individuals who do not reach a specifieddistance or exceed the time limit are eliminated These twocriteria act as a constraint and correspond to the limitationsformulated in the guidelines of the race competition On theother hand the criteria f 2 and f 3 have continuous nature andplay very important role in the fitness functionThey are veryneeded to evaluate continuously the individuals that are veryclose to and very far from the extremum

The argument of cos() function is not related to anangle However the usage of the cos() function is needed to

10 Journal of Advanced Transportation

Table 1 Research object main parameters

Type of the motor PM BLDCTransmission unit Toothed synchronous beltThe minimum turning radius 8 [m]The battery type and capacity Lithium-ion polymer 2100[mAh]Mass of the vehicle 42 [kg]Mass with the driver min 92 [kg]Diameter of wheels 0478 [m]Moment of inertia of the front wheel 119868119896119875 0023 [kgm2]Moment of inertia of the rear wheel 119868119896119879 0023[kgm2]Drag coefficient cx (see Table 2) 022 ndash 023Frontal area A [m2] (see Table 2) 0275 - 0297The total rolling coefficient crr (see Table 4) 00035 ndash 00058

eliminate the possibility of dividing by zero In addition theform of the cos() function is preferred At the initial stage ofoptimization when the simulation time t119904119894119898 and the distancex119904119894119898 differ significantly from the maximum time T119898119886119909 andthe specified distance D119888 a small change will have a greatereffect on the value of the fitness function At the final stageof optimization the function 119891V1198861198972 is more dependent on thesimulated energy consumption of the vehicle related to thefactor f 1 and thanks to the cos() function it is less dependentto the factors f 2 and f 3 The proposed function does notrequire the introduction of weights and therefore it is easierto use this function in other applications eg to find optimalvelocity strategies for different routes

It should be noted that fitness functions 119891val have beenwritten in such a way as to ensure that the optimizationalgorithm will look for a minimum of these functions

5 Case Study

As described in Sections 3 and 4 process of modelling andoptimization was applied and verified using a prototypeelectric vehicle on street race circuit in Rotterdam Themethodology was also carried out on the experimental ridestrack of the Fiat ChryslerAutomobiles Poland factory locatedin Tychy Based on (5)-(12) the simulation model was cre-ated in the MATLABSimulink environment Optimizationwas also carried out in MATLAB using the evolutionaryalgorithms available in the Global Optimization Toolbox Thelibrary of functions for simulating optimizing analyzingand presenting results has been developed

51 Research Object Light electric vehicle was a researchobject The vehicle shown in Figure 9 is a three-wheeledself-supporting structure The vehicle fuselage is made ofcomposites based on epoxy resin and woven of carbon andaramid fibre [21]

The dimensions of the vehicle and basic data are shownin Figure 10 and in Table 1

Identification of parameters for the mathematicalmodel of a research object was carried out by numericalsimulations tests on specially designed test bench [27]

Figure 9 Research object prototype electric vehicle ldquoMuSHELLkardquo(photo by M Wylezoł 2012)

and during conducted experiments in real environment[28]

The vehicle can be driven by two types of drive unit(i) DT1 drive unit based on PM BLDC motors and belt

transmission Drive wheel is equippedwith a one-wayclutch

(ii) DT2 a high-torque PMBLDCmotor mounted insidethe drive wheel The torque generated by the motor isdirectly transmitted to the rear drive wheel

The catalogue data can be used for creating the mathematicalmodel of the DT1 motor but for identifying the exactparameters it was necessary to carry out experimental testsThe manufacturer of the DT2 motor does not provide muchinformation so it was necessary to test the drive unit aswell DT1 drivetrain efficiencywas estimated using aBG75x50motor with toothed synchronous belt transmission ( z1= 28teeth z2 = 200 teeth i119879119878 = 714) The map of the efficiencywas shown on Figure 11(a) The same test was carried out forDT2 drive unit with a motor directly mounted on the drivewheel (Figure 11(b)) The obtained efficiency maps were usedto build the simulationmodel of the tested drivetrain systems

52 Determination of Air Drag Coefficient The air dragcoefficient c119909 was estimated as a result of CFD analysis usingANSYS software [24] and it was also verified by the researchin wind tunnel at the Institute of Aviation inWarsaw Frontalarea of vehicle A was determined from a three-dimensionalmodel in CAD environment Catia V5 The values of dragcoefficient c119909 and frontal area A are shown in Table 2

Journal of Advanced Transportation 11

623

972

1600

2605

Figure 10 Dimensions of the vehicle

(a) DT1 (b) DT2

Figure 11 Maps of the efficiency of tested drivetrain systems

Table 2 The air drag coefficient and frontal area

cx numericalsimulation

cx experimentalresearch Frontal area A [m2]

023 022 0275 0297

53 Determination of Rolling Resistance According to for-mula (7) the rolling resistance depends on the weight of thevehicle (Table 1) the tires rolling resistance coefficient andthe resistance of the bearings Depending on the drive unit(DT1 DT2) used in the vehicle additional resistance has to beadded In theDT1 system there is a one-way clutchwhich alsogenerates some resistance torque The DT2 system cannot bemechanically disconnected and therefore has a higher rollingresistance As a result of the coast down test the total rollingresistance of the vehicle has been identified for the four typesof tiresThe test was performed only with theDT1 system iethe systemwith the clutch Table 3 shows the basic parametersof the tires used in the experiments

The prototype vehicle can be equipped with speciallymanufactured Michelin tires with a low rolling resistantcoefficient of c119903119903 = 00014

In addition to the specialMichelin tires three other typesof tires were tested The identification of rolling resistance

coefficients was also estimated using a coast down test Themeasurements were made as follows

(i) The driver accelerated the vehicle to a fixed speed(ii) At themoment of crossing themarked gate the driver

pressed the marker button to save the flag in theacquired data

(iii) The run continued until free braking after which thedriver switched off the measuring system

(iv) The measurements were made at both directions ofthe road to minimize influence of the wind

(v) Before the attempts wind velocity temperature andatmospheric pressure were measured

(vi) The distance of the road was measured using ameasurement system mounted on the vehicle and itwas also verified using distance measuring wheel

On the basis of the experimental data the total rolling resis-tance coefficient of the vehicle was determined Table 4 showsthe coefficients of rolling resistance of the vehicle dependingon the tire used during the test Total resistance includesthe tire rolling coefficient the bearings resistance and theresistance of the clutch Verification of the data derived fromthe simulation and the experiment was conducted using

12 Journal of Advanced Transportation

Table 3 The types of tires used in the prototype vehicle

Tiresmarker Name of the tire Tirersquos

symbol Shape Type of tread Workingpressure

W1

Michelin ShellEco-marathon 4575R16 Rectangular Slick max500 [kPa]

W2

SchwalbeUl-Termo 23-406 Round Slick 600-1100 [kPa]

W3

Continental SportContact 28-406 Round Slick 600 [kPa]

W4

SchwalbeMarathon 40-406 Round Symmetrical 400-700 [kPa]

Table 4 The total rolling coefficient depending on the tires

Tiresmarker Name of the tire The total rolling coefficient crr mMAPE []

W1 Michelin ShellEco-marathon 00035 784W2 Schwalbe Ultermo 00043 1103W3 Continental SportContact 00058 1252W4 Schwalbe Marathon 00053 445

0

1

2

3

4

5

6

7

8

V [m

s]

100 200 300 400 500 6000x [m]

W1rW1simW2rW2sim

W3rW3simW4rW4sim

Figure 12 Velocity of the vehicle during coast down test

mMAPE (modifiable Mean Absolute Percentage Error) Forvelocity simulationmMAPE can be determined by

119898119872119860119875119864 = 1001119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119881119903 minus 119881119904119894119898119881119898119886119909 minus 119881119898119894119899

10038161003816100381610038161003816100381610038161003816 (29)

Figure 12 shows the experimental data obtained in a coastdown test compared with the results obtained during thecomputer simulation

54 Model of the Race Circuit In accordance with themethodology presented in Section 32 three routes have beendescribed

(i) Route 1 a street race circuit at the Shell Eco-marathoncompetition in Rotterdam

Figure 13 Plan view of the path of the drive on route 1 in Rotterdam

(ii) Routes 2 and 3 on the experimental rides track of theFiat Chrysler Automobiles Poland factory located inTychy in the south of Poland

The Shell Eco-marathon competition is held on a streetcircuit in Rotterdam One lap is 1630 meters long Vehicleshave to cover ten laps in no longer than 39 minutes so suchrequirements impose an averageminimum speed of 25 kmh

The trajectory of the vehicle path was developed usingsatellite images The vehicle trajectory was determined usingthe maximum curvature possible that could be obtained onthe existing roads

Movement of the vehicle in a curved motion causesthe centrifugal force Centrifugal force creates additionalresistance This resistance is inversely proportional to theradius of the path (8) so it is justified to select the largestradius In addition if the centrifugal force exceeds thelimit value it could provide to the side slip of the vehicleAccording to drawings in AutoCAD Civil 3D the lengths ofstraight sections and the lengths and the radius of arcs wereobtained Figure 13 shows a plan view of the path of the drive

Driving the prototype vehicle on public roads is prohib-ited and can be dangerous Vehicle testing was also carried

Journal of Advanced Transportation 13

Table 5 Travel times and total lengths of the routes

Route Length of the lap D [m] The numberof laps The total length of the route Dc [m] Travel time Tmax [s]

Route 1Rotterdam 1630 10 16 300 2340

Route 2Tychy 640 5 3200 460

Route 3Tychy 1000 5 5000 720

Figure 14 Plan view of the path of the drive on route 3 in Tychy

out on the experimental rides track of the Fiat ChryslerAutomobiles Poland factory

For the track in Tychy geodetic measurements weretaken using theDGPS (Differential Global Positioning System)technology The measuring points were collected along theaxis of the road with the distance between points amountingto 10 meters If on the measured route direction or elevationwere changed the frequency of measurement was increasedGeodetic coordinates were also imported intoAutoCADCivil3D and were used to prepare data concerning the route thatwas imported into the simulation environment MATLAB-Simulink Figures 14 and 15 show the path and elevationprofile respectively

Selected routes 2 and 3 have significant differences com-pared to route 1 especially in the height profile This set ofroutes was selected to verify the effect of the route profile onthe achieved results and to verify the proposed optimizationmethods for various road conditions The routes in Tychyare located in an open area there are no large buildingswhich guarantees stability of wind conditions The technicalcondition of the surface on routes 2 and 3 is much worsethan on route 1 which has a significant influence on therolling resistance Rolling resistance was also identified andintroduced into the simulation model For route 2 the c119903119903coefficient was 00056 and for route 3 was 00068

55 Verification of the Simulation Model In order to verifythe compatibility of the identified simulation model a seriesof numerical simulations and experimental tests were per-formed The first experiment consisted of running 300 [m]with a control strategy of 50 [m] with the workingmotor andafter that the vehicle was moving freely for the next 50 [m]The motor is turned on three times Figures 16(a) and 16(b)show the velocity of the vehicle and the power of the motorin function of the distance determined during the experiment

(red curves) and during the numerical simulations (greencurves)

Verification of the data derived from the simulation andthe experimentwas conducted usingmMAPE (29) Formotorpower simulationmMAPE can be determined by

119898119872119860119875119864119875 = 1001119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119875119903 minus 119875119904119894119898119875119898119886119909 minus 119875119898119894119899

10038161003816100381610038161003816100381610038161003816 (30)

where P119903 is the motor power measured during experimentand P119904119894119898 is the motor power conducted in simulation

As a result of the model validation tests estimationerror of the velocity was on level between 235 and 534However the motor power error level was greater It wasbetween 802 and 998

56 Determination of the Optimal Control Strategy Thelength of route 1 and the number of laps are determined bythe organizers of the Shell Eco-marathon competition Thelength of routes 2 and 3 is derived from the existing road planwhere it was possible to carry out trials in real conditionsThenumber of laps for routes 2 and 3 was assumed arbitrarily

The travel time for route 1 is based on the rules of therace which determine the minimum average speed of thevehicle Based on the average speed and the length of routes 2and 3 the travel times for these routes were determined Themaximum travel times and the total length of the route aswell as the number and length of one lap D are summarizedin Table 5

Evolutionary algorithms which are available in theMAT-LAB Global Optimization Toolbox were used From theMATLAB workspace the algorithm ran a simulation modelin a Simulink environment During optimization while usingevolutionary algorithms the maximum number of fitnessfunction evaluations 119873119891V119886119897

is the product of the populationsize 119873119901119900119901 and number of generations 119873119892119890119899

It was assumed that the total number of fitness functionevaluations was equal to 104 therefore should this value beexceeded the calculation would be cancelled Therefore thetotal number of generations 119873119892119890119899 is dependent on the valueof population size 119873119901119900119901

As part of this work phase the vectors st119880 st119881 15 andst119881 10 of the optimum control strategy for an electric vehiclefor routes 1 2 and 3 were determined During evolutionaryoptimization the heuristic method of crossing was usedand the probability of crossing was established on the basisof previous studies at the level of 08 [24 29] At the

14 Journal of Advanced Transportation

0+000

106410

minus164 minus492minus166 minus012 minus018 minus082 minus035 059 031

811

0+100 0+200 0+300 0+400 0+500 0+600 0+700 0+800 0+900 1+000

Figure 15 Profile of the path on route 3 in Tychy

50 100 150 200 250 3000X [m]

0

2

4

6

8

10

V [m

s]

(a) DT1

0

100

200

300

400

500

P [W

]50 100 150 200 250 3000

X [m]

(b) DT1

Figure 16 The velocity and the power determined with used DT1 drive unit

stage of reproduction the elitist succession method wasapplied where the best adapted two individuals in the currentpopulation passed to the next population An adaptivemethod of mutation was used The remaining parameters ofthe algorithm remain the default for the MATLAB GlobalOptimization Toolbox

The first case was the search st119880 vector for route 1Figures 17(a)ndash17(c) show the vehicle velocity V119904119894119898 obtainedby computer simulation The graph of the st119880 control signalis graphically displayed Figure 17 shows the results wherethe optimal control strategy st119880119900119901119905 was used and populationwas 119873119901119900119901=100 and 119873119892119890119899=100 The total energy consumptionwas estimated as r119904119894119898=527633 [km kWh] Figure 17(a) showsthe vehicle speed and control signal st119880 during the first lapwhile Figure 17(b) shows center laps and Figure 17(c) showsthe last lap Figure 17(d) shows the curves of the mean valuesof the fitness functions f 119907119886119897 depending on the number ofcalculations of these functions during the optimization ofthe control strategy There are eight curves in the graph(Figure 17(d)) for each of the 119873119901119900119901 parameters used in thealgorithm

When analyzing the vehicle velocity chart on the last lapof route 1 (Figure 17(c)) it can be seen that according tothe determined control strategy the propulsion system of thevehicle should no longer be used The vehicle should use thestored kinetic energy

The analysis of vehicle velocity V119904119894119898 during the last lapindicates that at the moment of reaching the given distancethe speed was still about 2 [ms] This demonstrates thatthe simulated vehicle has kinetic energy that would haveto be dispersed by the braking system or recovered by the

electric motor Having such a speed does not mean that thereis still possibility for improvement Lower speed at the endof the route has to cause higher speed of the earlier partsof the route This speed is the optimum speed due to thechosen criterion From the analysis of the shape of the fitnessfunction (Figure 17(d)) it can be seen that for route 1 itis preferable to use a smaller population of 119873119901119900119901=25 andincrease the number of 119873119892119890119899=400 The curve shape for thiscase is steep and it falls to the minimum value of the fitnessfunction which may indicate that the algorithm has reacheda convergence

Results of the optimization where B type of coding wasused were analyzed The results obtained as the mean of ther119904119894119898 result together with the standard deviation from all thetests were summarized in Table 6

By analyzing the results in Table 6 it can be seen thatfor route 1 better results were obtained (reduced simulatedtotal energy consumption) using A coding compared to Bespecially for st119881 15 whose results are characterized by thehighest standard deviation For routes 2 and 3 the same as forroute 1 the procedure was followed Optimization strategieshave been optimized for all variants of control vector st119880st119881 15 st10

The results using the control strategy st119881 10 are shownin Figures 18(a)ndash18(c) (119873119901119900119901=100 where r119904119894119898=351795 [km kWh]) Figure 18(d) illustrates the graph of the value of thefitness function

The results obtained for route 2 are presented in Table 7For route 2 compared to route 1 the best results were

achieved using the stV10 vector When using vectors st119880 andstV15 the results were slightly worse Having analyzed the size

Journal of Advanced Transportation 15

0

2

4

6

8

10V

[ms

]

VsimstU

500 1000 15000X [m]

(a) Lap 1

0

2

4

6

8

10

V [m

s]

2500 30002000X [m]

VsimstU

(b) Laps 2-9

0

2

4

6

8

10

V [m

s]

155 1615X [m]

Vsimstu

times104

(c) Lap 10

times10minus3

Npop=25Npop=50Npop=75Npop=100

Npop=125Npop=150Npop=175Npop=200

15

2

25

3

35

4f va

l

2000 4000 6000 8000 100000Nfval

(d) Mean values of the fitness functions

Figure 17 Vehicle speed and control signal st119880 for route 1

Table 6 The results for route 1

The type of coding A The type of coding Bst119880 st11988115 st11988110119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 52465 1459 42845 1741 51569 5477550 52579 10053 44431 22486 51492 3409475 52497 39913 43842 28173 51256 80682100 52589 18128 42232 1797 51166 49379125 52625 13862 42733 39616 51341 70765150 5243 2979 4435 47701 51486 27086175 52513 2511 41428 27299 51838 19358200 52579 19666 42337 25776 51204 78357

16 Journal of Advanced Transportation

100 200 300 400 500 6000X [m]

0

2

4

6

8

10V

[ms

]

VsimstV10

USET

(a) Lap 1

0

2

4

6

8

10

V [m

s]

800 900 1000 1100 1200700X [m]

VsimstV10

USET

(b) Laps 2-4

0

2

4

6

8

10

V [m

s]

2700 2800 2900 3000 3100 32002600X [m]

VsimstV10

USET

(c) Lap 5

times10minus3

Npop=25Npop=50Npop=75Npop=100

Npop=125Npop=150Npop=175Npop=200

275

28

285

29

295

3

305

f val

2000 4000 6000 8000 100000Nfval

(d) Mean values of the fitness functions

Figure 18 Vehicle speed and control signal st11988110 for route 2

of the population used in the optimization process it shouldbe noted that for route 2 it is preferable to use higher value of119873119901119900119901 For all the analyzed cases the best average results for119873119901119900119901=200 were obtained Table 8 summarizes the results forroute 3

For route 3 the average results were reported for a largerpopulation of119873119901119900119901 with B coding In the case of using vectorwith A type coding no characteristic change was notedAs expected comparing the standard deviation betweenalgorithms using B coding the standard deviation is less forthe less variance range

Evolutionary algorithms are not complete search algo-rithms therefore it is not possible to determine whetherthe solution found is best for the chosen criterion and theconstraints assumed

57 Applying the Optimal Control Strategy in Real ConditionsElectric vehicle energy consumption optimization was finallyverified in real conditions at the European edition of the ShellEco-marathon held on 16-18 May 2014 in Rotterdam

Optimal control strategy st119880was displayed by a prototypevisualization system Visualization unit is installed in the

Journal of Advanced Transportation 17

Table 7 The results for route 2

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 34138 66734 34294 23839 34873 5353250 34573 46359 35003 462 3506 3886275 34512 55134 34961 33476 35419 067858100 34836 45332 35253 26117 3544 19295125 34632 52704 35017 49039 35483 14756150 34552 63714 35326 14885 35343 071015175 35063 18728 35274 47141 35564 038022200 35073 14496 3540 13389 35569 14942

Table 8 The results for route 3

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 28071 10173 28643 7323 30994 277650 29346 6142 29581 7894 30874 439975 29711 5002 29217 7367 31141 1856100 29826 3231 29515 7022 30957 4049125 29781 2980 29866 12977 31168 3445150 29453 3346 30217 9623 31288 1249175 29234 2317 30621 6816 31481 1261200 29686 2337 30531 11737 31089 4880

Table 9 Comparison of simulation results with experimental tests

Number of attempts 119903119878119864ndash119898 119903119903 119903119904119894119898 119903119900119901119905 119890119898 119890119894 119890119904119905Attempt 1 3654 3608 - - 125 - -Attempt 2 4813 5082 5148 5265 558 129 36Attempt 3 4873 5127 5198 5265 521 139 269Attempt 4 Failed attempt damaged tires during 1st lap

steering wheel of the vehicle The visualization system showsthe basic data such as instantaneous speed average speedtravel time and distance In addition the visualization systemprovides information on which part of the track the drivershould press the acceleration button to execute the optimalcontrol strategy Measurement of the position on the track iscarried out by the odometrical measuring system Due to thepossibility of accumulating errors in the measurement of theroad the driver will reset the measuring system every timeheshe exceeds the lap line

Table 9 presents the results of all the measurementsconducted during the Shell Eco-marathonThe columns in theTable 9 contain

(i) r119878119864119898 [kmkWh] the result recorded during the raceby the measuring device provided by the organizerthe results are available on the Shell Eco-marathonofficial website

(ii) r119903 [kWkWh] the result based on the indications of aprototypemeasuring system permanently installed inthe vehicle

(iii) r119904119894119898 the result estimated by computer simulationusing recorded real control signal U119903

(iv) r119900119901119905 the result obtained by computer simulation usingthe optimal control strategy U119900119901119905

Table 9 also includes the following

(i) Measurement error

119890119898 = 1003816100381610038161003816119903119878119864119898 minus 1199031199031003816100381610038161003816119903119878119864119898 100 (31)

(ii) Identification error

119890119894 =1003816100381610038161003816119903119903 minus 1199031199041198941198981003816100381610038161003816119903119903 100 (32)

(iii) Strategy implementation error

119890119904119905 =10038161003816100381610038161003816119903119903 minus 11990311990011990111990510038161003816100381610038161003816119903119903 100 (33)

18 Journal of Advanced Transportation

There were four measurement trials available Duringrun 1 a much weaker result was obtained than estimated bysimulation The driver performed run 1 without a definedcontrol strategy As part of the experiment the driver andthe support team were asked to select the optimal tires forthe vehicle and to implement the proposed control strategyDuring run 1 only the travel time of individual laps waschecked According to the choice of the team in run 1 tiresW2 were selected (Table 4) During this test the worst resultwas obtained about 24 and 25 worse than in the othertrials In subsequent runs 2 and 3 the vehicle was equippedwith the best W1 tires (Table 4) The driver has implementedan algorithm-based optimal control strategy Strategy infor-mation was provided by the visualization system During run3 the best result was recorded This result was taken intoaccount in the classification of competitions where the teamplaced in 12 positions out of 28 classified teams Trials 4 dueto damage to the tires were not successful

Measurement error was from 125 to 558 dependingon the sample The measurement system installed perma-nently in the vehicle is a prototype system This systemhas been calibrated using available laboratory equipmentMeasurement errors indicate that other measuring devices ofthe higher accuracy class should be used

Based on the measurement data obtained during testdrives the model was tuned thus reducing the identificationerror The competition took place in stable weather thedivergence of results was small and was about 129 forsample 2 and 139 for sample 3

The difference between the results determined duringnumerical simulation and that obtained in the real run was36 for sample 2 and 269 for sample 3 The difference atthis level was considered to be small Searching for optimalcontrol strategy has not taken into account possible rdquoerrorsrdquowhich could be made by the driver and which result fromthe current situation on the route for example selecting thepath and using the route by other participants in the raceIncluding driver behaviour in the simulation model shouldbe the subject of further work

Figure 19 shows the vehicle velocity together with thecontrol signals recorded during run 2 The black curvesrepresent the real vehicle velocity V119903 and the control signalGreen curves are the optimum control strategy st119880 andthe optimal velocity V119900119901119905 determined by the simulationThe graph shows the entire distance travelled (10 laps) Theanalysis of the graph shows that the driver did not performthe exact planned strategy Errors in the implementationof the strategy are related to the disruptions During thecompetition the driver is not alone on the track in certainsituations the driver cannot overtake other participants andcannot take the optimal path In addition weather conditionsuch as wind has influence on the motion resistance In suchcases the driver has to modify the optimal control strategy

In Figure 20 the velocity recorded during the race V119903(black) and the velocity obtained by the computer simulationV119904119894119898 (red) were shown V119904119894119898 was determined by computersimulation by using real control signal The purpose of thissimulation was to investigate the correctness of identification

VrVopt

Ur Uopt

2000 4000 6000 8000 10000 12000 14000 16000 180000X [m]

05

10152025303540

V [k

mh

]

Figure 19 Comparison of speed and control signal during attempt2

2000 4000 6000 8000 10000 12000 14000 16000 180000x [m]

05

10152025303540

V [k

mh

]

Ur

VrVsim

Figure 20 Comparison of speed registered in real conditions withthe speed determined by computer simulation

of the simulation model and to identify the identificationerror

Compared to the Shell Eco-marathon competitions heldin 2012 and 2013 our performance has improved The resultsin these years were equal to 425 [km kWh] and 454[km kWh] respectively In 2012 and 2013 the controlstrategy was chosen on the basis of the simulation modelbut the model was not adequately identified and the controlstrategy had to be modified In previous editions of therace the implementation of optimal control strategy was notsupported by the visualization system which would informthe driver of the need to take specific actions (pressing orreleasing the accelerator button)

6 Conclusion

The presented method was developed and tested for aprototype electric racing car that has been designed for theShell Eco-marathon race As it was shown the results of thenumerical simulations were very similar to the outcomes ofthe real races in the context of the final result of energyconsumption and the profile of velocity of the car during therace The method has been developed and applied since 2012

Journal of Advanced Transportation 19

and led in 2014 to achieving the optimal result for this type ofthe vehicle

The optimization method was evaluated The resultsachieved during the race attempts where the optimal con-trol strategy was applied (4813 and 4873 kmkWh) werecompared to the result where the strategy was proposed bythe experts (3654 kmkWh) who already had contact withthe results of similar optimization models Optimal attemptswere better by over 30 despite errors in the implementationof the strategy by the driver In the case of experts who did nothave such experiences the differences were even greater

Further improvement of the control strategy is impossiblefor this type of a vehicle and the best way to reduce energyconsumption is by improving the mechanical design It wasthe reason to develop new racing cars for UrbanConceptBattery Electric and Hydrogen competitions The developedresearch methodology for vehicle optimization and controlstrategies has been developed and implemented in the ShellEco-marathon in 2015 which has improved the score to 504km kWhHowever the research has shown that the potentialfor improved performance of the MuSHELLka vehicle hasbeen exhausted No major structural changes in the vehiclecan significantly improve the result so in the followingyears the race was abandoned and the focus was on thedevelopment of the HydroGENIUS the electric vehicle ofUrbanConcept class with fuel cell stack as power sourcewhich eventually scored vice Championship in SEM 2016 Inthe further work it is planned to improve the optimizationresults by using the presented methodology in the case ofthe models of newly constructed vehicles The developmentof the optimization method should take into considerationthe uncertainty resulting from the given velocity strategyconsidering the real conditions of the race It is also possibleto use this method for controlling vehicles in traffic To dothis it is necessary to completely change the way of the routemodelling and the driving conditions modelling as well as todevelop a new optimization method for obtaining results inreal time

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] W Skarka ldquoReducing the Energy Consumption of ElectricVehiclesrdquo in Proceedings of the 22nd ISPE-Inc InternationalConference on Concurrent Engineering Location R Curran NWognumM Borsato et al Eds Advances in TransdisciplinaryEngineering pp 500ndash509 IOS Press Delft Netherlands 2015

[2] R Andrzejewski and J Awrejcewicz Nonlinear Dynamics of aWheeled Vehicle vol 10 Springer-Verlag New York NY USA2005

[3] D W Gao C Mi and A Emadi ldquoModeling and simulation ofelectric and hybrid vehiclesrdquo Proceedings of the IEEE vol 95 no4 pp 729ndash745 2007

[4] ldquoAdvisor documentationrdquo httpadv-vehiclesimsourceforgenet

[5] TMarkel A Brooker THendricks et al ldquoADVISORA systemsanalysis tool for advanced vehicle modelingrdquo Journal of PowerSources vol 110 no 1 pp 255ndash266 2002

[6] K B Wipke M R Cuddy and S D Burch ldquoADVISOR21 a user-friendly advanced powertrain simulation using acombined backwardforward approachrdquo IEEE Transactions onVehicular Technology vol 48 no 6 pp 1751ndash1761 1999

[7] ldquoWebsiterdquo 2014 httpwwwtransportationanlgovmodeling[8] ldquoWebsiterdquo 2014 httpwwwautonomienet[9] K Krykowski J Hetmanczyk Z Gałuszkiewicz and R Mik-

siewicz ldquoComputer analysis of high-speed PM BLDC motorpropertiesrdquo COMPEL - The International Journal for Computa-tion and Mathematics in Electrical and Electronic Engineeringvol 30 no 3 pp 941ndash956 2011

[10] M Vaillant M Eckert and F Gauterin ldquoEnergy managementstrategy to be used in design space exploration for electricpowertrain optimizationrdquo inProceedings of the 2014 9th Interna-tional Conference on Ecological Vehicles and Renewable EnergiesEVER 2014 mco March 2014

[11] A T Nguyen S Reiter and P Rigo ldquoA review on simulation-based optimization methods applied to building performanceanalysisrdquo Applied Energy vol 113 pp 1043ndash1058 2014

[12] W Silka and W Siłka Energy Intensity in the Car Traffic InPolish WNT Warszawa 1997

[13] T J Barlow S Latham I S Mrcrae and P Boulter A referencebook of driving cycles for use in the measurement of roadvehicle emissions TRL 2009 httpswwwgovukgovernmentuploadssystemdata

[14] R N Jazar Vehicle Dynamics Theory and Application SpringerUS Boston MA 2008

[15] MMeywerk ldquoVehicle Dynamicsrdquo inWest Sussex JohnWiley ampSons Lecture Notes to theMOOCVehicle Dynamics of iversity1st edition 2015

[16] MMitschke andHWallentowitzDynamik der KraftfahrzeugeSpringer Berlin Germany 1972

[17] T Stefanski and Ł Zawarczynski ldquoParametric identification ofPM motor mathematical modelsrdquo Przegląd Elektrotechnicznyvol 88 no 4 B pp 224ndash229 2012

[18] A Cameron ldquoMeasuring drive-train efficiencyrdquoHuman Powervol 46

[19] B Rohloff and P Greb ldquoEfficiency measurements of bicycletransmissions a neverending storyrdquo Human Power vol 55 p11 2004

[20] J B Spicer C J K Richardson M J Ehrlich J R BernsteinM Fukuda and M Terada ldquoEffects of frictional loss on bicyclechain drive efficiencyrdquo Journal of Mechanical Design vol 123no 4 pp 598ndash605 2001

[21] K Sternal A Cholewa W Skarka and M Targosz ldquoElec-tric vehicle for the studentsrsquo shell eco-marathon competitionDesign of the car and telemetry systemrdquo Communications inComputer and Information Science vol 329 pp 26ndash33 2012

[22] K Cichonski and W Skarka ldquoInnovative control system forhigh efficiency electric urban vehiclerdquo Communications inComputer and Information Science vol 531 pp 121ndash130 2015

[23] M J Er and R J Oentaryo ldquoComputational IntelligenceMethods andTechniques (Rutkowski L 2008) [BookReview]rdquoIEEE Computational Intelligence Magazine vol 6 no 4 pp 76ndash78 2011

[24] M Targosz M Szumowski W Skarka and P PrzystałkaldquoVelocity Planning of an Electric Vehicle Using an Evolutionary

Journal of Advanced Transportation 7

Mechanical systemHigh-level control system Motor controller

Transmissionsystem

Currentcontroller

Angularvelocity

measuringsystem

Positionmeasuring

system

MotorDecisionmodule

Driverrsquos decision

Binary control

signal U (x)SET

USET ISET５ＬＲＧ ＲＬ ＲＬ ＲＬ

intint

Figure 6 Drive system diagram control scheme A

High-level control system

Decisionmodule

Velocitycontroller

Mechanical systemMotor controller

Transmissionsystem

Currentcontroller

Angular velocitymeasuring

system

Positionmeasuring system

Motor

Linear velocitymeasuring system

-

Driverrsquos decision

Velocity profileV (x)SET

VSET evＲＧ

Ｒm

USET Ur ISET ＲＬ ＲＬint int

ＲＬ

Figure 7 Drive system diagram control scheme B

the exact way The input control signal U119903 is always differentfrom the signal 119880SET in real conditions It means that thesignal 119880SET is mainly employed by the driver to know whenthe acceleration treadle should be used

In the case of the control scheme B (Figure 7) the generalgoal of the optimization task is the same as in the previouscase However the formal definition of the problem is quitedifferent because in this case the optimal form of the velocitysignal is searched according to the position of the vehicle onthe routeV119878119864119879 = f (x(t))The velocity controller compares thesetpoint signalV119878119864119879 with themeasured velocity of the vehicleand for certain controller setting as well as for control errore119907 it generates the control signal 119880SET As in the previouscase the supervisory role of the driver is included in thedecision module However the main difference is that in theoptimization process the setpoint signal V119878119864119879 can be limitedin the direct way

According to control schemes A and B the input controlsignal U119903 is used by the motor control unit where theemended current regulator normally outputs the correspond-ing signals to the motor terminals The driving torque of themotor shaft is transmitted through the transmission systemto the wheels of the vehicle

4 Evolutionary Optimization of theVelocity Strategy

41 Formulation of the Optimization Problem One of theways to define and to solve the dynamic optimization taskof the velocity strategy of the vehicle is to reduce sucha problem to the static optimization task through the so-called discretization of the independent variable If oneassumes that the independent variable is the position ofthe vehicle (a travelled distance) x(t) then the velocitystrategy st can be represented by a vector of instanta-neous values 119880SET or V119878119864119879 for discrete parts of the routeFigure 8 illustrates the idea of dividing the route into seg-ments

The path is divided into n segments O119894 each of the lengthL119894 where the sum of the lengths of the segments is equal tothe length of the total path For each segment it is necessaryto determine the 119880119878119864119879119894 or 119881119878119864119879119894 setpoint The task is to findthe optimal velocity strategy for control scheme A in thefollowing form

st119900119901119905U = [1198801198781198641198791 1198801198781198641198792 119880119878119864119879119899]119879 119880119878119864119879119894 isin 0 1 (13)

8 Journal of Advanced Transportation

D

L2L1 Ln

O2O1 On

Figure 8 Concept of discretization of the route

whereas in the second case for control scheme B

st119900119901119905V = [1198811198781198641198791 1198811198781198641198792 119881119878119864119879119899]119879 119881119878119864119879119894 isin 119881119898119894119899 119881119898119886119909

(14)

where119881min and119881max can be determined in different ways egbased on the minimummaximum vehicle speed or based onthe simple calculation corresponding to guidelines of the racecompetition

Evolutionary algorithms can be used to solve this prob-lem In the case of the search for strategy st119900119901119905119880 it is preferableto use a classical genetic algorithm In this instance the genesin a chromosome of the individual can be encoded directlyas the binary values of the control signal 119880119878119864119879119894 Thereforethe length of the chromosome N119888ℎ is equal to the number ofsections of the route

In accordance with the control scheme B the velocityprofile is determined as the vector including setpoint valuesof the velocity st119900119901119905119881 The components of the st119900119901119905119881 vectorare floating point values hence it is possible to use anevolutionary strategy proposed in [23] Each of the genes inthe chromosomeof the individual corresponds to the setpointvalue of the velocity during a part of the route

42 Chromosome Codding for Different Velocity StrategiesFor a vehicle that is equipped with a binary control systemof the motor the chromosome can be represented as theoptimal vector of the control signal in the following formst119900119901119905119880 = [1198801198781198641198791 1198801198781198641198792 119880119878119864119879119899]119879 119880119878119864119879119894 isin0 1 for eachsegment O119894 of the route (for control scheme A) or the

optimal vector of the control signal in the second form st119900119901119905119881= [1198811198781198641198791 1198811198781198641198792 119881119878119864119879119899]119879 119881119878119864119879119894 isin [119881min 119881max] for eachsegment O119894 of the route (for control scheme B)

In this optimization task the total distance of the roadD119862is composed of SEM race laps N119905119900 isin1 2 119873 The divisionof the whole route on a finite number of segments O119894 is notrecommended because it can lead to unnecessary increase inthe length of the vector st If the route consists of a minimumof four laps it is possible to limit the search of vector st toonly three types of laps

(i) the initial lap marked by 119874119894119904(ii) the middle laps marked by 119874119894119898(iii) the last lap marked as 119874119894119891Such assumption can be proven for at least three reasons(1) In the practical implementation of velocity strategies

the driver should not implement different control rules foreach lap The master control unit informs the driver aboutthe current velocity strategy but despite all the driver shouldremember this strategy to some extent

(2)The limitation of the velocity strategy only to the threetypes of laps reduces the length of the vector st In this waythe number of elements of the vector st corresponds to thenumber of decision variables of the optimization task

(3) Such division is reasonable by the nature of the laps Inthe initial lap it is necessary to accelerate the vehicle Withinthe middle laps the velocity profile of the vehicle should bethe same During the last lap the previously acquired kineticenergy E119896 is utilized

The task of finding the optimal vector st119900119901119905 can be solvedusing two types of evolutionary algorithms

(i) Classical genetic algorithm for control without avelocity regulator (according to control scheme A presentedin Figure 6)

(ii) Evolutionary strategy for the control system of thevehicle with a velocity regulator (according to control schemeB shown in Figure 7)

Theusage of two algorithms forces the appropriate codingof the velocity strategy which is described in the next twoparagraphs

421 Chromosome Coding For Control Scheme A The phe-notype of each individual determines the control vector st119906that means each gene of the individual of the population isthe value of the control signal 119880119878119864119879119894 for each section of thesegment O119894 of the route Assuming that we are looking for avelocity strategy of only three types of laps the phenotype canbe written as (for short form U equiv 119880SET)

st119880 = [ 1198801119904 1198802119904 119880119899119904 1198801119898 1198802119898 119880119899119904 1198801119891 1198802119891 119880119899119891 ]119879 (15)

where 119880119894119904 119880119894119898 119880119894119891 are the control signals for the initial lapmiddle laps and the last lap

422 Chromosome Coding for Control Scheme B In thiscase the elements in the vector 119881119878119864119879119894 change over a wide

Journal of Advanced Transportation 9

range and can assign real number values In the evolutionarystrategy the phenotype of each individual takes the followingformst119881

= [ 1198811119904 1198812119904 119881119899119904 1198811119898 1198812119898 119881119899119904 1198811119891 1198812119891 119881119899119891 ]119879 (16)

119881119894119904 119881119894119898 119881119894119891 are the setting values of velocity for the initiallap middle laps and the last lap

In the control mode according to scheme B the controlsignal is generated by the velocity controller based on thecontrol error

e119881 = 119881119878119864119879 minus 119881119904119894119898 (17)

where

U119878119864119879 = 1 for e119881 ge 10 otherwise

(18)

The coding for control scheme B in comparison withthe coding for control scheme A has undoubtedly oneadvantage namely the possibility of introducing a velocitylimit during the simulation of the passage of a given sectionof the route A velocity limitation is of great practicalimportance In many situations it is necessary to reducethe velocity of the vehicle during certain parts of theroute for example during cornering Accordingly in caseof control scheme B two velocity vectors are designated asfollows

(i) st11988115 for 119881119878119864119879119894 = [0 15] ms although it is formallylimited to 15ms it can never be achieved because themaximum vehicle speed (based on maximum enginespeed) is approximately 15ms

(ii) st11988110 for 119881119878119864119879119894 = [0 10] ms

43 The Fitness Functions In the case of evolutionary opti-mization the fitness function f 119907119886119897 has to be designed Thissection describes the formulas used to calculate the fitnessfunction of an individual that is needed for solving a task ofevolutionary optimization Each chromosome is a potentialsolution Each control strategy st is used during numericalsimulation The value of the fitness function f 119907119886119897 can becalculated based on the outcomes of the simulation suchas

(i) the total energy consumption r119904119894119898 [kmkWh](ii) the simulation time t119904119894119898(iii) the distance x119904119894119898

and limitations such as

(i) the maximum travel time T119898119886119909(ii) the total distance of the vehicle D119862The value of the function is also used to evaluate the

velocity strategy of the vehicle In the preliminary studies[24] the following fitness function f 119907119886119897 was used

Fitness Function 1

119891V1198861198971 = 11990811198911 + 11990821198912 + 11990831198913 (19)

where

1198911 = [1 + 1199031205821119904119894119898]1205821 (20)

1198912 = [119867 (119863119888 minus 119909119904119894119898) 1003816100381610038161003816119863119888 minus 1199091199041198941198981003816100381610038161003816119863119888 ]1205822 (21)

1198913 = [119867 (119905119904119894119898 minus 119879max)1003816100381610038161003816119879max minus 1199051199041198941198981003816100381610038161003816119879max

]1205822 (22)

where the weights w1 = 050E05 w2 = w3 = 025 andcoefficients 1205821 = minus2 1205822 = 1 were chosen experimentally Thepenalty functions f 2 and f 3 were introduced The Heavisidestep functionH() is used to penalize individuals representingunacceptable solutions [25 26] eg those that exceed themaximum time of the simulation H(t119904119894119898 minus T119898119886119909) or do notreach the specified distance H(D119888 minus x119904119894119898)

Fitness Function 2 In this study the authors have proposedthe fitness function which would lead to the convergenceof the evolutionary algorithm without searching for optimalvalues of weights Such a function is shown and describedbelow

119891V1198861198972 = 1 + 1198914 + 1198915119891111989121198913 (23)

1198911 = 119903119904119894119898 (24)

1198912 = cos(1003816100381610038161003816119863119888 minus 1198891199041198941198981003816100381610038161003816119863119888 ) (25)

1198913 = cos(1003816100381610038161003816119879max minus 1199051199041198941198981003816100381610038161003816119879max) (26)

1198914 = 120594 sdot 119867 (119863119888 minus 119889119904119894119898) (27)

1198915 = 120594 sdot 119867 (119879max minus 119905119904119894119898) (28)

where f 1 is a measure related to the simulated energyconsumption of the vehicle f 2 and f 3 correspond to thelimitations such as the maximum travel time and the totaldistance of the vehicle f 4 and f 5 also correspond to the limi-tations but these play strong penalty role and 120594 is arbitrarilylarge value eg significantly higher than maximal valuesf 2=f 3 =1 In this variant of the fitness function death penalty[26] is applied for unacceptable individuals in the form offactors f 4 and f 5 Individuals who do not reach a specifieddistance or exceed the time limit are eliminated These twocriteria act as a constraint and correspond to the limitationsformulated in the guidelines of the race competition On theother hand the criteria f 2 and f 3 have continuous nature andplay very important role in the fitness functionThey are veryneeded to evaluate continuously the individuals that are veryclose to and very far from the extremum

The argument of cos() function is not related to anangle However the usage of the cos() function is needed to

10 Journal of Advanced Transportation

Table 1 Research object main parameters

Type of the motor PM BLDCTransmission unit Toothed synchronous beltThe minimum turning radius 8 [m]The battery type and capacity Lithium-ion polymer 2100[mAh]Mass of the vehicle 42 [kg]Mass with the driver min 92 [kg]Diameter of wheels 0478 [m]Moment of inertia of the front wheel 119868119896119875 0023 [kgm2]Moment of inertia of the rear wheel 119868119896119879 0023[kgm2]Drag coefficient cx (see Table 2) 022 ndash 023Frontal area A [m2] (see Table 2) 0275 - 0297The total rolling coefficient crr (see Table 4) 00035 ndash 00058

eliminate the possibility of dividing by zero In addition theform of the cos() function is preferred At the initial stage ofoptimization when the simulation time t119904119894119898 and the distancex119904119894119898 differ significantly from the maximum time T119898119886119909 andthe specified distance D119888 a small change will have a greatereffect on the value of the fitness function At the final stageof optimization the function 119891V1198861198972 is more dependent on thesimulated energy consumption of the vehicle related to thefactor f 1 and thanks to the cos() function it is less dependentto the factors f 2 and f 3 The proposed function does notrequire the introduction of weights and therefore it is easierto use this function in other applications eg to find optimalvelocity strategies for different routes

It should be noted that fitness functions 119891val have beenwritten in such a way as to ensure that the optimizationalgorithm will look for a minimum of these functions

5 Case Study

As described in Sections 3 and 4 process of modelling andoptimization was applied and verified using a prototypeelectric vehicle on street race circuit in Rotterdam Themethodology was also carried out on the experimental ridestrack of the Fiat ChryslerAutomobiles Poland factory locatedin Tychy Based on (5)-(12) the simulation model was cre-ated in the MATLABSimulink environment Optimizationwas also carried out in MATLAB using the evolutionaryalgorithms available in the Global Optimization Toolbox Thelibrary of functions for simulating optimizing analyzingand presenting results has been developed

51 Research Object Light electric vehicle was a researchobject The vehicle shown in Figure 9 is a three-wheeledself-supporting structure The vehicle fuselage is made ofcomposites based on epoxy resin and woven of carbon andaramid fibre [21]

The dimensions of the vehicle and basic data are shownin Figure 10 and in Table 1

Identification of parameters for the mathematicalmodel of a research object was carried out by numericalsimulations tests on specially designed test bench [27]

Figure 9 Research object prototype electric vehicle ldquoMuSHELLkardquo(photo by M Wylezoł 2012)

and during conducted experiments in real environment[28]

The vehicle can be driven by two types of drive unit(i) DT1 drive unit based on PM BLDC motors and belt

transmission Drive wheel is equippedwith a one-wayclutch

(ii) DT2 a high-torque PMBLDCmotor mounted insidethe drive wheel The torque generated by the motor isdirectly transmitted to the rear drive wheel

The catalogue data can be used for creating the mathematicalmodel of the DT1 motor but for identifying the exactparameters it was necessary to carry out experimental testsThe manufacturer of the DT2 motor does not provide muchinformation so it was necessary to test the drive unit aswell DT1 drivetrain efficiencywas estimated using aBG75x50motor with toothed synchronous belt transmission ( z1= 28teeth z2 = 200 teeth i119879119878 = 714) The map of the efficiencywas shown on Figure 11(a) The same test was carried out forDT2 drive unit with a motor directly mounted on the drivewheel (Figure 11(b)) The obtained efficiency maps were usedto build the simulationmodel of the tested drivetrain systems

52 Determination of Air Drag Coefficient The air dragcoefficient c119909 was estimated as a result of CFD analysis usingANSYS software [24] and it was also verified by the researchin wind tunnel at the Institute of Aviation inWarsaw Frontalarea of vehicle A was determined from a three-dimensionalmodel in CAD environment Catia V5 The values of dragcoefficient c119909 and frontal area A are shown in Table 2

Journal of Advanced Transportation 11

623

972

1600

2605

Figure 10 Dimensions of the vehicle

(a) DT1 (b) DT2

Figure 11 Maps of the efficiency of tested drivetrain systems

Table 2 The air drag coefficient and frontal area

cx numericalsimulation

cx experimentalresearch Frontal area A [m2]

023 022 0275 0297

53 Determination of Rolling Resistance According to for-mula (7) the rolling resistance depends on the weight of thevehicle (Table 1) the tires rolling resistance coefficient andthe resistance of the bearings Depending on the drive unit(DT1 DT2) used in the vehicle additional resistance has to beadded In theDT1 system there is a one-way clutchwhich alsogenerates some resistance torque The DT2 system cannot bemechanically disconnected and therefore has a higher rollingresistance As a result of the coast down test the total rollingresistance of the vehicle has been identified for the four typesof tiresThe test was performed only with theDT1 system iethe systemwith the clutch Table 3 shows the basic parametersof the tires used in the experiments

The prototype vehicle can be equipped with speciallymanufactured Michelin tires with a low rolling resistantcoefficient of c119903119903 = 00014

In addition to the specialMichelin tires three other typesof tires were tested The identification of rolling resistance

coefficients was also estimated using a coast down test Themeasurements were made as follows

(i) The driver accelerated the vehicle to a fixed speed(ii) At themoment of crossing themarked gate the driver

pressed the marker button to save the flag in theacquired data

(iii) The run continued until free braking after which thedriver switched off the measuring system

(iv) The measurements were made at both directions ofthe road to minimize influence of the wind

(v) Before the attempts wind velocity temperature andatmospheric pressure were measured

(vi) The distance of the road was measured using ameasurement system mounted on the vehicle and itwas also verified using distance measuring wheel

On the basis of the experimental data the total rolling resis-tance coefficient of the vehicle was determined Table 4 showsthe coefficients of rolling resistance of the vehicle dependingon the tire used during the test Total resistance includesthe tire rolling coefficient the bearings resistance and theresistance of the clutch Verification of the data derived fromthe simulation and the experiment was conducted using

12 Journal of Advanced Transportation

Table 3 The types of tires used in the prototype vehicle

Tiresmarker Name of the tire Tirersquos

symbol Shape Type of tread Workingpressure

W1

Michelin ShellEco-marathon 4575R16 Rectangular Slick max500 [kPa]

W2

SchwalbeUl-Termo 23-406 Round Slick 600-1100 [kPa]

W3

Continental SportContact 28-406 Round Slick 600 [kPa]

W4

SchwalbeMarathon 40-406 Round Symmetrical 400-700 [kPa]

Table 4 The total rolling coefficient depending on the tires

Tiresmarker Name of the tire The total rolling coefficient crr mMAPE []

W1 Michelin ShellEco-marathon 00035 784W2 Schwalbe Ultermo 00043 1103W3 Continental SportContact 00058 1252W4 Schwalbe Marathon 00053 445

0

1

2

3

4

5

6

7

8

V [m

s]

100 200 300 400 500 6000x [m]

W1rW1simW2rW2sim

W3rW3simW4rW4sim

Figure 12 Velocity of the vehicle during coast down test

mMAPE (modifiable Mean Absolute Percentage Error) Forvelocity simulationmMAPE can be determined by

119898119872119860119875119864 = 1001119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119881119903 minus 119881119904119894119898119881119898119886119909 minus 119881119898119894119899

10038161003816100381610038161003816100381610038161003816 (29)

Figure 12 shows the experimental data obtained in a coastdown test compared with the results obtained during thecomputer simulation

54 Model of the Race Circuit In accordance with themethodology presented in Section 32 three routes have beendescribed

(i) Route 1 a street race circuit at the Shell Eco-marathoncompetition in Rotterdam

Figure 13 Plan view of the path of the drive on route 1 in Rotterdam

(ii) Routes 2 and 3 on the experimental rides track of theFiat Chrysler Automobiles Poland factory located inTychy in the south of Poland

The Shell Eco-marathon competition is held on a streetcircuit in Rotterdam One lap is 1630 meters long Vehicleshave to cover ten laps in no longer than 39 minutes so suchrequirements impose an averageminimum speed of 25 kmh

The trajectory of the vehicle path was developed usingsatellite images The vehicle trajectory was determined usingthe maximum curvature possible that could be obtained onthe existing roads

Movement of the vehicle in a curved motion causesthe centrifugal force Centrifugal force creates additionalresistance This resistance is inversely proportional to theradius of the path (8) so it is justified to select the largestradius In addition if the centrifugal force exceeds thelimit value it could provide to the side slip of the vehicleAccording to drawings in AutoCAD Civil 3D the lengths ofstraight sections and the lengths and the radius of arcs wereobtained Figure 13 shows a plan view of the path of the drive

Driving the prototype vehicle on public roads is prohib-ited and can be dangerous Vehicle testing was also carried

Journal of Advanced Transportation 13

Table 5 Travel times and total lengths of the routes

Route Length of the lap D [m] The numberof laps The total length of the route Dc [m] Travel time Tmax [s]

Route 1Rotterdam 1630 10 16 300 2340

Route 2Tychy 640 5 3200 460

Route 3Tychy 1000 5 5000 720

Figure 14 Plan view of the path of the drive on route 3 in Tychy

out on the experimental rides track of the Fiat ChryslerAutomobiles Poland factory

For the track in Tychy geodetic measurements weretaken using theDGPS (Differential Global Positioning System)technology The measuring points were collected along theaxis of the road with the distance between points amountingto 10 meters If on the measured route direction or elevationwere changed the frequency of measurement was increasedGeodetic coordinates were also imported intoAutoCADCivil3D and were used to prepare data concerning the route thatwas imported into the simulation environment MATLAB-Simulink Figures 14 and 15 show the path and elevationprofile respectively

Selected routes 2 and 3 have significant differences com-pared to route 1 especially in the height profile This set ofroutes was selected to verify the effect of the route profile onthe achieved results and to verify the proposed optimizationmethods for various road conditions The routes in Tychyare located in an open area there are no large buildingswhich guarantees stability of wind conditions The technicalcondition of the surface on routes 2 and 3 is much worsethan on route 1 which has a significant influence on therolling resistance Rolling resistance was also identified andintroduced into the simulation model For route 2 the c119903119903coefficient was 00056 and for route 3 was 00068

55 Verification of the Simulation Model In order to verifythe compatibility of the identified simulation model a seriesof numerical simulations and experimental tests were per-formed The first experiment consisted of running 300 [m]with a control strategy of 50 [m] with the workingmotor andafter that the vehicle was moving freely for the next 50 [m]The motor is turned on three times Figures 16(a) and 16(b)show the velocity of the vehicle and the power of the motorin function of the distance determined during the experiment

(red curves) and during the numerical simulations (greencurves)

Verification of the data derived from the simulation andthe experimentwas conducted usingmMAPE (29) Formotorpower simulationmMAPE can be determined by

119898119872119860119875119864119875 = 1001119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119875119903 minus 119875119904119894119898119875119898119886119909 minus 119875119898119894119899

10038161003816100381610038161003816100381610038161003816 (30)

where P119903 is the motor power measured during experimentand P119904119894119898 is the motor power conducted in simulation

As a result of the model validation tests estimationerror of the velocity was on level between 235 and 534However the motor power error level was greater It wasbetween 802 and 998

56 Determination of the Optimal Control Strategy Thelength of route 1 and the number of laps are determined bythe organizers of the Shell Eco-marathon competition Thelength of routes 2 and 3 is derived from the existing road planwhere it was possible to carry out trials in real conditionsThenumber of laps for routes 2 and 3 was assumed arbitrarily

The travel time for route 1 is based on the rules of therace which determine the minimum average speed of thevehicle Based on the average speed and the length of routes 2and 3 the travel times for these routes were determined Themaximum travel times and the total length of the route aswell as the number and length of one lap D are summarizedin Table 5

Evolutionary algorithms which are available in theMAT-LAB Global Optimization Toolbox were used From theMATLAB workspace the algorithm ran a simulation modelin a Simulink environment During optimization while usingevolutionary algorithms the maximum number of fitnessfunction evaluations 119873119891V119886119897

is the product of the populationsize 119873119901119900119901 and number of generations 119873119892119890119899

It was assumed that the total number of fitness functionevaluations was equal to 104 therefore should this value beexceeded the calculation would be cancelled Therefore thetotal number of generations 119873119892119890119899 is dependent on the valueof population size 119873119901119900119901

As part of this work phase the vectors st119880 st119881 15 andst119881 10 of the optimum control strategy for an electric vehiclefor routes 1 2 and 3 were determined During evolutionaryoptimization the heuristic method of crossing was usedand the probability of crossing was established on the basisof previous studies at the level of 08 [24 29] At the

14 Journal of Advanced Transportation

0+000

106410

minus164 minus492minus166 minus012 minus018 minus082 minus035 059 031

811

0+100 0+200 0+300 0+400 0+500 0+600 0+700 0+800 0+900 1+000

Figure 15 Profile of the path on route 3 in Tychy

50 100 150 200 250 3000X [m]

0

2

4

6

8

10

V [m

s]

(a) DT1

0

100

200

300

400

500

P [W

]50 100 150 200 250 3000

X [m]

(b) DT1

Figure 16 The velocity and the power determined with used DT1 drive unit

stage of reproduction the elitist succession method wasapplied where the best adapted two individuals in the currentpopulation passed to the next population An adaptivemethod of mutation was used The remaining parameters ofthe algorithm remain the default for the MATLAB GlobalOptimization Toolbox

The first case was the search st119880 vector for route 1Figures 17(a)ndash17(c) show the vehicle velocity V119904119894119898 obtainedby computer simulation The graph of the st119880 control signalis graphically displayed Figure 17 shows the results wherethe optimal control strategy st119880119900119901119905 was used and populationwas 119873119901119900119901=100 and 119873119892119890119899=100 The total energy consumptionwas estimated as r119904119894119898=527633 [km kWh] Figure 17(a) showsthe vehicle speed and control signal st119880 during the first lapwhile Figure 17(b) shows center laps and Figure 17(c) showsthe last lap Figure 17(d) shows the curves of the mean valuesof the fitness functions f 119907119886119897 depending on the number ofcalculations of these functions during the optimization ofthe control strategy There are eight curves in the graph(Figure 17(d)) for each of the 119873119901119900119901 parameters used in thealgorithm

When analyzing the vehicle velocity chart on the last lapof route 1 (Figure 17(c)) it can be seen that according tothe determined control strategy the propulsion system of thevehicle should no longer be used The vehicle should use thestored kinetic energy

The analysis of vehicle velocity V119904119894119898 during the last lapindicates that at the moment of reaching the given distancethe speed was still about 2 [ms] This demonstrates thatthe simulated vehicle has kinetic energy that would haveto be dispersed by the braking system or recovered by the

electric motor Having such a speed does not mean that thereis still possibility for improvement Lower speed at the endof the route has to cause higher speed of the earlier partsof the route This speed is the optimum speed due to thechosen criterion From the analysis of the shape of the fitnessfunction (Figure 17(d)) it can be seen that for route 1 itis preferable to use a smaller population of 119873119901119900119901=25 andincrease the number of 119873119892119890119899=400 The curve shape for thiscase is steep and it falls to the minimum value of the fitnessfunction which may indicate that the algorithm has reacheda convergence

Results of the optimization where B type of coding wasused were analyzed The results obtained as the mean of ther119904119894119898 result together with the standard deviation from all thetests were summarized in Table 6

By analyzing the results in Table 6 it can be seen thatfor route 1 better results were obtained (reduced simulatedtotal energy consumption) using A coding compared to Bespecially for st119881 15 whose results are characterized by thehighest standard deviation For routes 2 and 3 the same as forroute 1 the procedure was followed Optimization strategieshave been optimized for all variants of control vector st119880st119881 15 st10

The results using the control strategy st119881 10 are shownin Figures 18(a)ndash18(c) (119873119901119900119901=100 where r119904119894119898=351795 [km kWh]) Figure 18(d) illustrates the graph of the value of thefitness function

The results obtained for route 2 are presented in Table 7For route 2 compared to route 1 the best results were

achieved using the stV10 vector When using vectors st119880 andstV15 the results were slightly worse Having analyzed the size

Journal of Advanced Transportation 15

0

2

4

6

8

10V

[ms

]

VsimstU

500 1000 15000X [m]

(a) Lap 1

0

2

4

6

8

10

V [m

s]

2500 30002000X [m]

VsimstU

(b) Laps 2-9

0

2

4

6

8

10

V [m

s]

155 1615X [m]

Vsimstu

times104

(c) Lap 10

times10minus3

Npop=25Npop=50Npop=75Npop=100

Npop=125Npop=150Npop=175Npop=200

15

2

25

3

35

4f va

l

2000 4000 6000 8000 100000Nfval

(d) Mean values of the fitness functions

Figure 17 Vehicle speed and control signal st119880 for route 1

Table 6 The results for route 1

The type of coding A The type of coding Bst119880 st11988115 st11988110119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 52465 1459 42845 1741 51569 5477550 52579 10053 44431 22486 51492 3409475 52497 39913 43842 28173 51256 80682100 52589 18128 42232 1797 51166 49379125 52625 13862 42733 39616 51341 70765150 5243 2979 4435 47701 51486 27086175 52513 2511 41428 27299 51838 19358200 52579 19666 42337 25776 51204 78357

16 Journal of Advanced Transportation

100 200 300 400 500 6000X [m]

0

2

4

6

8

10V

[ms

]

VsimstV10

USET

(a) Lap 1

0

2

4

6

8

10

V [m

s]

800 900 1000 1100 1200700X [m]

VsimstV10

USET

(b) Laps 2-4

0

2

4

6

8

10

V [m

s]

2700 2800 2900 3000 3100 32002600X [m]

VsimstV10

USET

(c) Lap 5

times10minus3

Npop=25Npop=50Npop=75Npop=100

Npop=125Npop=150Npop=175Npop=200

275

28

285

29

295

3

305

f val

2000 4000 6000 8000 100000Nfval

(d) Mean values of the fitness functions

Figure 18 Vehicle speed and control signal st11988110 for route 2

of the population used in the optimization process it shouldbe noted that for route 2 it is preferable to use higher value of119873119901119900119901 For all the analyzed cases the best average results for119873119901119900119901=200 were obtained Table 8 summarizes the results forroute 3

For route 3 the average results were reported for a largerpopulation of119873119901119900119901 with B coding In the case of using vectorwith A type coding no characteristic change was notedAs expected comparing the standard deviation betweenalgorithms using B coding the standard deviation is less forthe less variance range

Evolutionary algorithms are not complete search algo-rithms therefore it is not possible to determine whetherthe solution found is best for the chosen criterion and theconstraints assumed

57 Applying the Optimal Control Strategy in Real ConditionsElectric vehicle energy consumption optimization was finallyverified in real conditions at the European edition of the ShellEco-marathon held on 16-18 May 2014 in Rotterdam

Optimal control strategy st119880was displayed by a prototypevisualization system Visualization unit is installed in the

Journal of Advanced Transportation 17

Table 7 The results for route 2

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 34138 66734 34294 23839 34873 5353250 34573 46359 35003 462 3506 3886275 34512 55134 34961 33476 35419 067858100 34836 45332 35253 26117 3544 19295125 34632 52704 35017 49039 35483 14756150 34552 63714 35326 14885 35343 071015175 35063 18728 35274 47141 35564 038022200 35073 14496 3540 13389 35569 14942

Table 8 The results for route 3

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 28071 10173 28643 7323 30994 277650 29346 6142 29581 7894 30874 439975 29711 5002 29217 7367 31141 1856100 29826 3231 29515 7022 30957 4049125 29781 2980 29866 12977 31168 3445150 29453 3346 30217 9623 31288 1249175 29234 2317 30621 6816 31481 1261200 29686 2337 30531 11737 31089 4880

Table 9 Comparison of simulation results with experimental tests

Number of attempts 119903119878119864ndash119898 119903119903 119903119904119894119898 119903119900119901119905 119890119898 119890119894 119890119904119905Attempt 1 3654 3608 - - 125 - -Attempt 2 4813 5082 5148 5265 558 129 36Attempt 3 4873 5127 5198 5265 521 139 269Attempt 4 Failed attempt damaged tires during 1st lap

steering wheel of the vehicle The visualization system showsthe basic data such as instantaneous speed average speedtravel time and distance In addition the visualization systemprovides information on which part of the track the drivershould press the acceleration button to execute the optimalcontrol strategy Measurement of the position on the track iscarried out by the odometrical measuring system Due to thepossibility of accumulating errors in the measurement of theroad the driver will reset the measuring system every timeheshe exceeds the lap line

Table 9 presents the results of all the measurementsconducted during the Shell Eco-marathonThe columns in theTable 9 contain

(i) r119878119864119898 [kmkWh] the result recorded during the raceby the measuring device provided by the organizerthe results are available on the Shell Eco-marathonofficial website

(ii) r119903 [kWkWh] the result based on the indications of aprototypemeasuring system permanently installed inthe vehicle

(iii) r119904119894119898 the result estimated by computer simulationusing recorded real control signal U119903

(iv) r119900119901119905 the result obtained by computer simulation usingthe optimal control strategy U119900119901119905

Table 9 also includes the following

(i) Measurement error

119890119898 = 1003816100381610038161003816119903119878119864119898 minus 1199031199031003816100381610038161003816119903119878119864119898 100 (31)

(ii) Identification error

119890119894 =1003816100381610038161003816119903119903 minus 1199031199041198941198981003816100381610038161003816119903119903 100 (32)

(iii) Strategy implementation error

119890119904119905 =10038161003816100381610038161003816119903119903 minus 11990311990011990111990510038161003816100381610038161003816119903119903 100 (33)

18 Journal of Advanced Transportation

There were four measurement trials available Duringrun 1 a much weaker result was obtained than estimated bysimulation The driver performed run 1 without a definedcontrol strategy As part of the experiment the driver andthe support team were asked to select the optimal tires forthe vehicle and to implement the proposed control strategyDuring run 1 only the travel time of individual laps waschecked According to the choice of the team in run 1 tiresW2 were selected (Table 4) During this test the worst resultwas obtained about 24 and 25 worse than in the othertrials In subsequent runs 2 and 3 the vehicle was equippedwith the best W1 tires (Table 4) The driver has implementedan algorithm-based optimal control strategy Strategy infor-mation was provided by the visualization system During run3 the best result was recorded This result was taken intoaccount in the classification of competitions where the teamplaced in 12 positions out of 28 classified teams Trials 4 dueto damage to the tires were not successful

Measurement error was from 125 to 558 dependingon the sample The measurement system installed perma-nently in the vehicle is a prototype system This systemhas been calibrated using available laboratory equipmentMeasurement errors indicate that other measuring devices ofthe higher accuracy class should be used

Based on the measurement data obtained during testdrives the model was tuned thus reducing the identificationerror The competition took place in stable weather thedivergence of results was small and was about 129 forsample 2 and 139 for sample 3

The difference between the results determined duringnumerical simulation and that obtained in the real run was36 for sample 2 and 269 for sample 3 The difference atthis level was considered to be small Searching for optimalcontrol strategy has not taken into account possible rdquoerrorsrdquowhich could be made by the driver and which result fromthe current situation on the route for example selecting thepath and using the route by other participants in the raceIncluding driver behaviour in the simulation model shouldbe the subject of further work

Figure 19 shows the vehicle velocity together with thecontrol signals recorded during run 2 The black curvesrepresent the real vehicle velocity V119903 and the control signalGreen curves are the optimum control strategy st119880 andthe optimal velocity V119900119901119905 determined by the simulationThe graph shows the entire distance travelled (10 laps) Theanalysis of the graph shows that the driver did not performthe exact planned strategy Errors in the implementationof the strategy are related to the disruptions During thecompetition the driver is not alone on the track in certainsituations the driver cannot overtake other participants andcannot take the optimal path In addition weather conditionsuch as wind has influence on the motion resistance In suchcases the driver has to modify the optimal control strategy

In Figure 20 the velocity recorded during the race V119903(black) and the velocity obtained by the computer simulationV119904119894119898 (red) were shown V119904119894119898 was determined by computersimulation by using real control signal The purpose of thissimulation was to investigate the correctness of identification

VrVopt

Ur Uopt

2000 4000 6000 8000 10000 12000 14000 16000 180000X [m]

05

10152025303540

V [k

mh

]

Figure 19 Comparison of speed and control signal during attempt2

2000 4000 6000 8000 10000 12000 14000 16000 180000x [m]

05

10152025303540

V [k

mh

]

Ur

VrVsim

Figure 20 Comparison of speed registered in real conditions withthe speed determined by computer simulation

of the simulation model and to identify the identificationerror

Compared to the Shell Eco-marathon competitions heldin 2012 and 2013 our performance has improved The resultsin these years were equal to 425 [km kWh] and 454[km kWh] respectively In 2012 and 2013 the controlstrategy was chosen on the basis of the simulation modelbut the model was not adequately identified and the controlstrategy had to be modified In previous editions of therace the implementation of optimal control strategy was notsupported by the visualization system which would informthe driver of the need to take specific actions (pressing orreleasing the accelerator button)

6 Conclusion

The presented method was developed and tested for aprototype electric racing car that has been designed for theShell Eco-marathon race As it was shown the results of thenumerical simulations were very similar to the outcomes ofthe real races in the context of the final result of energyconsumption and the profile of velocity of the car during therace The method has been developed and applied since 2012

Journal of Advanced Transportation 19

and led in 2014 to achieving the optimal result for this type ofthe vehicle

The optimization method was evaluated The resultsachieved during the race attempts where the optimal con-trol strategy was applied (4813 and 4873 kmkWh) werecompared to the result where the strategy was proposed bythe experts (3654 kmkWh) who already had contact withthe results of similar optimization models Optimal attemptswere better by over 30 despite errors in the implementationof the strategy by the driver In the case of experts who did nothave such experiences the differences were even greater

Further improvement of the control strategy is impossiblefor this type of a vehicle and the best way to reduce energyconsumption is by improving the mechanical design It wasthe reason to develop new racing cars for UrbanConceptBattery Electric and Hydrogen competitions The developedresearch methodology for vehicle optimization and controlstrategies has been developed and implemented in the ShellEco-marathon in 2015 which has improved the score to 504km kWhHowever the research has shown that the potentialfor improved performance of the MuSHELLka vehicle hasbeen exhausted No major structural changes in the vehiclecan significantly improve the result so in the followingyears the race was abandoned and the focus was on thedevelopment of the HydroGENIUS the electric vehicle ofUrbanConcept class with fuel cell stack as power sourcewhich eventually scored vice Championship in SEM 2016 Inthe further work it is planned to improve the optimizationresults by using the presented methodology in the case ofthe models of newly constructed vehicles The developmentof the optimization method should take into considerationthe uncertainty resulting from the given velocity strategyconsidering the real conditions of the race It is also possibleto use this method for controlling vehicles in traffic To dothis it is necessary to completely change the way of the routemodelling and the driving conditions modelling as well as todevelop a new optimization method for obtaining results inreal time

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] W Skarka ldquoReducing the Energy Consumption of ElectricVehiclesrdquo in Proceedings of the 22nd ISPE-Inc InternationalConference on Concurrent Engineering Location R Curran NWognumM Borsato et al Eds Advances in TransdisciplinaryEngineering pp 500ndash509 IOS Press Delft Netherlands 2015

[2] R Andrzejewski and J Awrejcewicz Nonlinear Dynamics of aWheeled Vehicle vol 10 Springer-Verlag New York NY USA2005

[3] D W Gao C Mi and A Emadi ldquoModeling and simulation ofelectric and hybrid vehiclesrdquo Proceedings of the IEEE vol 95 no4 pp 729ndash745 2007

[4] ldquoAdvisor documentationrdquo httpadv-vehiclesimsourceforgenet

[5] TMarkel A Brooker THendricks et al ldquoADVISORA systemsanalysis tool for advanced vehicle modelingrdquo Journal of PowerSources vol 110 no 1 pp 255ndash266 2002

[6] K B Wipke M R Cuddy and S D Burch ldquoADVISOR21 a user-friendly advanced powertrain simulation using acombined backwardforward approachrdquo IEEE Transactions onVehicular Technology vol 48 no 6 pp 1751ndash1761 1999

[7] ldquoWebsiterdquo 2014 httpwwwtransportationanlgovmodeling[8] ldquoWebsiterdquo 2014 httpwwwautonomienet[9] K Krykowski J Hetmanczyk Z Gałuszkiewicz and R Mik-

siewicz ldquoComputer analysis of high-speed PM BLDC motorpropertiesrdquo COMPEL - The International Journal for Computa-tion and Mathematics in Electrical and Electronic Engineeringvol 30 no 3 pp 941ndash956 2011

[10] M Vaillant M Eckert and F Gauterin ldquoEnergy managementstrategy to be used in design space exploration for electricpowertrain optimizationrdquo inProceedings of the 2014 9th Interna-tional Conference on Ecological Vehicles and Renewable EnergiesEVER 2014 mco March 2014

[11] A T Nguyen S Reiter and P Rigo ldquoA review on simulation-based optimization methods applied to building performanceanalysisrdquo Applied Energy vol 113 pp 1043ndash1058 2014

[12] W Silka and W Siłka Energy Intensity in the Car Traffic InPolish WNT Warszawa 1997

[13] T J Barlow S Latham I S Mrcrae and P Boulter A referencebook of driving cycles for use in the measurement of roadvehicle emissions TRL 2009 httpswwwgovukgovernmentuploadssystemdata

[14] R N Jazar Vehicle Dynamics Theory and Application SpringerUS Boston MA 2008

[15] MMeywerk ldquoVehicle Dynamicsrdquo inWest Sussex JohnWiley ampSons Lecture Notes to theMOOCVehicle Dynamics of iversity1st edition 2015

[16] MMitschke andHWallentowitzDynamik der KraftfahrzeugeSpringer Berlin Germany 1972

[17] T Stefanski and Ł Zawarczynski ldquoParametric identification ofPM motor mathematical modelsrdquo Przegląd Elektrotechnicznyvol 88 no 4 B pp 224ndash229 2012

[18] A Cameron ldquoMeasuring drive-train efficiencyrdquoHuman Powervol 46

[19] B Rohloff and P Greb ldquoEfficiency measurements of bicycletransmissions a neverending storyrdquo Human Power vol 55 p11 2004

[20] J B Spicer C J K Richardson M J Ehrlich J R BernsteinM Fukuda and M Terada ldquoEffects of frictional loss on bicyclechain drive efficiencyrdquo Journal of Mechanical Design vol 123no 4 pp 598ndash605 2001

[21] K Sternal A Cholewa W Skarka and M Targosz ldquoElec-tric vehicle for the studentsrsquo shell eco-marathon competitionDesign of the car and telemetry systemrdquo Communications inComputer and Information Science vol 329 pp 26ndash33 2012

[22] K Cichonski and W Skarka ldquoInnovative control system forhigh efficiency electric urban vehiclerdquo Communications inComputer and Information Science vol 531 pp 121ndash130 2015

[23] M J Er and R J Oentaryo ldquoComputational IntelligenceMethods andTechniques (Rutkowski L 2008) [BookReview]rdquoIEEE Computational Intelligence Magazine vol 6 no 4 pp 76ndash78 2011

[24] M Targosz M Szumowski W Skarka and P PrzystałkaldquoVelocity Planning of an Electric Vehicle Using an Evolutionary

8 Journal of Advanced Transportation

D

L2L1 Ln

O2O1 On

Figure 8 Concept of discretization of the route

whereas in the second case for control scheme B

st119900119901119905V = [1198811198781198641198791 1198811198781198641198792 119881119878119864119879119899]119879 119881119878119864119879119894 isin 119881119898119894119899 119881119898119886119909

(14)

where119881min and119881max can be determined in different ways egbased on the minimummaximum vehicle speed or based onthe simple calculation corresponding to guidelines of the racecompetition

Evolutionary algorithms can be used to solve this prob-lem In the case of the search for strategy st119900119901119905119880 it is preferableto use a classical genetic algorithm In this instance the genesin a chromosome of the individual can be encoded directlyas the binary values of the control signal 119880119878119864119879119894 Thereforethe length of the chromosome N119888ℎ is equal to the number ofsections of the route

In accordance with the control scheme B the velocityprofile is determined as the vector including setpoint valuesof the velocity st119900119901119905119881 The components of the st119900119901119905119881 vectorare floating point values hence it is possible to use anevolutionary strategy proposed in [23] Each of the genes inthe chromosomeof the individual corresponds to the setpointvalue of the velocity during a part of the route

42 Chromosome Codding for Different Velocity StrategiesFor a vehicle that is equipped with a binary control systemof the motor the chromosome can be represented as theoptimal vector of the control signal in the following formst119900119901119905119880 = [1198801198781198641198791 1198801198781198641198792 119880119878119864119879119899]119879 119880119878119864119879119894 isin0 1 for eachsegment O119894 of the route (for control scheme A) or the

optimal vector of the control signal in the second form st119900119901119905119881= [1198811198781198641198791 1198811198781198641198792 119881119878119864119879119899]119879 119881119878119864119879119894 isin [119881min 119881max] for eachsegment O119894 of the route (for control scheme B)

In this optimization task the total distance of the roadD119862is composed of SEM race laps N119905119900 isin1 2 119873 The divisionof the whole route on a finite number of segments O119894 is notrecommended because it can lead to unnecessary increase inthe length of the vector st If the route consists of a minimumof four laps it is possible to limit the search of vector st toonly three types of laps

(i) the initial lap marked by 119874119894119904(ii) the middle laps marked by 119874119894119898(iii) the last lap marked as 119874119894119891Such assumption can be proven for at least three reasons(1) In the practical implementation of velocity strategies

the driver should not implement different control rules foreach lap The master control unit informs the driver aboutthe current velocity strategy but despite all the driver shouldremember this strategy to some extent

(2)The limitation of the velocity strategy only to the threetypes of laps reduces the length of the vector st In this waythe number of elements of the vector st corresponds to thenumber of decision variables of the optimization task

(3) Such division is reasonable by the nature of the laps Inthe initial lap it is necessary to accelerate the vehicle Withinthe middle laps the velocity profile of the vehicle should bethe same During the last lap the previously acquired kineticenergy E119896 is utilized

The task of finding the optimal vector st119900119901119905 can be solvedusing two types of evolutionary algorithms

(i) Classical genetic algorithm for control without avelocity regulator (according to control scheme A presentedin Figure 6)

(ii) Evolutionary strategy for the control system of thevehicle with a velocity regulator (according to control schemeB shown in Figure 7)

Theusage of two algorithms forces the appropriate codingof the velocity strategy which is described in the next twoparagraphs

421 Chromosome Coding For Control Scheme A The phe-notype of each individual determines the control vector st119906that means each gene of the individual of the population isthe value of the control signal 119880119878119864119879119894 for each section of thesegment O119894 of the route Assuming that we are looking for avelocity strategy of only three types of laps the phenotype canbe written as (for short form U equiv 119880SET)

st119880 = [ 1198801119904 1198802119904 119880119899119904 1198801119898 1198802119898 119880119899119904 1198801119891 1198802119891 119880119899119891 ]119879 (15)

where 119880119894119904 119880119894119898 119880119894119891 are the control signals for the initial lapmiddle laps and the last lap

422 Chromosome Coding for Control Scheme B In thiscase the elements in the vector 119881119878119864119879119894 change over a wide

Journal of Advanced Transportation 9

range and can assign real number values In the evolutionarystrategy the phenotype of each individual takes the followingformst119881

= [ 1198811119904 1198812119904 119881119899119904 1198811119898 1198812119898 119881119899119904 1198811119891 1198812119891 119881119899119891 ]119879 (16)

119881119894119904 119881119894119898 119881119894119891 are the setting values of velocity for the initiallap middle laps and the last lap

In the control mode according to scheme B the controlsignal is generated by the velocity controller based on thecontrol error

e119881 = 119881119878119864119879 minus 119881119904119894119898 (17)

where

U119878119864119879 = 1 for e119881 ge 10 otherwise

(18)

The coding for control scheme B in comparison withthe coding for control scheme A has undoubtedly oneadvantage namely the possibility of introducing a velocitylimit during the simulation of the passage of a given sectionof the route A velocity limitation is of great practicalimportance In many situations it is necessary to reducethe velocity of the vehicle during certain parts of theroute for example during cornering Accordingly in caseof control scheme B two velocity vectors are designated asfollows

(i) st11988115 for 119881119878119864119879119894 = [0 15] ms although it is formallylimited to 15ms it can never be achieved because themaximum vehicle speed (based on maximum enginespeed) is approximately 15ms

(ii) st11988110 for 119881119878119864119879119894 = [0 10] ms

43 The Fitness Functions In the case of evolutionary opti-mization the fitness function f 119907119886119897 has to be designed Thissection describes the formulas used to calculate the fitnessfunction of an individual that is needed for solving a task ofevolutionary optimization Each chromosome is a potentialsolution Each control strategy st is used during numericalsimulation The value of the fitness function f 119907119886119897 can becalculated based on the outcomes of the simulation suchas

(i) the total energy consumption r119904119894119898 [kmkWh](ii) the simulation time t119904119894119898(iii) the distance x119904119894119898

and limitations such as

(i) the maximum travel time T119898119886119909(ii) the total distance of the vehicle D119862The value of the function is also used to evaluate the

velocity strategy of the vehicle In the preliminary studies[24] the following fitness function f 119907119886119897 was used

Fitness Function 1

119891V1198861198971 = 11990811198911 + 11990821198912 + 11990831198913 (19)

where

1198911 = [1 + 1199031205821119904119894119898]1205821 (20)

1198912 = [119867 (119863119888 minus 119909119904119894119898) 1003816100381610038161003816119863119888 minus 1199091199041198941198981003816100381610038161003816119863119888 ]1205822 (21)

1198913 = [119867 (119905119904119894119898 minus 119879max)1003816100381610038161003816119879max minus 1199051199041198941198981003816100381610038161003816119879max

]1205822 (22)

where the weights w1 = 050E05 w2 = w3 = 025 andcoefficients 1205821 = minus2 1205822 = 1 were chosen experimentally Thepenalty functions f 2 and f 3 were introduced The Heavisidestep functionH() is used to penalize individuals representingunacceptable solutions [25 26] eg those that exceed themaximum time of the simulation H(t119904119894119898 minus T119898119886119909) or do notreach the specified distance H(D119888 minus x119904119894119898)

Fitness Function 2 In this study the authors have proposedthe fitness function which would lead to the convergenceof the evolutionary algorithm without searching for optimalvalues of weights Such a function is shown and describedbelow

119891V1198861198972 = 1 + 1198914 + 1198915119891111989121198913 (23)

1198911 = 119903119904119894119898 (24)

1198912 = cos(1003816100381610038161003816119863119888 minus 1198891199041198941198981003816100381610038161003816119863119888 ) (25)

1198913 = cos(1003816100381610038161003816119879max minus 1199051199041198941198981003816100381610038161003816119879max) (26)

1198914 = 120594 sdot 119867 (119863119888 minus 119889119904119894119898) (27)

1198915 = 120594 sdot 119867 (119879max minus 119905119904119894119898) (28)

where f 1 is a measure related to the simulated energyconsumption of the vehicle f 2 and f 3 correspond to thelimitations such as the maximum travel time and the totaldistance of the vehicle f 4 and f 5 also correspond to the limi-tations but these play strong penalty role and 120594 is arbitrarilylarge value eg significantly higher than maximal valuesf 2=f 3 =1 In this variant of the fitness function death penalty[26] is applied for unacceptable individuals in the form offactors f 4 and f 5 Individuals who do not reach a specifieddistance or exceed the time limit are eliminated These twocriteria act as a constraint and correspond to the limitationsformulated in the guidelines of the race competition On theother hand the criteria f 2 and f 3 have continuous nature andplay very important role in the fitness functionThey are veryneeded to evaluate continuously the individuals that are veryclose to and very far from the extremum

The argument of cos() function is not related to anangle However the usage of the cos() function is needed to

10 Journal of Advanced Transportation

Table 1 Research object main parameters

Type of the motor PM BLDCTransmission unit Toothed synchronous beltThe minimum turning radius 8 [m]The battery type and capacity Lithium-ion polymer 2100[mAh]Mass of the vehicle 42 [kg]Mass with the driver min 92 [kg]Diameter of wheels 0478 [m]Moment of inertia of the front wheel 119868119896119875 0023 [kgm2]Moment of inertia of the rear wheel 119868119896119879 0023[kgm2]Drag coefficient cx (see Table 2) 022 ndash 023Frontal area A [m2] (see Table 2) 0275 - 0297The total rolling coefficient crr (see Table 4) 00035 ndash 00058

eliminate the possibility of dividing by zero In addition theform of the cos() function is preferred At the initial stage ofoptimization when the simulation time t119904119894119898 and the distancex119904119894119898 differ significantly from the maximum time T119898119886119909 andthe specified distance D119888 a small change will have a greatereffect on the value of the fitness function At the final stageof optimization the function 119891V1198861198972 is more dependent on thesimulated energy consumption of the vehicle related to thefactor f 1 and thanks to the cos() function it is less dependentto the factors f 2 and f 3 The proposed function does notrequire the introduction of weights and therefore it is easierto use this function in other applications eg to find optimalvelocity strategies for different routes

It should be noted that fitness functions 119891val have beenwritten in such a way as to ensure that the optimizationalgorithm will look for a minimum of these functions

5 Case Study

As described in Sections 3 and 4 process of modelling andoptimization was applied and verified using a prototypeelectric vehicle on street race circuit in Rotterdam Themethodology was also carried out on the experimental ridestrack of the Fiat ChryslerAutomobiles Poland factory locatedin Tychy Based on (5)-(12) the simulation model was cre-ated in the MATLABSimulink environment Optimizationwas also carried out in MATLAB using the evolutionaryalgorithms available in the Global Optimization Toolbox Thelibrary of functions for simulating optimizing analyzingand presenting results has been developed

51 Research Object Light electric vehicle was a researchobject The vehicle shown in Figure 9 is a three-wheeledself-supporting structure The vehicle fuselage is made ofcomposites based on epoxy resin and woven of carbon andaramid fibre [21]

The dimensions of the vehicle and basic data are shownin Figure 10 and in Table 1

Identification of parameters for the mathematicalmodel of a research object was carried out by numericalsimulations tests on specially designed test bench [27]

Figure 9 Research object prototype electric vehicle ldquoMuSHELLkardquo(photo by M Wylezoł 2012)

and during conducted experiments in real environment[28]

The vehicle can be driven by two types of drive unit(i) DT1 drive unit based on PM BLDC motors and belt

transmission Drive wheel is equippedwith a one-wayclutch

(ii) DT2 a high-torque PMBLDCmotor mounted insidethe drive wheel The torque generated by the motor isdirectly transmitted to the rear drive wheel

The catalogue data can be used for creating the mathematicalmodel of the DT1 motor but for identifying the exactparameters it was necessary to carry out experimental testsThe manufacturer of the DT2 motor does not provide muchinformation so it was necessary to test the drive unit aswell DT1 drivetrain efficiencywas estimated using aBG75x50motor with toothed synchronous belt transmission ( z1= 28teeth z2 = 200 teeth i119879119878 = 714) The map of the efficiencywas shown on Figure 11(a) The same test was carried out forDT2 drive unit with a motor directly mounted on the drivewheel (Figure 11(b)) The obtained efficiency maps were usedto build the simulationmodel of the tested drivetrain systems

52 Determination of Air Drag Coefficient The air dragcoefficient c119909 was estimated as a result of CFD analysis usingANSYS software [24] and it was also verified by the researchin wind tunnel at the Institute of Aviation inWarsaw Frontalarea of vehicle A was determined from a three-dimensionalmodel in CAD environment Catia V5 The values of dragcoefficient c119909 and frontal area A are shown in Table 2

Journal of Advanced Transportation 11

623

972

1600

2605

Figure 10 Dimensions of the vehicle

(a) DT1 (b) DT2

Figure 11 Maps of the efficiency of tested drivetrain systems

Table 2 The air drag coefficient and frontal area

cx numericalsimulation

cx experimentalresearch Frontal area A [m2]

023 022 0275 0297

53 Determination of Rolling Resistance According to for-mula (7) the rolling resistance depends on the weight of thevehicle (Table 1) the tires rolling resistance coefficient andthe resistance of the bearings Depending on the drive unit(DT1 DT2) used in the vehicle additional resistance has to beadded In theDT1 system there is a one-way clutchwhich alsogenerates some resistance torque The DT2 system cannot bemechanically disconnected and therefore has a higher rollingresistance As a result of the coast down test the total rollingresistance of the vehicle has been identified for the four typesof tiresThe test was performed only with theDT1 system iethe systemwith the clutch Table 3 shows the basic parametersof the tires used in the experiments

The prototype vehicle can be equipped with speciallymanufactured Michelin tires with a low rolling resistantcoefficient of c119903119903 = 00014

In addition to the specialMichelin tires three other typesof tires were tested The identification of rolling resistance

coefficients was also estimated using a coast down test Themeasurements were made as follows

(i) The driver accelerated the vehicle to a fixed speed(ii) At themoment of crossing themarked gate the driver

pressed the marker button to save the flag in theacquired data

(iii) The run continued until free braking after which thedriver switched off the measuring system

(iv) The measurements were made at both directions ofthe road to minimize influence of the wind

(v) Before the attempts wind velocity temperature andatmospheric pressure were measured

(vi) The distance of the road was measured using ameasurement system mounted on the vehicle and itwas also verified using distance measuring wheel

On the basis of the experimental data the total rolling resis-tance coefficient of the vehicle was determined Table 4 showsthe coefficients of rolling resistance of the vehicle dependingon the tire used during the test Total resistance includesthe tire rolling coefficient the bearings resistance and theresistance of the clutch Verification of the data derived fromthe simulation and the experiment was conducted using

12 Journal of Advanced Transportation

Table 3 The types of tires used in the prototype vehicle

Tiresmarker Name of the tire Tirersquos

symbol Shape Type of tread Workingpressure

W1

Michelin ShellEco-marathon 4575R16 Rectangular Slick max500 [kPa]

W2

SchwalbeUl-Termo 23-406 Round Slick 600-1100 [kPa]

W3

Continental SportContact 28-406 Round Slick 600 [kPa]

W4

SchwalbeMarathon 40-406 Round Symmetrical 400-700 [kPa]

Table 4 The total rolling coefficient depending on the tires

Tiresmarker Name of the tire The total rolling coefficient crr mMAPE []

W1 Michelin ShellEco-marathon 00035 784W2 Schwalbe Ultermo 00043 1103W3 Continental SportContact 00058 1252W4 Schwalbe Marathon 00053 445

0

1

2

3

4

5

6

7

8

V [m

s]

100 200 300 400 500 6000x [m]

W1rW1simW2rW2sim

W3rW3simW4rW4sim

Figure 12 Velocity of the vehicle during coast down test

mMAPE (modifiable Mean Absolute Percentage Error) Forvelocity simulationmMAPE can be determined by

119898119872119860119875119864 = 1001119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119881119903 minus 119881119904119894119898119881119898119886119909 minus 119881119898119894119899

10038161003816100381610038161003816100381610038161003816 (29)

Figure 12 shows the experimental data obtained in a coastdown test compared with the results obtained during thecomputer simulation

54 Model of the Race Circuit In accordance with themethodology presented in Section 32 three routes have beendescribed

(i) Route 1 a street race circuit at the Shell Eco-marathoncompetition in Rotterdam

Figure 13 Plan view of the path of the drive on route 1 in Rotterdam

(ii) Routes 2 and 3 on the experimental rides track of theFiat Chrysler Automobiles Poland factory located inTychy in the south of Poland

The Shell Eco-marathon competition is held on a streetcircuit in Rotterdam One lap is 1630 meters long Vehicleshave to cover ten laps in no longer than 39 minutes so suchrequirements impose an averageminimum speed of 25 kmh

The trajectory of the vehicle path was developed usingsatellite images The vehicle trajectory was determined usingthe maximum curvature possible that could be obtained onthe existing roads

Movement of the vehicle in a curved motion causesthe centrifugal force Centrifugal force creates additionalresistance This resistance is inversely proportional to theradius of the path (8) so it is justified to select the largestradius In addition if the centrifugal force exceeds thelimit value it could provide to the side slip of the vehicleAccording to drawings in AutoCAD Civil 3D the lengths ofstraight sections and the lengths and the radius of arcs wereobtained Figure 13 shows a plan view of the path of the drive

Driving the prototype vehicle on public roads is prohib-ited and can be dangerous Vehicle testing was also carried

Journal of Advanced Transportation 13

Table 5 Travel times and total lengths of the routes

Route Length of the lap D [m] The numberof laps The total length of the route Dc [m] Travel time Tmax [s]

Route 1Rotterdam 1630 10 16 300 2340

Route 2Tychy 640 5 3200 460

Route 3Tychy 1000 5 5000 720

Figure 14 Plan view of the path of the drive on route 3 in Tychy

out on the experimental rides track of the Fiat ChryslerAutomobiles Poland factory

For the track in Tychy geodetic measurements weretaken using theDGPS (Differential Global Positioning System)technology The measuring points were collected along theaxis of the road with the distance between points amountingto 10 meters If on the measured route direction or elevationwere changed the frequency of measurement was increasedGeodetic coordinates were also imported intoAutoCADCivil3D and were used to prepare data concerning the route thatwas imported into the simulation environment MATLAB-Simulink Figures 14 and 15 show the path and elevationprofile respectively

Selected routes 2 and 3 have significant differences com-pared to route 1 especially in the height profile This set ofroutes was selected to verify the effect of the route profile onthe achieved results and to verify the proposed optimizationmethods for various road conditions The routes in Tychyare located in an open area there are no large buildingswhich guarantees stability of wind conditions The technicalcondition of the surface on routes 2 and 3 is much worsethan on route 1 which has a significant influence on therolling resistance Rolling resistance was also identified andintroduced into the simulation model For route 2 the c119903119903coefficient was 00056 and for route 3 was 00068

55 Verification of the Simulation Model In order to verifythe compatibility of the identified simulation model a seriesof numerical simulations and experimental tests were per-formed The first experiment consisted of running 300 [m]with a control strategy of 50 [m] with the workingmotor andafter that the vehicle was moving freely for the next 50 [m]The motor is turned on three times Figures 16(a) and 16(b)show the velocity of the vehicle and the power of the motorin function of the distance determined during the experiment

(red curves) and during the numerical simulations (greencurves)

Verification of the data derived from the simulation andthe experimentwas conducted usingmMAPE (29) Formotorpower simulationmMAPE can be determined by

119898119872119860119875119864119875 = 1001119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119875119903 minus 119875119904119894119898119875119898119886119909 minus 119875119898119894119899

10038161003816100381610038161003816100381610038161003816 (30)

where P119903 is the motor power measured during experimentand P119904119894119898 is the motor power conducted in simulation

As a result of the model validation tests estimationerror of the velocity was on level between 235 and 534However the motor power error level was greater It wasbetween 802 and 998

56 Determination of the Optimal Control Strategy Thelength of route 1 and the number of laps are determined bythe organizers of the Shell Eco-marathon competition Thelength of routes 2 and 3 is derived from the existing road planwhere it was possible to carry out trials in real conditionsThenumber of laps for routes 2 and 3 was assumed arbitrarily

The travel time for route 1 is based on the rules of therace which determine the minimum average speed of thevehicle Based on the average speed and the length of routes 2and 3 the travel times for these routes were determined Themaximum travel times and the total length of the route aswell as the number and length of one lap D are summarizedin Table 5

Evolutionary algorithms which are available in theMAT-LAB Global Optimization Toolbox were used From theMATLAB workspace the algorithm ran a simulation modelin a Simulink environment During optimization while usingevolutionary algorithms the maximum number of fitnessfunction evaluations 119873119891V119886119897

is the product of the populationsize 119873119901119900119901 and number of generations 119873119892119890119899

It was assumed that the total number of fitness functionevaluations was equal to 104 therefore should this value beexceeded the calculation would be cancelled Therefore thetotal number of generations 119873119892119890119899 is dependent on the valueof population size 119873119901119900119901

As part of this work phase the vectors st119880 st119881 15 andst119881 10 of the optimum control strategy for an electric vehiclefor routes 1 2 and 3 were determined During evolutionaryoptimization the heuristic method of crossing was usedand the probability of crossing was established on the basisof previous studies at the level of 08 [24 29] At the

14 Journal of Advanced Transportation

0+000

106410

minus164 minus492minus166 minus012 minus018 minus082 minus035 059 031

811

0+100 0+200 0+300 0+400 0+500 0+600 0+700 0+800 0+900 1+000

Figure 15 Profile of the path on route 3 in Tychy

50 100 150 200 250 3000X [m]

0

2

4

6

8

10

V [m

s]

(a) DT1

0

100

200

300

400

500

P [W

]50 100 150 200 250 3000

X [m]

(b) DT1

Figure 16 The velocity and the power determined with used DT1 drive unit

stage of reproduction the elitist succession method wasapplied where the best adapted two individuals in the currentpopulation passed to the next population An adaptivemethod of mutation was used The remaining parameters ofthe algorithm remain the default for the MATLAB GlobalOptimization Toolbox

The first case was the search st119880 vector for route 1Figures 17(a)ndash17(c) show the vehicle velocity V119904119894119898 obtainedby computer simulation The graph of the st119880 control signalis graphically displayed Figure 17 shows the results wherethe optimal control strategy st119880119900119901119905 was used and populationwas 119873119901119900119901=100 and 119873119892119890119899=100 The total energy consumptionwas estimated as r119904119894119898=527633 [km kWh] Figure 17(a) showsthe vehicle speed and control signal st119880 during the first lapwhile Figure 17(b) shows center laps and Figure 17(c) showsthe last lap Figure 17(d) shows the curves of the mean valuesof the fitness functions f 119907119886119897 depending on the number ofcalculations of these functions during the optimization ofthe control strategy There are eight curves in the graph(Figure 17(d)) for each of the 119873119901119900119901 parameters used in thealgorithm

When analyzing the vehicle velocity chart on the last lapof route 1 (Figure 17(c)) it can be seen that according tothe determined control strategy the propulsion system of thevehicle should no longer be used The vehicle should use thestored kinetic energy

The analysis of vehicle velocity V119904119894119898 during the last lapindicates that at the moment of reaching the given distancethe speed was still about 2 [ms] This demonstrates thatthe simulated vehicle has kinetic energy that would haveto be dispersed by the braking system or recovered by the

electric motor Having such a speed does not mean that thereis still possibility for improvement Lower speed at the endof the route has to cause higher speed of the earlier partsof the route This speed is the optimum speed due to thechosen criterion From the analysis of the shape of the fitnessfunction (Figure 17(d)) it can be seen that for route 1 itis preferable to use a smaller population of 119873119901119900119901=25 andincrease the number of 119873119892119890119899=400 The curve shape for thiscase is steep and it falls to the minimum value of the fitnessfunction which may indicate that the algorithm has reacheda convergence

Results of the optimization where B type of coding wasused were analyzed The results obtained as the mean of ther119904119894119898 result together with the standard deviation from all thetests were summarized in Table 6

By analyzing the results in Table 6 it can be seen thatfor route 1 better results were obtained (reduced simulatedtotal energy consumption) using A coding compared to Bespecially for st119881 15 whose results are characterized by thehighest standard deviation For routes 2 and 3 the same as forroute 1 the procedure was followed Optimization strategieshave been optimized for all variants of control vector st119880st119881 15 st10

The results using the control strategy st119881 10 are shownin Figures 18(a)ndash18(c) (119873119901119900119901=100 where r119904119894119898=351795 [km kWh]) Figure 18(d) illustrates the graph of the value of thefitness function

The results obtained for route 2 are presented in Table 7For route 2 compared to route 1 the best results were

achieved using the stV10 vector When using vectors st119880 andstV15 the results were slightly worse Having analyzed the size

Journal of Advanced Transportation 15

0

2

4

6

8

10V

[ms

]

VsimstU

500 1000 15000X [m]

(a) Lap 1

0

2

4

6

8

10

V [m

s]

2500 30002000X [m]

VsimstU

(b) Laps 2-9

0

2

4

6

8

10

V [m

s]

155 1615X [m]

Vsimstu

times104

(c) Lap 10

times10minus3

Npop=25Npop=50Npop=75Npop=100

Npop=125Npop=150Npop=175Npop=200

15

2

25

3

35

4f va

l

2000 4000 6000 8000 100000Nfval

(d) Mean values of the fitness functions

Figure 17 Vehicle speed and control signal st119880 for route 1

Table 6 The results for route 1

The type of coding A The type of coding Bst119880 st11988115 st11988110119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 52465 1459 42845 1741 51569 5477550 52579 10053 44431 22486 51492 3409475 52497 39913 43842 28173 51256 80682100 52589 18128 42232 1797 51166 49379125 52625 13862 42733 39616 51341 70765150 5243 2979 4435 47701 51486 27086175 52513 2511 41428 27299 51838 19358200 52579 19666 42337 25776 51204 78357

16 Journal of Advanced Transportation

100 200 300 400 500 6000X [m]

0

2

4

6

8

10V

[ms

]

VsimstV10

USET

(a) Lap 1

0

2

4

6

8

10

V [m

s]

800 900 1000 1100 1200700X [m]

VsimstV10

USET

(b) Laps 2-4

0

2

4

6

8

10

V [m

s]

2700 2800 2900 3000 3100 32002600X [m]

VsimstV10

USET

(c) Lap 5

times10minus3

Npop=25Npop=50Npop=75Npop=100

Npop=125Npop=150Npop=175Npop=200

275

28

285

29

295

3

305

f val

2000 4000 6000 8000 100000Nfval

(d) Mean values of the fitness functions

Figure 18 Vehicle speed and control signal st11988110 for route 2

of the population used in the optimization process it shouldbe noted that for route 2 it is preferable to use higher value of119873119901119900119901 For all the analyzed cases the best average results for119873119901119900119901=200 were obtained Table 8 summarizes the results forroute 3

For route 3 the average results were reported for a largerpopulation of119873119901119900119901 with B coding In the case of using vectorwith A type coding no characteristic change was notedAs expected comparing the standard deviation betweenalgorithms using B coding the standard deviation is less forthe less variance range

Evolutionary algorithms are not complete search algo-rithms therefore it is not possible to determine whetherthe solution found is best for the chosen criterion and theconstraints assumed

57 Applying the Optimal Control Strategy in Real ConditionsElectric vehicle energy consumption optimization was finallyverified in real conditions at the European edition of the ShellEco-marathon held on 16-18 May 2014 in Rotterdam

Optimal control strategy st119880was displayed by a prototypevisualization system Visualization unit is installed in the

Journal of Advanced Transportation 17

Table 7 The results for route 2

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 34138 66734 34294 23839 34873 5353250 34573 46359 35003 462 3506 3886275 34512 55134 34961 33476 35419 067858100 34836 45332 35253 26117 3544 19295125 34632 52704 35017 49039 35483 14756150 34552 63714 35326 14885 35343 071015175 35063 18728 35274 47141 35564 038022200 35073 14496 3540 13389 35569 14942

Table 8 The results for route 3

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 28071 10173 28643 7323 30994 277650 29346 6142 29581 7894 30874 439975 29711 5002 29217 7367 31141 1856100 29826 3231 29515 7022 30957 4049125 29781 2980 29866 12977 31168 3445150 29453 3346 30217 9623 31288 1249175 29234 2317 30621 6816 31481 1261200 29686 2337 30531 11737 31089 4880

Table 9 Comparison of simulation results with experimental tests

Number of attempts 119903119878119864ndash119898 119903119903 119903119904119894119898 119903119900119901119905 119890119898 119890119894 119890119904119905Attempt 1 3654 3608 - - 125 - -Attempt 2 4813 5082 5148 5265 558 129 36Attempt 3 4873 5127 5198 5265 521 139 269Attempt 4 Failed attempt damaged tires during 1st lap

steering wheel of the vehicle The visualization system showsthe basic data such as instantaneous speed average speedtravel time and distance In addition the visualization systemprovides information on which part of the track the drivershould press the acceleration button to execute the optimalcontrol strategy Measurement of the position on the track iscarried out by the odometrical measuring system Due to thepossibility of accumulating errors in the measurement of theroad the driver will reset the measuring system every timeheshe exceeds the lap line

Table 9 presents the results of all the measurementsconducted during the Shell Eco-marathonThe columns in theTable 9 contain

(i) r119878119864119898 [kmkWh] the result recorded during the raceby the measuring device provided by the organizerthe results are available on the Shell Eco-marathonofficial website

(ii) r119903 [kWkWh] the result based on the indications of aprototypemeasuring system permanently installed inthe vehicle

(iii) r119904119894119898 the result estimated by computer simulationusing recorded real control signal U119903

(iv) r119900119901119905 the result obtained by computer simulation usingthe optimal control strategy U119900119901119905

Table 9 also includes the following

(i) Measurement error

119890119898 = 1003816100381610038161003816119903119878119864119898 minus 1199031199031003816100381610038161003816119903119878119864119898 100 (31)

(ii) Identification error

119890119894 =1003816100381610038161003816119903119903 minus 1199031199041198941198981003816100381610038161003816119903119903 100 (32)

(iii) Strategy implementation error

119890119904119905 =10038161003816100381610038161003816119903119903 minus 11990311990011990111990510038161003816100381610038161003816119903119903 100 (33)

18 Journal of Advanced Transportation

There were four measurement trials available Duringrun 1 a much weaker result was obtained than estimated bysimulation The driver performed run 1 without a definedcontrol strategy As part of the experiment the driver andthe support team were asked to select the optimal tires forthe vehicle and to implement the proposed control strategyDuring run 1 only the travel time of individual laps waschecked According to the choice of the team in run 1 tiresW2 were selected (Table 4) During this test the worst resultwas obtained about 24 and 25 worse than in the othertrials In subsequent runs 2 and 3 the vehicle was equippedwith the best W1 tires (Table 4) The driver has implementedan algorithm-based optimal control strategy Strategy infor-mation was provided by the visualization system During run3 the best result was recorded This result was taken intoaccount in the classification of competitions where the teamplaced in 12 positions out of 28 classified teams Trials 4 dueto damage to the tires were not successful

Measurement error was from 125 to 558 dependingon the sample The measurement system installed perma-nently in the vehicle is a prototype system This systemhas been calibrated using available laboratory equipmentMeasurement errors indicate that other measuring devices ofthe higher accuracy class should be used

Based on the measurement data obtained during testdrives the model was tuned thus reducing the identificationerror The competition took place in stable weather thedivergence of results was small and was about 129 forsample 2 and 139 for sample 3

The difference between the results determined duringnumerical simulation and that obtained in the real run was36 for sample 2 and 269 for sample 3 The difference atthis level was considered to be small Searching for optimalcontrol strategy has not taken into account possible rdquoerrorsrdquowhich could be made by the driver and which result fromthe current situation on the route for example selecting thepath and using the route by other participants in the raceIncluding driver behaviour in the simulation model shouldbe the subject of further work

Figure 19 shows the vehicle velocity together with thecontrol signals recorded during run 2 The black curvesrepresent the real vehicle velocity V119903 and the control signalGreen curves are the optimum control strategy st119880 andthe optimal velocity V119900119901119905 determined by the simulationThe graph shows the entire distance travelled (10 laps) Theanalysis of the graph shows that the driver did not performthe exact planned strategy Errors in the implementationof the strategy are related to the disruptions During thecompetition the driver is not alone on the track in certainsituations the driver cannot overtake other participants andcannot take the optimal path In addition weather conditionsuch as wind has influence on the motion resistance In suchcases the driver has to modify the optimal control strategy

In Figure 20 the velocity recorded during the race V119903(black) and the velocity obtained by the computer simulationV119904119894119898 (red) were shown V119904119894119898 was determined by computersimulation by using real control signal The purpose of thissimulation was to investigate the correctness of identification

VrVopt

Ur Uopt

2000 4000 6000 8000 10000 12000 14000 16000 180000X [m]

05

10152025303540

V [k

mh

]

Figure 19 Comparison of speed and control signal during attempt2

2000 4000 6000 8000 10000 12000 14000 16000 180000x [m]

05

10152025303540

V [k

mh

]

Ur

VrVsim

Figure 20 Comparison of speed registered in real conditions withthe speed determined by computer simulation

of the simulation model and to identify the identificationerror

Compared to the Shell Eco-marathon competitions heldin 2012 and 2013 our performance has improved The resultsin these years were equal to 425 [km kWh] and 454[km kWh] respectively In 2012 and 2013 the controlstrategy was chosen on the basis of the simulation modelbut the model was not adequately identified and the controlstrategy had to be modified In previous editions of therace the implementation of optimal control strategy was notsupported by the visualization system which would informthe driver of the need to take specific actions (pressing orreleasing the accelerator button)

6 Conclusion

The presented method was developed and tested for aprototype electric racing car that has been designed for theShell Eco-marathon race As it was shown the results of thenumerical simulations were very similar to the outcomes ofthe real races in the context of the final result of energyconsumption and the profile of velocity of the car during therace The method has been developed and applied since 2012

Journal of Advanced Transportation 19

and led in 2014 to achieving the optimal result for this type ofthe vehicle

The optimization method was evaluated The resultsachieved during the race attempts where the optimal con-trol strategy was applied (4813 and 4873 kmkWh) werecompared to the result where the strategy was proposed bythe experts (3654 kmkWh) who already had contact withthe results of similar optimization models Optimal attemptswere better by over 30 despite errors in the implementationof the strategy by the driver In the case of experts who did nothave such experiences the differences were even greater

Further improvement of the control strategy is impossiblefor this type of a vehicle and the best way to reduce energyconsumption is by improving the mechanical design It wasthe reason to develop new racing cars for UrbanConceptBattery Electric and Hydrogen competitions The developedresearch methodology for vehicle optimization and controlstrategies has been developed and implemented in the ShellEco-marathon in 2015 which has improved the score to 504km kWhHowever the research has shown that the potentialfor improved performance of the MuSHELLka vehicle hasbeen exhausted No major structural changes in the vehiclecan significantly improve the result so in the followingyears the race was abandoned and the focus was on thedevelopment of the HydroGENIUS the electric vehicle ofUrbanConcept class with fuel cell stack as power sourcewhich eventually scored vice Championship in SEM 2016 Inthe further work it is planned to improve the optimizationresults by using the presented methodology in the case ofthe models of newly constructed vehicles The developmentof the optimization method should take into considerationthe uncertainty resulting from the given velocity strategyconsidering the real conditions of the race It is also possibleto use this method for controlling vehicles in traffic To dothis it is necessary to completely change the way of the routemodelling and the driving conditions modelling as well as todevelop a new optimization method for obtaining results inreal time

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] W Skarka ldquoReducing the Energy Consumption of ElectricVehiclesrdquo in Proceedings of the 22nd ISPE-Inc InternationalConference on Concurrent Engineering Location R Curran NWognumM Borsato et al Eds Advances in TransdisciplinaryEngineering pp 500ndash509 IOS Press Delft Netherlands 2015

[2] R Andrzejewski and J Awrejcewicz Nonlinear Dynamics of aWheeled Vehicle vol 10 Springer-Verlag New York NY USA2005

[3] D W Gao C Mi and A Emadi ldquoModeling and simulation ofelectric and hybrid vehiclesrdquo Proceedings of the IEEE vol 95 no4 pp 729ndash745 2007

[4] ldquoAdvisor documentationrdquo httpadv-vehiclesimsourceforgenet

[5] TMarkel A Brooker THendricks et al ldquoADVISORA systemsanalysis tool for advanced vehicle modelingrdquo Journal of PowerSources vol 110 no 1 pp 255ndash266 2002

[6] K B Wipke M R Cuddy and S D Burch ldquoADVISOR21 a user-friendly advanced powertrain simulation using acombined backwardforward approachrdquo IEEE Transactions onVehicular Technology vol 48 no 6 pp 1751ndash1761 1999

[7] ldquoWebsiterdquo 2014 httpwwwtransportationanlgovmodeling[8] ldquoWebsiterdquo 2014 httpwwwautonomienet[9] K Krykowski J Hetmanczyk Z Gałuszkiewicz and R Mik-

siewicz ldquoComputer analysis of high-speed PM BLDC motorpropertiesrdquo COMPEL - The International Journal for Computa-tion and Mathematics in Electrical and Electronic Engineeringvol 30 no 3 pp 941ndash956 2011

[10] M Vaillant M Eckert and F Gauterin ldquoEnergy managementstrategy to be used in design space exploration for electricpowertrain optimizationrdquo inProceedings of the 2014 9th Interna-tional Conference on Ecological Vehicles and Renewable EnergiesEVER 2014 mco March 2014

[11] A T Nguyen S Reiter and P Rigo ldquoA review on simulation-based optimization methods applied to building performanceanalysisrdquo Applied Energy vol 113 pp 1043ndash1058 2014

[12] W Silka and W Siłka Energy Intensity in the Car Traffic InPolish WNT Warszawa 1997

[13] T J Barlow S Latham I S Mrcrae and P Boulter A referencebook of driving cycles for use in the measurement of roadvehicle emissions TRL 2009 httpswwwgovukgovernmentuploadssystemdata

[14] R N Jazar Vehicle Dynamics Theory and Application SpringerUS Boston MA 2008

[15] MMeywerk ldquoVehicle Dynamicsrdquo inWest Sussex JohnWiley ampSons Lecture Notes to theMOOCVehicle Dynamics of iversity1st edition 2015

[16] MMitschke andHWallentowitzDynamik der KraftfahrzeugeSpringer Berlin Germany 1972

[17] T Stefanski and Ł Zawarczynski ldquoParametric identification ofPM motor mathematical modelsrdquo Przegląd Elektrotechnicznyvol 88 no 4 B pp 224ndash229 2012

[18] A Cameron ldquoMeasuring drive-train efficiencyrdquoHuman Powervol 46

[19] B Rohloff and P Greb ldquoEfficiency measurements of bicycletransmissions a neverending storyrdquo Human Power vol 55 p11 2004

[20] J B Spicer C J K Richardson M J Ehrlich J R BernsteinM Fukuda and M Terada ldquoEffects of frictional loss on bicyclechain drive efficiencyrdquo Journal of Mechanical Design vol 123no 4 pp 598ndash605 2001

[21] K Sternal A Cholewa W Skarka and M Targosz ldquoElec-tric vehicle for the studentsrsquo shell eco-marathon competitionDesign of the car and telemetry systemrdquo Communications inComputer and Information Science vol 329 pp 26ndash33 2012

[22] K Cichonski and W Skarka ldquoInnovative control system forhigh efficiency electric urban vehiclerdquo Communications inComputer and Information Science vol 531 pp 121ndash130 2015

[23] M J Er and R J Oentaryo ldquoComputational IntelligenceMethods andTechniques (Rutkowski L 2008) [BookReview]rdquoIEEE Computational Intelligence Magazine vol 6 no 4 pp 76ndash78 2011

[24] M Targosz M Szumowski W Skarka and P PrzystałkaldquoVelocity Planning of an Electric Vehicle Using an Evolutionary

Journal of Advanced Transportation 9

range and can assign real number values In the evolutionarystrategy the phenotype of each individual takes the followingformst119881

= [ 1198811119904 1198812119904 119881119899119904 1198811119898 1198812119898 119881119899119904 1198811119891 1198812119891 119881119899119891 ]119879 (16)

119881119894119904 119881119894119898 119881119894119891 are the setting values of velocity for the initiallap middle laps and the last lap

In the control mode according to scheme B the controlsignal is generated by the velocity controller based on thecontrol error

e119881 = 119881119878119864119879 minus 119881119904119894119898 (17)

where

U119878119864119879 = 1 for e119881 ge 10 otherwise

(18)

The coding for control scheme B in comparison withthe coding for control scheme A has undoubtedly oneadvantage namely the possibility of introducing a velocitylimit during the simulation of the passage of a given sectionof the route A velocity limitation is of great practicalimportance In many situations it is necessary to reducethe velocity of the vehicle during certain parts of theroute for example during cornering Accordingly in caseof control scheme B two velocity vectors are designated asfollows

(i) st11988115 for 119881119878119864119879119894 = [0 15] ms although it is formallylimited to 15ms it can never be achieved because themaximum vehicle speed (based on maximum enginespeed) is approximately 15ms

(ii) st11988110 for 119881119878119864119879119894 = [0 10] ms

43 The Fitness Functions In the case of evolutionary opti-mization the fitness function f 119907119886119897 has to be designed Thissection describes the formulas used to calculate the fitnessfunction of an individual that is needed for solving a task ofevolutionary optimization Each chromosome is a potentialsolution Each control strategy st is used during numericalsimulation The value of the fitness function f 119907119886119897 can becalculated based on the outcomes of the simulation suchas

(i) the total energy consumption r119904119894119898 [kmkWh](ii) the simulation time t119904119894119898(iii) the distance x119904119894119898

and limitations such as

(i) the maximum travel time T119898119886119909(ii) the total distance of the vehicle D119862The value of the function is also used to evaluate the

velocity strategy of the vehicle In the preliminary studies[24] the following fitness function f 119907119886119897 was used

Fitness Function 1

119891V1198861198971 = 11990811198911 + 11990821198912 + 11990831198913 (19)

where

1198911 = [1 + 1199031205821119904119894119898]1205821 (20)

1198912 = [119867 (119863119888 minus 119909119904119894119898) 1003816100381610038161003816119863119888 minus 1199091199041198941198981003816100381610038161003816119863119888 ]1205822 (21)

1198913 = [119867 (119905119904119894119898 minus 119879max)1003816100381610038161003816119879max minus 1199051199041198941198981003816100381610038161003816119879max

]1205822 (22)

where the weights w1 = 050E05 w2 = w3 = 025 andcoefficients 1205821 = minus2 1205822 = 1 were chosen experimentally Thepenalty functions f 2 and f 3 were introduced The Heavisidestep functionH() is used to penalize individuals representingunacceptable solutions [25 26] eg those that exceed themaximum time of the simulation H(t119904119894119898 minus T119898119886119909) or do notreach the specified distance H(D119888 minus x119904119894119898)

Fitness Function 2 In this study the authors have proposedthe fitness function which would lead to the convergenceof the evolutionary algorithm without searching for optimalvalues of weights Such a function is shown and describedbelow

119891V1198861198972 = 1 + 1198914 + 1198915119891111989121198913 (23)

1198911 = 119903119904119894119898 (24)

1198912 = cos(1003816100381610038161003816119863119888 minus 1198891199041198941198981003816100381610038161003816119863119888 ) (25)

1198913 = cos(1003816100381610038161003816119879max minus 1199051199041198941198981003816100381610038161003816119879max) (26)

1198914 = 120594 sdot 119867 (119863119888 minus 119889119904119894119898) (27)

1198915 = 120594 sdot 119867 (119879max minus 119905119904119894119898) (28)

where f 1 is a measure related to the simulated energyconsumption of the vehicle f 2 and f 3 correspond to thelimitations such as the maximum travel time and the totaldistance of the vehicle f 4 and f 5 also correspond to the limi-tations but these play strong penalty role and 120594 is arbitrarilylarge value eg significantly higher than maximal valuesf 2=f 3 =1 In this variant of the fitness function death penalty[26] is applied for unacceptable individuals in the form offactors f 4 and f 5 Individuals who do not reach a specifieddistance or exceed the time limit are eliminated These twocriteria act as a constraint and correspond to the limitationsformulated in the guidelines of the race competition On theother hand the criteria f 2 and f 3 have continuous nature andplay very important role in the fitness functionThey are veryneeded to evaluate continuously the individuals that are veryclose to and very far from the extremum

The argument of cos() function is not related to anangle However the usage of the cos() function is needed to

10 Journal of Advanced Transportation

Table 1 Research object main parameters

Type of the motor PM BLDCTransmission unit Toothed synchronous beltThe minimum turning radius 8 [m]The battery type and capacity Lithium-ion polymer 2100[mAh]Mass of the vehicle 42 [kg]Mass with the driver min 92 [kg]Diameter of wheels 0478 [m]Moment of inertia of the front wheel 119868119896119875 0023 [kgm2]Moment of inertia of the rear wheel 119868119896119879 0023[kgm2]Drag coefficient cx (see Table 2) 022 ndash 023Frontal area A [m2] (see Table 2) 0275 - 0297The total rolling coefficient crr (see Table 4) 00035 ndash 00058

eliminate the possibility of dividing by zero In addition theform of the cos() function is preferred At the initial stage ofoptimization when the simulation time t119904119894119898 and the distancex119904119894119898 differ significantly from the maximum time T119898119886119909 andthe specified distance D119888 a small change will have a greatereffect on the value of the fitness function At the final stageof optimization the function 119891V1198861198972 is more dependent on thesimulated energy consumption of the vehicle related to thefactor f 1 and thanks to the cos() function it is less dependentto the factors f 2 and f 3 The proposed function does notrequire the introduction of weights and therefore it is easierto use this function in other applications eg to find optimalvelocity strategies for different routes

It should be noted that fitness functions 119891val have beenwritten in such a way as to ensure that the optimizationalgorithm will look for a minimum of these functions

5 Case Study

As described in Sections 3 and 4 process of modelling andoptimization was applied and verified using a prototypeelectric vehicle on street race circuit in Rotterdam Themethodology was also carried out on the experimental ridestrack of the Fiat ChryslerAutomobiles Poland factory locatedin Tychy Based on (5)-(12) the simulation model was cre-ated in the MATLABSimulink environment Optimizationwas also carried out in MATLAB using the evolutionaryalgorithms available in the Global Optimization Toolbox Thelibrary of functions for simulating optimizing analyzingand presenting results has been developed

51 Research Object Light electric vehicle was a researchobject The vehicle shown in Figure 9 is a three-wheeledself-supporting structure The vehicle fuselage is made ofcomposites based on epoxy resin and woven of carbon andaramid fibre [21]

The dimensions of the vehicle and basic data are shownin Figure 10 and in Table 1

Identification of parameters for the mathematicalmodel of a research object was carried out by numericalsimulations tests on specially designed test bench [27]

Figure 9 Research object prototype electric vehicle ldquoMuSHELLkardquo(photo by M Wylezoł 2012)

and during conducted experiments in real environment[28]

The vehicle can be driven by two types of drive unit(i) DT1 drive unit based on PM BLDC motors and belt

transmission Drive wheel is equippedwith a one-wayclutch

(ii) DT2 a high-torque PMBLDCmotor mounted insidethe drive wheel The torque generated by the motor isdirectly transmitted to the rear drive wheel

The catalogue data can be used for creating the mathematicalmodel of the DT1 motor but for identifying the exactparameters it was necessary to carry out experimental testsThe manufacturer of the DT2 motor does not provide muchinformation so it was necessary to test the drive unit aswell DT1 drivetrain efficiencywas estimated using aBG75x50motor with toothed synchronous belt transmission ( z1= 28teeth z2 = 200 teeth i119879119878 = 714) The map of the efficiencywas shown on Figure 11(a) The same test was carried out forDT2 drive unit with a motor directly mounted on the drivewheel (Figure 11(b)) The obtained efficiency maps were usedto build the simulationmodel of the tested drivetrain systems

52 Determination of Air Drag Coefficient The air dragcoefficient c119909 was estimated as a result of CFD analysis usingANSYS software [24] and it was also verified by the researchin wind tunnel at the Institute of Aviation inWarsaw Frontalarea of vehicle A was determined from a three-dimensionalmodel in CAD environment Catia V5 The values of dragcoefficient c119909 and frontal area A are shown in Table 2

Journal of Advanced Transportation 11

623

972

1600

2605

Figure 10 Dimensions of the vehicle

(a) DT1 (b) DT2

Figure 11 Maps of the efficiency of tested drivetrain systems

Table 2 The air drag coefficient and frontal area

cx numericalsimulation

cx experimentalresearch Frontal area A [m2]

023 022 0275 0297

53 Determination of Rolling Resistance According to for-mula (7) the rolling resistance depends on the weight of thevehicle (Table 1) the tires rolling resistance coefficient andthe resistance of the bearings Depending on the drive unit(DT1 DT2) used in the vehicle additional resistance has to beadded In theDT1 system there is a one-way clutchwhich alsogenerates some resistance torque The DT2 system cannot bemechanically disconnected and therefore has a higher rollingresistance As a result of the coast down test the total rollingresistance of the vehicle has been identified for the four typesof tiresThe test was performed only with theDT1 system iethe systemwith the clutch Table 3 shows the basic parametersof the tires used in the experiments

The prototype vehicle can be equipped with speciallymanufactured Michelin tires with a low rolling resistantcoefficient of c119903119903 = 00014

In addition to the specialMichelin tires three other typesof tires were tested The identification of rolling resistance

coefficients was also estimated using a coast down test Themeasurements were made as follows

(i) The driver accelerated the vehicle to a fixed speed(ii) At themoment of crossing themarked gate the driver

pressed the marker button to save the flag in theacquired data

(iii) The run continued until free braking after which thedriver switched off the measuring system

(iv) The measurements were made at both directions ofthe road to minimize influence of the wind

(v) Before the attempts wind velocity temperature andatmospheric pressure were measured

(vi) The distance of the road was measured using ameasurement system mounted on the vehicle and itwas also verified using distance measuring wheel

On the basis of the experimental data the total rolling resis-tance coefficient of the vehicle was determined Table 4 showsthe coefficients of rolling resistance of the vehicle dependingon the tire used during the test Total resistance includesthe tire rolling coefficient the bearings resistance and theresistance of the clutch Verification of the data derived fromthe simulation and the experiment was conducted using

12 Journal of Advanced Transportation

Table 3 The types of tires used in the prototype vehicle

Tiresmarker Name of the tire Tirersquos

symbol Shape Type of tread Workingpressure

W1

Michelin ShellEco-marathon 4575R16 Rectangular Slick max500 [kPa]

W2

SchwalbeUl-Termo 23-406 Round Slick 600-1100 [kPa]

W3

Continental SportContact 28-406 Round Slick 600 [kPa]

W4

SchwalbeMarathon 40-406 Round Symmetrical 400-700 [kPa]

Table 4 The total rolling coefficient depending on the tires

Tiresmarker Name of the tire The total rolling coefficient crr mMAPE []

W1 Michelin ShellEco-marathon 00035 784W2 Schwalbe Ultermo 00043 1103W3 Continental SportContact 00058 1252W4 Schwalbe Marathon 00053 445

0

1

2

3

4

5

6

7

8

V [m

s]

100 200 300 400 500 6000x [m]

W1rW1simW2rW2sim

W3rW3simW4rW4sim

Figure 12 Velocity of the vehicle during coast down test

mMAPE (modifiable Mean Absolute Percentage Error) Forvelocity simulationmMAPE can be determined by

119898119872119860119875119864 = 1001119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119881119903 minus 119881119904119894119898119881119898119886119909 minus 119881119898119894119899

10038161003816100381610038161003816100381610038161003816 (29)

Figure 12 shows the experimental data obtained in a coastdown test compared with the results obtained during thecomputer simulation

54 Model of the Race Circuit In accordance with themethodology presented in Section 32 three routes have beendescribed

(i) Route 1 a street race circuit at the Shell Eco-marathoncompetition in Rotterdam

Figure 13 Plan view of the path of the drive on route 1 in Rotterdam

(ii) Routes 2 and 3 on the experimental rides track of theFiat Chrysler Automobiles Poland factory located inTychy in the south of Poland

The Shell Eco-marathon competition is held on a streetcircuit in Rotterdam One lap is 1630 meters long Vehicleshave to cover ten laps in no longer than 39 minutes so suchrequirements impose an averageminimum speed of 25 kmh

The trajectory of the vehicle path was developed usingsatellite images The vehicle trajectory was determined usingthe maximum curvature possible that could be obtained onthe existing roads

Movement of the vehicle in a curved motion causesthe centrifugal force Centrifugal force creates additionalresistance This resistance is inversely proportional to theradius of the path (8) so it is justified to select the largestradius In addition if the centrifugal force exceeds thelimit value it could provide to the side slip of the vehicleAccording to drawings in AutoCAD Civil 3D the lengths ofstraight sections and the lengths and the radius of arcs wereobtained Figure 13 shows a plan view of the path of the drive

Driving the prototype vehicle on public roads is prohib-ited and can be dangerous Vehicle testing was also carried

Journal of Advanced Transportation 13

Table 5 Travel times and total lengths of the routes

Route Length of the lap D [m] The numberof laps The total length of the route Dc [m] Travel time Tmax [s]

Route 1Rotterdam 1630 10 16 300 2340

Route 2Tychy 640 5 3200 460

Route 3Tychy 1000 5 5000 720

Figure 14 Plan view of the path of the drive on route 3 in Tychy

out on the experimental rides track of the Fiat ChryslerAutomobiles Poland factory

For the track in Tychy geodetic measurements weretaken using theDGPS (Differential Global Positioning System)technology The measuring points were collected along theaxis of the road with the distance between points amountingto 10 meters If on the measured route direction or elevationwere changed the frequency of measurement was increasedGeodetic coordinates were also imported intoAutoCADCivil3D and were used to prepare data concerning the route thatwas imported into the simulation environment MATLAB-Simulink Figures 14 and 15 show the path and elevationprofile respectively

Selected routes 2 and 3 have significant differences com-pared to route 1 especially in the height profile This set ofroutes was selected to verify the effect of the route profile onthe achieved results and to verify the proposed optimizationmethods for various road conditions The routes in Tychyare located in an open area there are no large buildingswhich guarantees stability of wind conditions The technicalcondition of the surface on routes 2 and 3 is much worsethan on route 1 which has a significant influence on therolling resistance Rolling resistance was also identified andintroduced into the simulation model For route 2 the c119903119903coefficient was 00056 and for route 3 was 00068

55 Verification of the Simulation Model In order to verifythe compatibility of the identified simulation model a seriesof numerical simulations and experimental tests were per-formed The first experiment consisted of running 300 [m]with a control strategy of 50 [m] with the workingmotor andafter that the vehicle was moving freely for the next 50 [m]The motor is turned on three times Figures 16(a) and 16(b)show the velocity of the vehicle and the power of the motorin function of the distance determined during the experiment

(red curves) and during the numerical simulations (greencurves)

Verification of the data derived from the simulation andthe experimentwas conducted usingmMAPE (29) Formotorpower simulationmMAPE can be determined by

119898119872119860119875119864119875 = 1001119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119875119903 minus 119875119904119894119898119875119898119886119909 minus 119875119898119894119899

10038161003816100381610038161003816100381610038161003816 (30)

where P119903 is the motor power measured during experimentand P119904119894119898 is the motor power conducted in simulation

As a result of the model validation tests estimationerror of the velocity was on level between 235 and 534However the motor power error level was greater It wasbetween 802 and 998

56 Determination of the Optimal Control Strategy Thelength of route 1 and the number of laps are determined bythe organizers of the Shell Eco-marathon competition Thelength of routes 2 and 3 is derived from the existing road planwhere it was possible to carry out trials in real conditionsThenumber of laps for routes 2 and 3 was assumed arbitrarily

The travel time for route 1 is based on the rules of therace which determine the minimum average speed of thevehicle Based on the average speed and the length of routes 2and 3 the travel times for these routes were determined Themaximum travel times and the total length of the route aswell as the number and length of one lap D are summarizedin Table 5

Evolutionary algorithms which are available in theMAT-LAB Global Optimization Toolbox were used From theMATLAB workspace the algorithm ran a simulation modelin a Simulink environment During optimization while usingevolutionary algorithms the maximum number of fitnessfunction evaluations 119873119891V119886119897

is the product of the populationsize 119873119901119900119901 and number of generations 119873119892119890119899

It was assumed that the total number of fitness functionevaluations was equal to 104 therefore should this value beexceeded the calculation would be cancelled Therefore thetotal number of generations 119873119892119890119899 is dependent on the valueof population size 119873119901119900119901

As part of this work phase the vectors st119880 st119881 15 andst119881 10 of the optimum control strategy for an electric vehiclefor routes 1 2 and 3 were determined During evolutionaryoptimization the heuristic method of crossing was usedand the probability of crossing was established on the basisof previous studies at the level of 08 [24 29] At the

14 Journal of Advanced Transportation

0+000

106410

minus164 minus492minus166 minus012 minus018 minus082 minus035 059 031

811

0+100 0+200 0+300 0+400 0+500 0+600 0+700 0+800 0+900 1+000

Figure 15 Profile of the path on route 3 in Tychy

50 100 150 200 250 3000X [m]

0

2

4

6

8

10

V [m

s]

(a) DT1

0

100

200

300

400

500

P [W

]50 100 150 200 250 3000

X [m]

(b) DT1

Figure 16 The velocity and the power determined with used DT1 drive unit

stage of reproduction the elitist succession method wasapplied where the best adapted two individuals in the currentpopulation passed to the next population An adaptivemethod of mutation was used The remaining parameters ofthe algorithm remain the default for the MATLAB GlobalOptimization Toolbox

The first case was the search st119880 vector for route 1Figures 17(a)ndash17(c) show the vehicle velocity V119904119894119898 obtainedby computer simulation The graph of the st119880 control signalis graphically displayed Figure 17 shows the results wherethe optimal control strategy st119880119900119901119905 was used and populationwas 119873119901119900119901=100 and 119873119892119890119899=100 The total energy consumptionwas estimated as r119904119894119898=527633 [km kWh] Figure 17(a) showsthe vehicle speed and control signal st119880 during the first lapwhile Figure 17(b) shows center laps and Figure 17(c) showsthe last lap Figure 17(d) shows the curves of the mean valuesof the fitness functions f 119907119886119897 depending on the number ofcalculations of these functions during the optimization ofthe control strategy There are eight curves in the graph(Figure 17(d)) for each of the 119873119901119900119901 parameters used in thealgorithm

When analyzing the vehicle velocity chart on the last lapof route 1 (Figure 17(c)) it can be seen that according tothe determined control strategy the propulsion system of thevehicle should no longer be used The vehicle should use thestored kinetic energy

The analysis of vehicle velocity V119904119894119898 during the last lapindicates that at the moment of reaching the given distancethe speed was still about 2 [ms] This demonstrates thatthe simulated vehicle has kinetic energy that would haveto be dispersed by the braking system or recovered by the

electric motor Having such a speed does not mean that thereis still possibility for improvement Lower speed at the endof the route has to cause higher speed of the earlier partsof the route This speed is the optimum speed due to thechosen criterion From the analysis of the shape of the fitnessfunction (Figure 17(d)) it can be seen that for route 1 itis preferable to use a smaller population of 119873119901119900119901=25 andincrease the number of 119873119892119890119899=400 The curve shape for thiscase is steep and it falls to the minimum value of the fitnessfunction which may indicate that the algorithm has reacheda convergence

Results of the optimization where B type of coding wasused were analyzed The results obtained as the mean of ther119904119894119898 result together with the standard deviation from all thetests were summarized in Table 6

By analyzing the results in Table 6 it can be seen thatfor route 1 better results were obtained (reduced simulatedtotal energy consumption) using A coding compared to Bespecially for st119881 15 whose results are characterized by thehighest standard deviation For routes 2 and 3 the same as forroute 1 the procedure was followed Optimization strategieshave been optimized for all variants of control vector st119880st119881 15 st10

The results using the control strategy st119881 10 are shownin Figures 18(a)ndash18(c) (119873119901119900119901=100 where r119904119894119898=351795 [km kWh]) Figure 18(d) illustrates the graph of the value of thefitness function

The results obtained for route 2 are presented in Table 7For route 2 compared to route 1 the best results were

achieved using the stV10 vector When using vectors st119880 andstV15 the results were slightly worse Having analyzed the size

Journal of Advanced Transportation 15

0

2

4

6

8

10V

[ms

]

VsimstU

500 1000 15000X [m]

(a) Lap 1

0

2

4

6

8

10

V [m

s]

2500 30002000X [m]

VsimstU

(b) Laps 2-9

0

2

4

6

8

10

V [m

s]

155 1615X [m]

Vsimstu

times104

(c) Lap 10

times10minus3

Npop=25Npop=50Npop=75Npop=100

Npop=125Npop=150Npop=175Npop=200

15

2

25

3

35

4f va

l

2000 4000 6000 8000 100000Nfval

(d) Mean values of the fitness functions

Figure 17 Vehicle speed and control signal st119880 for route 1

Table 6 The results for route 1

The type of coding A The type of coding Bst119880 st11988115 st11988110119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 52465 1459 42845 1741 51569 5477550 52579 10053 44431 22486 51492 3409475 52497 39913 43842 28173 51256 80682100 52589 18128 42232 1797 51166 49379125 52625 13862 42733 39616 51341 70765150 5243 2979 4435 47701 51486 27086175 52513 2511 41428 27299 51838 19358200 52579 19666 42337 25776 51204 78357

16 Journal of Advanced Transportation

100 200 300 400 500 6000X [m]

0

2

4

6

8

10V

[ms

]

VsimstV10

USET

(a) Lap 1

0

2

4

6

8

10

V [m

s]

800 900 1000 1100 1200700X [m]

VsimstV10

USET

(b) Laps 2-4

0

2

4

6

8

10

V [m

s]

2700 2800 2900 3000 3100 32002600X [m]

VsimstV10

USET

(c) Lap 5

times10minus3

Npop=25Npop=50Npop=75Npop=100

Npop=125Npop=150Npop=175Npop=200

275

28

285

29

295

3

305

f val

2000 4000 6000 8000 100000Nfval

(d) Mean values of the fitness functions

Figure 18 Vehicle speed and control signal st11988110 for route 2

of the population used in the optimization process it shouldbe noted that for route 2 it is preferable to use higher value of119873119901119900119901 For all the analyzed cases the best average results for119873119901119900119901=200 were obtained Table 8 summarizes the results forroute 3

For route 3 the average results were reported for a largerpopulation of119873119901119900119901 with B coding In the case of using vectorwith A type coding no characteristic change was notedAs expected comparing the standard deviation betweenalgorithms using B coding the standard deviation is less forthe less variance range

Evolutionary algorithms are not complete search algo-rithms therefore it is not possible to determine whetherthe solution found is best for the chosen criterion and theconstraints assumed

57 Applying the Optimal Control Strategy in Real ConditionsElectric vehicle energy consumption optimization was finallyverified in real conditions at the European edition of the ShellEco-marathon held on 16-18 May 2014 in Rotterdam

Optimal control strategy st119880was displayed by a prototypevisualization system Visualization unit is installed in the

Journal of Advanced Transportation 17

Table 7 The results for route 2

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 34138 66734 34294 23839 34873 5353250 34573 46359 35003 462 3506 3886275 34512 55134 34961 33476 35419 067858100 34836 45332 35253 26117 3544 19295125 34632 52704 35017 49039 35483 14756150 34552 63714 35326 14885 35343 071015175 35063 18728 35274 47141 35564 038022200 35073 14496 3540 13389 35569 14942

Table 8 The results for route 3

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 28071 10173 28643 7323 30994 277650 29346 6142 29581 7894 30874 439975 29711 5002 29217 7367 31141 1856100 29826 3231 29515 7022 30957 4049125 29781 2980 29866 12977 31168 3445150 29453 3346 30217 9623 31288 1249175 29234 2317 30621 6816 31481 1261200 29686 2337 30531 11737 31089 4880

Table 9 Comparison of simulation results with experimental tests

Number of attempts 119903119878119864ndash119898 119903119903 119903119904119894119898 119903119900119901119905 119890119898 119890119894 119890119904119905Attempt 1 3654 3608 - - 125 - -Attempt 2 4813 5082 5148 5265 558 129 36Attempt 3 4873 5127 5198 5265 521 139 269Attempt 4 Failed attempt damaged tires during 1st lap

steering wheel of the vehicle The visualization system showsthe basic data such as instantaneous speed average speedtravel time and distance In addition the visualization systemprovides information on which part of the track the drivershould press the acceleration button to execute the optimalcontrol strategy Measurement of the position on the track iscarried out by the odometrical measuring system Due to thepossibility of accumulating errors in the measurement of theroad the driver will reset the measuring system every timeheshe exceeds the lap line

Table 9 presents the results of all the measurementsconducted during the Shell Eco-marathonThe columns in theTable 9 contain

(i) r119878119864119898 [kmkWh] the result recorded during the raceby the measuring device provided by the organizerthe results are available on the Shell Eco-marathonofficial website

(ii) r119903 [kWkWh] the result based on the indications of aprototypemeasuring system permanently installed inthe vehicle

(iii) r119904119894119898 the result estimated by computer simulationusing recorded real control signal U119903

(iv) r119900119901119905 the result obtained by computer simulation usingthe optimal control strategy U119900119901119905

Table 9 also includes the following

(i) Measurement error

119890119898 = 1003816100381610038161003816119903119878119864119898 minus 1199031199031003816100381610038161003816119903119878119864119898 100 (31)

(ii) Identification error

119890119894 =1003816100381610038161003816119903119903 minus 1199031199041198941198981003816100381610038161003816119903119903 100 (32)

(iii) Strategy implementation error

119890119904119905 =10038161003816100381610038161003816119903119903 minus 11990311990011990111990510038161003816100381610038161003816119903119903 100 (33)

18 Journal of Advanced Transportation

There were four measurement trials available Duringrun 1 a much weaker result was obtained than estimated bysimulation The driver performed run 1 without a definedcontrol strategy As part of the experiment the driver andthe support team were asked to select the optimal tires forthe vehicle and to implement the proposed control strategyDuring run 1 only the travel time of individual laps waschecked According to the choice of the team in run 1 tiresW2 were selected (Table 4) During this test the worst resultwas obtained about 24 and 25 worse than in the othertrials In subsequent runs 2 and 3 the vehicle was equippedwith the best W1 tires (Table 4) The driver has implementedan algorithm-based optimal control strategy Strategy infor-mation was provided by the visualization system During run3 the best result was recorded This result was taken intoaccount in the classification of competitions where the teamplaced in 12 positions out of 28 classified teams Trials 4 dueto damage to the tires were not successful

Measurement error was from 125 to 558 dependingon the sample The measurement system installed perma-nently in the vehicle is a prototype system This systemhas been calibrated using available laboratory equipmentMeasurement errors indicate that other measuring devices ofthe higher accuracy class should be used

Based on the measurement data obtained during testdrives the model was tuned thus reducing the identificationerror The competition took place in stable weather thedivergence of results was small and was about 129 forsample 2 and 139 for sample 3

The difference between the results determined duringnumerical simulation and that obtained in the real run was36 for sample 2 and 269 for sample 3 The difference atthis level was considered to be small Searching for optimalcontrol strategy has not taken into account possible rdquoerrorsrdquowhich could be made by the driver and which result fromthe current situation on the route for example selecting thepath and using the route by other participants in the raceIncluding driver behaviour in the simulation model shouldbe the subject of further work

Figure 19 shows the vehicle velocity together with thecontrol signals recorded during run 2 The black curvesrepresent the real vehicle velocity V119903 and the control signalGreen curves are the optimum control strategy st119880 andthe optimal velocity V119900119901119905 determined by the simulationThe graph shows the entire distance travelled (10 laps) Theanalysis of the graph shows that the driver did not performthe exact planned strategy Errors in the implementationof the strategy are related to the disruptions During thecompetition the driver is not alone on the track in certainsituations the driver cannot overtake other participants andcannot take the optimal path In addition weather conditionsuch as wind has influence on the motion resistance In suchcases the driver has to modify the optimal control strategy

In Figure 20 the velocity recorded during the race V119903(black) and the velocity obtained by the computer simulationV119904119894119898 (red) were shown V119904119894119898 was determined by computersimulation by using real control signal The purpose of thissimulation was to investigate the correctness of identification

VrVopt

Ur Uopt

2000 4000 6000 8000 10000 12000 14000 16000 180000X [m]

05

10152025303540

V [k

mh

]

Figure 19 Comparison of speed and control signal during attempt2

2000 4000 6000 8000 10000 12000 14000 16000 180000x [m]

05

10152025303540

V [k

mh

]

Ur

VrVsim

Figure 20 Comparison of speed registered in real conditions withthe speed determined by computer simulation

of the simulation model and to identify the identificationerror

Compared to the Shell Eco-marathon competitions heldin 2012 and 2013 our performance has improved The resultsin these years were equal to 425 [km kWh] and 454[km kWh] respectively In 2012 and 2013 the controlstrategy was chosen on the basis of the simulation modelbut the model was not adequately identified and the controlstrategy had to be modified In previous editions of therace the implementation of optimal control strategy was notsupported by the visualization system which would informthe driver of the need to take specific actions (pressing orreleasing the accelerator button)

6 Conclusion

The presented method was developed and tested for aprototype electric racing car that has been designed for theShell Eco-marathon race As it was shown the results of thenumerical simulations were very similar to the outcomes ofthe real races in the context of the final result of energyconsumption and the profile of velocity of the car during therace The method has been developed and applied since 2012

Journal of Advanced Transportation 19

and led in 2014 to achieving the optimal result for this type ofthe vehicle

The optimization method was evaluated The resultsachieved during the race attempts where the optimal con-trol strategy was applied (4813 and 4873 kmkWh) werecompared to the result where the strategy was proposed bythe experts (3654 kmkWh) who already had contact withthe results of similar optimization models Optimal attemptswere better by over 30 despite errors in the implementationof the strategy by the driver In the case of experts who did nothave such experiences the differences were even greater

Further improvement of the control strategy is impossiblefor this type of a vehicle and the best way to reduce energyconsumption is by improving the mechanical design It wasthe reason to develop new racing cars for UrbanConceptBattery Electric and Hydrogen competitions The developedresearch methodology for vehicle optimization and controlstrategies has been developed and implemented in the ShellEco-marathon in 2015 which has improved the score to 504km kWhHowever the research has shown that the potentialfor improved performance of the MuSHELLka vehicle hasbeen exhausted No major structural changes in the vehiclecan significantly improve the result so in the followingyears the race was abandoned and the focus was on thedevelopment of the HydroGENIUS the electric vehicle ofUrbanConcept class with fuel cell stack as power sourcewhich eventually scored vice Championship in SEM 2016 Inthe further work it is planned to improve the optimizationresults by using the presented methodology in the case ofthe models of newly constructed vehicles The developmentof the optimization method should take into considerationthe uncertainty resulting from the given velocity strategyconsidering the real conditions of the race It is also possibleto use this method for controlling vehicles in traffic To dothis it is necessary to completely change the way of the routemodelling and the driving conditions modelling as well as todevelop a new optimization method for obtaining results inreal time

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] W Skarka ldquoReducing the Energy Consumption of ElectricVehiclesrdquo in Proceedings of the 22nd ISPE-Inc InternationalConference on Concurrent Engineering Location R Curran NWognumM Borsato et al Eds Advances in TransdisciplinaryEngineering pp 500ndash509 IOS Press Delft Netherlands 2015

[2] R Andrzejewski and J Awrejcewicz Nonlinear Dynamics of aWheeled Vehicle vol 10 Springer-Verlag New York NY USA2005

[3] D W Gao C Mi and A Emadi ldquoModeling and simulation ofelectric and hybrid vehiclesrdquo Proceedings of the IEEE vol 95 no4 pp 729ndash745 2007

[4] ldquoAdvisor documentationrdquo httpadv-vehiclesimsourceforgenet

[5] TMarkel A Brooker THendricks et al ldquoADVISORA systemsanalysis tool for advanced vehicle modelingrdquo Journal of PowerSources vol 110 no 1 pp 255ndash266 2002

[6] K B Wipke M R Cuddy and S D Burch ldquoADVISOR21 a user-friendly advanced powertrain simulation using acombined backwardforward approachrdquo IEEE Transactions onVehicular Technology vol 48 no 6 pp 1751ndash1761 1999

[7] ldquoWebsiterdquo 2014 httpwwwtransportationanlgovmodeling[8] ldquoWebsiterdquo 2014 httpwwwautonomienet[9] K Krykowski J Hetmanczyk Z Gałuszkiewicz and R Mik-

siewicz ldquoComputer analysis of high-speed PM BLDC motorpropertiesrdquo COMPEL - The International Journal for Computa-tion and Mathematics in Electrical and Electronic Engineeringvol 30 no 3 pp 941ndash956 2011

[10] M Vaillant M Eckert and F Gauterin ldquoEnergy managementstrategy to be used in design space exploration for electricpowertrain optimizationrdquo inProceedings of the 2014 9th Interna-tional Conference on Ecological Vehicles and Renewable EnergiesEVER 2014 mco March 2014

[11] A T Nguyen S Reiter and P Rigo ldquoA review on simulation-based optimization methods applied to building performanceanalysisrdquo Applied Energy vol 113 pp 1043ndash1058 2014

[12] W Silka and W Siłka Energy Intensity in the Car Traffic InPolish WNT Warszawa 1997

[13] T J Barlow S Latham I S Mrcrae and P Boulter A referencebook of driving cycles for use in the measurement of roadvehicle emissions TRL 2009 httpswwwgovukgovernmentuploadssystemdata

[14] R N Jazar Vehicle Dynamics Theory and Application SpringerUS Boston MA 2008

[15] MMeywerk ldquoVehicle Dynamicsrdquo inWest Sussex JohnWiley ampSons Lecture Notes to theMOOCVehicle Dynamics of iversity1st edition 2015

[16] MMitschke andHWallentowitzDynamik der KraftfahrzeugeSpringer Berlin Germany 1972

[17] T Stefanski and Ł Zawarczynski ldquoParametric identification ofPM motor mathematical modelsrdquo Przegląd Elektrotechnicznyvol 88 no 4 B pp 224ndash229 2012

[18] A Cameron ldquoMeasuring drive-train efficiencyrdquoHuman Powervol 46

[19] B Rohloff and P Greb ldquoEfficiency measurements of bicycletransmissions a neverending storyrdquo Human Power vol 55 p11 2004

[20] J B Spicer C J K Richardson M J Ehrlich J R BernsteinM Fukuda and M Terada ldquoEffects of frictional loss on bicyclechain drive efficiencyrdquo Journal of Mechanical Design vol 123no 4 pp 598ndash605 2001

[21] K Sternal A Cholewa W Skarka and M Targosz ldquoElec-tric vehicle for the studentsrsquo shell eco-marathon competitionDesign of the car and telemetry systemrdquo Communications inComputer and Information Science vol 329 pp 26ndash33 2012

[22] K Cichonski and W Skarka ldquoInnovative control system forhigh efficiency electric urban vehiclerdquo Communications inComputer and Information Science vol 531 pp 121ndash130 2015

[23] M J Er and R J Oentaryo ldquoComputational IntelligenceMethods andTechniques (Rutkowski L 2008) [BookReview]rdquoIEEE Computational Intelligence Magazine vol 6 no 4 pp 76ndash78 2011

[24] M Targosz M Szumowski W Skarka and P PrzystałkaldquoVelocity Planning of an Electric Vehicle Using an Evolutionary

10 Journal of Advanced Transportation

Table 1 Research object main parameters

Type of the motor PM BLDCTransmission unit Toothed synchronous beltThe minimum turning radius 8 [m]The battery type and capacity Lithium-ion polymer 2100[mAh]Mass of the vehicle 42 [kg]Mass with the driver min 92 [kg]Diameter of wheels 0478 [m]Moment of inertia of the front wheel 119868119896119875 0023 [kgm2]Moment of inertia of the rear wheel 119868119896119879 0023[kgm2]Drag coefficient cx (see Table 2) 022 ndash 023Frontal area A [m2] (see Table 2) 0275 - 0297The total rolling coefficient crr (see Table 4) 00035 ndash 00058

eliminate the possibility of dividing by zero In addition theform of the cos() function is preferred At the initial stage ofoptimization when the simulation time t119904119894119898 and the distancex119904119894119898 differ significantly from the maximum time T119898119886119909 andthe specified distance D119888 a small change will have a greatereffect on the value of the fitness function At the final stageof optimization the function 119891V1198861198972 is more dependent on thesimulated energy consumption of the vehicle related to thefactor f 1 and thanks to the cos() function it is less dependentto the factors f 2 and f 3 The proposed function does notrequire the introduction of weights and therefore it is easierto use this function in other applications eg to find optimalvelocity strategies for different routes

It should be noted that fitness functions 119891val have beenwritten in such a way as to ensure that the optimizationalgorithm will look for a minimum of these functions

5 Case Study

As described in Sections 3 and 4 process of modelling andoptimization was applied and verified using a prototypeelectric vehicle on street race circuit in Rotterdam Themethodology was also carried out on the experimental ridestrack of the Fiat ChryslerAutomobiles Poland factory locatedin Tychy Based on (5)-(12) the simulation model was cre-ated in the MATLABSimulink environment Optimizationwas also carried out in MATLAB using the evolutionaryalgorithms available in the Global Optimization Toolbox Thelibrary of functions for simulating optimizing analyzingand presenting results has been developed

51 Research Object Light electric vehicle was a researchobject The vehicle shown in Figure 9 is a three-wheeledself-supporting structure The vehicle fuselage is made ofcomposites based on epoxy resin and woven of carbon andaramid fibre [21]

The dimensions of the vehicle and basic data are shownin Figure 10 and in Table 1

Identification of parameters for the mathematicalmodel of a research object was carried out by numericalsimulations tests on specially designed test bench [27]

Figure 9 Research object prototype electric vehicle ldquoMuSHELLkardquo(photo by M Wylezoł 2012)

and during conducted experiments in real environment[28]

The vehicle can be driven by two types of drive unit(i) DT1 drive unit based on PM BLDC motors and belt

transmission Drive wheel is equippedwith a one-wayclutch

(ii) DT2 a high-torque PMBLDCmotor mounted insidethe drive wheel The torque generated by the motor isdirectly transmitted to the rear drive wheel

The catalogue data can be used for creating the mathematicalmodel of the DT1 motor but for identifying the exactparameters it was necessary to carry out experimental testsThe manufacturer of the DT2 motor does not provide muchinformation so it was necessary to test the drive unit aswell DT1 drivetrain efficiencywas estimated using aBG75x50motor with toothed synchronous belt transmission ( z1= 28teeth z2 = 200 teeth i119879119878 = 714) The map of the efficiencywas shown on Figure 11(a) The same test was carried out forDT2 drive unit with a motor directly mounted on the drivewheel (Figure 11(b)) The obtained efficiency maps were usedto build the simulationmodel of the tested drivetrain systems

52 Determination of Air Drag Coefficient The air dragcoefficient c119909 was estimated as a result of CFD analysis usingANSYS software [24] and it was also verified by the researchin wind tunnel at the Institute of Aviation inWarsaw Frontalarea of vehicle A was determined from a three-dimensionalmodel in CAD environment Catia V5 The values of dragcoefficient c119909 and frontal area A are shown in Table 2

Journal of Advanced Transportation 11

623

972

1600

2605

Figure 10 Dimensions of the vehicle

(a) DT1 (b) DT2

Figure 11 Maps of the efficiency of tested drivetrain systems

Table 2 The air drag coefficient and frontal area

cx numericalsimulation

cx experimentalresearch Frontal area A [m2]

023 022 0275 0297

53 Determination of Rolling Resistance According to for-mula (7) the rolling resistance depends on the weight of thevehicle (Table 1) the tires rolling resistance coefficient andthe resistance of the bearings Depending on the drive unit(DT1 DT2) used in the vehicle additional resistance has to beadded In theDT1 system there is a one-way clutchwhich alsogenerates some resistance torque The DT2 system cannot bemechanically disconnected and therefore has a higher rollingresistance As a result of the coast down test the total rollingresistance of the vehicle has been identified for the four typesof tiresThe test was performed only with theDT1 system iethe systemwith the clutch Table 3 shows the basic parametersof the tires used in the experiments

The prototype vehicle can be equipped with speciallymanufactured Michelin tires with a low rolling resistantcoefficient of c119903119903 = 00014

In addition to the specialMichelin tires three other typesof tires were tested The identification of rolling resistance

coefficients was also estimated using a coast down test Themeasurements were made as follows

(i) The driver accelerated the vehicle to a fixed speed(ii) At themoment of crossing themarked gate the driver

pressed the marker button to save the flag in theacquired data

(iii) The run continued until free braking after which thedriver switched off the measuring system

(iv) The measurements were made at both directions ofthe road to minimize influence of the wind

(v) Before the attempts wind velocity temperature andatmospheric pressure were measured

(vi) The distance of the road was measured using ameasurement system mounted on the vehicle and itwas also verified using distance measuring wheel

On the basis of the experimental data the total rolling resis-tance coefficient of the vehicle was determined Table 4 showsthe coefficients of rolling resistance of the vehicle dependingon the tire used during the test Total resistance includesthe tire rolling coefficient the bearings resistance and theresistance of the clutch Verification of the data derived fromthe simulation and the experiment was conducted using

12 Journal of Advanced Transportation

Table 3 The types of tires used in the prototype vehicle

Tiresmarker Name of the tire Tirersquos

symbol Shape Type of tread Workingpressure

W1

Michelin ShellEco-marathon 4575R16 Rectangular Slick max500 [kPa]

W2

SchwalbeUl-Termo 23-406 Round Slick 600-1100 [kPa]

W3

Continental SportContact 28-406 Round Slick 600 [kPa]

W4

SchwalbeMarathon 40-406 Round Symmetrical 400-700 [kPa]

Table 4 The total rolling coefficient depending on the tires

Tiresmarker Name of the tire The total rolling coefficient crr mMAPE []

W1 Michelin ShellEco-marathon 00035 784W2 Schwalbe Ultermo 00043 1103W3 Continental SportContact 00058 1252W4 Schwalbe Marathon 00053 445

0

1

2

3

4

5

6

7

8

V [m

s]

100 200 300 400 500 6000x [m]

W1rW1simW2rW2sim

W3rW3simW4rW4sim

Figure 12 Velocity of the vehicle during coast down test

mMAPE (modifiable Mean Absolute Percentage Error) Forvelocity simulationmMAPE can be determined by

119898119872119860119875119864 = 1001119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119881119903 minus 119881119904119894119898119881119898119886119909 minus 119881119898119894119899

10038161003816100381610038161003816100381610038161003816 (29)

Figure 12 shows the experimental data obtained in a coastdown test compared with the results obtained during thecomputer simulation

54 Model of the Race Circuit In accordance with themethodology presented in Section 32 three routes have beendescribed

(i) Route 1 a street race circuit at the Shell Eco-marathoncompetition in Rotterdam

Figure 13 Plan view of the path of the drive on route 1 in Rotterdam

(ii) Routes 2 and 3 on the experimental rides track of theFiat Chrysler Automobiles Poland factory located inTychy in the south of Poland

The Shell Eco-marathon competition is held on a streetcircuit in Rotterdam One lap is 1630 meters long Vehicleshave to cover ten laps in no longer than 39 minutes so suchrequirements impose an averageminimum speed of 25 kmh

The trajectory of the vehicle path was developed usingsatellite images The vehicle trajectory was determined usingthe maximum curvature possible that could be obtained onthe existing roads

Movement of the vehicle in a curved motion causesthe centrifugal force Centrifugal force creates additionalresistance This resistance is inversely proportional to theradius of the path (8) so it is justified to select the largestradius In addition if the centrifugal force exceeds thelimit value it could provide to the side slip of the vehicleAccording to drawings in AutoCAD Civil 3D the lengths ofstraight sections and the lengths and the radius of arcs wereobtained Figure 13 shows a plan view of the path of the drive

Driving the prototype vehicle on public roads is prohib-ited and can be dangerous Vehicle testing was also carried

Journal of Advanced Transportation 13

Table 5 Travel times and total lengths of the routes

Route Length of the lap D [m] The numberof laps The total length of the route Dc [m] Travel time Tmax [s]

Route 1Rotterdam 1630 10 16 300 2340

Route 2Tychy 640 5 3200 460

Route 3Tychy 1000 5 5000 720

Figure 14 Plan view of the path of the drive on route 3 in Tychy

out on the experimental rides track of the Fiat ChryslerAutomobiles Poland factory

For the track in Tychy geodetic measurements weretaken using theDGPS (Differential Global Positioning System)technology The measuring points were collected along theaxis of the road with the distance between points amountingto 10 meters If on the measured route direction or elevationwere changed the frequency of measurement was increasedGeodetic coordinates were also imported intoAutoCADCivil3D and were used to prepare data concerning the route thatwas imported into the simulation environment MATLAB-Simulink Figures 14 and 15 show the path and elevationprofile respectively

Selected routes 2 and 3 have significant differences com-pared to route 1 especially in the height profile This set ofroutes was selected to verify the effect of the route profile onthe achieved results and to verify the proposed optimizationmethods for various road conditions The routes in Tychyare located in an open area there are no large buildingswhich guarantees stability of wind conditions The technicalcondition of the surface on routes 2 and 3 is much worsethan on route 1 which has a significant influence on therolling resistance Rolling resistance was also identified andintroduced into the simulation model For route 2 the c119903119903coefficient was 00056 and for route 3 was 00068

55 Verification of the Simulation Model In order to verifythe compatibility of the identified simulation model a seriesof numerical simulations and experimental tests were per-formed The first experiment consisted of running 300 [m]with a control strategy of 50 [m] with the workingmotor andafter that the vehicle was moving freely for the next 50 [m]The motor is turned on three times Figures 16(a) and 16(b)show the velocity of the vehicle and the power of the motorin function of the distance determined during the experiment

(red curves) and during the numerical simulations (greencurves)

Verification of the data derived from the simulation andthe experimentwas conducted usingmMAPE (29) Formotorpower simulationmMAPE can be determined by

119898119872119860119875119864119875 = 1001119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119875119903 minus 119875119904119894119898119875119898119886119909 minus 119875119898119894119899

10038161003816100381610038161003816100381610038161003816 (30)

where P119903 is the motor power measured during experimentand P119904119894119898 is the motor power conducted in simulation

As a result of the model validation tests estimationerror of the velocity was on level between 235 and 534However the motor power error level was greater It wasbetween 802 and 998

56 Determination of the Optimal Control Strategy Thelength of route 1 and the number of laps are determined bythe organizers of the Shell Eco-marathon competition Thelength of routes 2 and 3 is derived from the existing road planwhere it was possible to carry out trials in real conditionsThenumber of laps for routes 2 and 3 was assumed arbitrarily

The travel time for route 1 is based on the rules of therace which determine the minimum average speed of thevehicle Based on the average speed and the length of routes 2and 3 the travel times for these routes were determined Themaximum travel times and the total length of the route aswell as the number and length of one lap D are summarizedin Table 5

Evolutionary algorithms which are available in theMAT-LAB Global Optimization Toolbox were used From theMATLAB workspace the algorithm ran a simulation modelin a Simulink environment During optimization while usingevolutionary algorithms the maximum number of fitnessfunction evaluations 119873119891V119886119897

is the product of the populationsize 119873119901119900119901 and number of generations 119873119892119890119899

It was assumed that the total number of fitness functionevaluations was equal to 104 therefore should this value beexceeded the calculation would be cancelled Therefore thetotal number of generations 119873119892119890119899 is dependent on the valueof population size 119873119901119900119901

As part of this work phase the vectors st119880 st119881 15 andst119881 10 of the optimum control strategy for an electric vehiclefor routes 1 2 and 3 were determined During evolutionaryoptimization the heuristic method of crossing was usedand the probability of crossing was established on the basisof previous studies at the level of 08 [24 29] At the

14 Journal of Advanced Transportation

0+000

106410

minus164 minus492minus166 minus012 minus018 minus082 minus035 059 031

811

0+100 0+200 0+300 0+400 0+500 0+600 0+700 0+800 0+900 1+000

Figure 15 Profile of the path on route 3 in Tychy

50 100 150 200 250 3000X [m]

0

2

4

6

8

10

V [m

s]

(a) DT1

0

100

200

300

400

500

P [W

]50 100 150 200 250 3000

X [m]

(b) DT1

Figure 16 The velocity and the power determined with used DT1 drive unit

stage of reproduction the elitist succession method wasapplied where the best adapted two individuals in the currentpopulation passed to the next population An adaptivemethod of mutation was used The remaining parameters ofthe algorithm remain the default for the MATLAB GlobalOptimization Toolbox

The first case was the search st119880 vector for route 1Figures 17(a)ndash17(c) show the vehicle velocity V119904119894119898 obtainedby computer simulation The graph of the st119880 control signalis graphically displayed Figure 17 shows the results wherethe optimal control strategy st119880119900119901119905 was used and populationwas 119873119901119900119901=100 and 119873119892119890119899=100 The total energy consumptionwas estimated as r119904119894119898=527633 [km kWh] Figure 17(a) showsthe vehicle speed and control signal st119880 during the first lapwhile Figure 17(b) shows center laps and Figure 17(c) showsthe last lap Figure 17(d) shows the curves of the mean valuesof the fitness functions f 119907119886119897 depending on the number ofcalculations of these functions during the optimization ofthe control strategy There are eight curves in the graph(Figure 17(d)) for each of the 119873119901119900119901 parameters used in thealgorithm

When analyzing the vehicle velocity chart on the last lapof route 1 (Figure 17(c)) it can be seen that according tothe determined control strategy the propulsion system of thevehicle should no longer be used The vehicle should use thestored kinetic energy

The analysis of vehicle velocity V119904119894119898 during the last lapindicates that at the moment of reaching the given distancethe speed was still about 2 [ms] This demonstrates thatthe simulated vehicle has kinetic energy that would haveto be dispersed by the braking system or recovered by the

electric motor Having such a speed does not mean that thereis still possibility for improvement Lower speed at the endof the route has to cause higher speed of the earlier partsof the route This speed is the optimum speed due to thechosen criterion From the analysis of the shape of the fitnessfunction (Figure 17(d)) it can be seen that for route 1 itis preferable to use a smaller population of 119873119901119900119901=25 andincrease the number of 119873119892119890119899=400 The curve shape for thiscase is steep and it falls to the minimum value of the fitnessfunction which may indicate that the algorithm has reacheda convergence

Results of the optimization where B type of coding wasused were analyzed The results obtained as the mean of ther119904119894119898 result together with the standard deviation from all thetests were summarized in Table 6

By analyzing the results in Table 6 it can be seen thatfor route 1 better results were obtained (reduced simulatedtotal energy consumption) using A coding compared to Bespecially for st119881 15 whose results are characterized by thehighest standard deviation For routes 2 and 3 the same as forroute 1 the procedure was followed Optimization strategieshave been optimized for all variants of control vector st119880st119881 15 st10

The results using the control strategy st119881 10 are shownin Figures 18(a)ndash18(c) (119873119901119900119901=100 where r119904119894119898=351795 [km kWh]) Figure 18(d) illustrates the graph of the value of thefitness function

The results obtained for route 2 are presented in Table 7For route 2 compared to route 1 the best results were

achieved using the stV10 vector When using vectors st119880 andstV15 the results were slightly worse Having analyzed the size

Journal of Advanced Transportation 15

0

2

4

6

8

10V

[ms

]

VsimstU

500 1000 15000X [m]

(a) Lap 1

0

2

4

6

8

10

V [m

s]

2500 30002000X [m]

VsimstU

(b) Laps 2-9

0

2

4

6

8

10

V [m

s]

155 1615X [m]

Vsimstu

times104

(c) Lap 10

times10minus3

Npop=25Npop=50Npop=75Npop=100

Npop=125Npop=150Npop=175Npop=200

15

2

25

3

35

4f va

l

2000 4000 6000 8000 100000Nfval

(d) Mean values of the fitness functions

Figure 17 Vehicle speed and control signal st119880 for route 1

Table 6 The results for route 1

The type of coding A The type of coding Bst119880 st11988115 st11988110119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 52465 1459 42845 1741 51569 5477550 52579 10053 44431 22486 51492 3409475 52497 39913 43842 28173 51256 80682100 52589 18128 42232 1797 51166 49379125 52625 13862 42733 39616 51341 70765150 5243 2979 4435 47701 51486 27086175 52513 2511 41428 27299 51838 19358200 52579 19666 42337 25776 51204 78357

16 Journal of Advanced Transportation

100 200 300 400 500 6000X [m]

0

2

4

6

8

10V

[ms

]

VsimstV10

USET

(a) Lap 1

0

2

4

6

8

10

V [m

s]

800 900 1000 1100 1200700X [m]

VsimstV10

USET

(b) Laps 2-4

0

2

4

6

8

10

V [m

s]

2700 2800 2900 3000 3100 32002600X [m]

VsimstV10

USET

(c) Lap 5

times10minus3

Npop=25Npop=50Npop=75Npop=100

Npop=125Npop=150Npop=175Npop=200

275

28

285

29

295

3

305

f val

2000 4000 6000 8000 100000Nfval

(d) Mean values of the fitness functions

Figure 18 Vehicle speed and control signal st11988110 for route 2

of the population used in the optimization process it shouldbe noted that for route 2 it is preferable to use higher value of119873119901119900119901 For all the analyzed cases the best average results for119873119901119900119901=200 were obtained Table 8 summarizes the results forroute 3

For route 3 the average results were reported for a largerpopulation of119873119901119900119901 with B coding In the case of using vectorwith A type coding no characteristic change was notedAs expected comparing the standard deviation betweenalgorithms using B coding the standard deviation is less forthe less variance range

Evolutionary algorithms are not complete search algo-rithms therefore it is not possible to determine whetherthe solution found is best for the chosen criterion and theconstraints assumed

57 Applying the Optimal Control Strategy in Real ConditionsElectric vehicle energy consumption optimization was finallyverified in real conditions at the European edition of the ShellEco-marathon held on 16-18 May 2014 in Rotterdam

Optimal control strategy st119880was displayed by a prototypevisualization system Visualization unit is installed in the

Journal of Advanced Transportation 17

Table 7 The results for route 2

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 34138 66734 34294 23839 34873 5353250 34573 46359 35003 462 3506 3886275 34512 55134 34961 33476 35419 067858100 34836 45332 35253 26117 3544 19295125 34632 52704 35017 49039 35483 14756150 34552 63714 35326 14885 35343 071015175 35063 18728 35274 47141 35564 038022200 35073 14496 3540 13389 35569 14942

Table 8 The results for route 3

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 28071 10173 28643 7323 30994 277650 29346 6142 29581 7894 30874 439975 29711 5002 29217 7367 31141 1856100 29826 3231 29515 7022 30957 4049125 29781 2980 29866 12977 31168 3445150 29453 3346 30217 9623 31288 1249175 29234 2317 30621 6816 31481 1261200 29686 2337 30531 11737 31089 4880

Table 9 Comparison of simulation results with experimental tests

Number of attempts 119903119878119864ndash119898 119903119903 119903119904119894119898 119903119900119901119905 119890119898 119890119894 119890119904119905Attempt 1 3654 3608 - - 125 - -Attempt 2 4813 5082 5148 5265 558 129 36Attempt 3 4873 5127 5198 5265 521 139 269Attempt 4 Failed attempt damaged tires during 1st lap

steering wheel of the vehicle The visualization system showsthe basic data such as instantaneous speed average speedtravel time and distance In addition the visualization systemprovides information on which part of the track the drivershould press the acceleration button to execute the optimalcontrol strategy Measurement of the position on the track iscarried out by the odometrical measuring system Due to thepossibility of accumulating errors in the measurement of theroad the driver will reset the measuring system every timeheshe exceeds the lap line

Table 9 presents the results of all the measurementsconducted during the Shell Eco-marathonThe columns in theTable 9 contain

(i) r119878119864119898 [kmkWh] the result recorded during the raceby the measuring device provided by the organizerthe results are available on the Shell Eco-marathonofficial website

(ii) r119903 [kWkWh] the result based on the indications of aprototypemeasuring system permanently installed inthe vehicle

(iii) r119904119894119898 the result estimated by computer simulationusing recorded real control signal U119903

(iv) r119900119901119905 the result obtained by computer simulation usingthe optimal control strategy U119900119901119905

Table 9 also includes the following

(i) Measurement error

119890119898 = 1003816100381610038161003816119903119878119864119898 minus 1199031199031003816100381610038161003816119903119878119864119898 100 (31)

(ii) Identification error

119890119894 =1003816100381610038161003816119903119903 minus 1199031199041198941198981003816100381610038161003816119903119903 100 (32)

(iii) Strategy implementation error

119890119904119905 =10038161003816100381610038161003816119903119903 minus 11990311990011990111990510038161003816100381610038161003816119903119903 100 (33)

18 Journal of Advanced Transportation

There were four measurement trials available Duringrun 1 a much weaker result was obtained than estimated bysimulation The driver performed run 1 without a definedcontrol strategy As part of the experiment the driver andthe support team were asked to select the optimal tires forthe vehicle and to implement the proposed control strategyDuring run 1 only the travel time of individual laps waschecked According to the choice of the team in run 1 tiresW2 were selected (Table 4) During this test the worst resultwas obtained about 24 and 25 worse than in the othertrials In subsequent runs 2 and 3 the vehicle was equippedwith the best W1 tires (Table 4) The driver has implementedan algorithm-based optimal control strategy Strategy infor-mation was provided by the visualization system During run3 the best result was recorded This result was taken intoaccount in the classification of competitions where the teamplaced in 12 positions out of 28 classified teams Trials 4 dueto damage to the tires were not successful

Measurement error was from 125 to 558 dependingon the sample The measurement system installed perma-nently in the vehicle is a prototype system This systemhas been calibrated using available laboratory equipmentMeasurement errors indicate that other measuring devices ofthe higher accuracy class should be used

Based on the measurement data obtained during testdrives the model was tuned thus reducing the identificationerror The competition took place in stable weather thedivergence of results was small and was about 129 forsample 2 and 139 for sample 3

The difference between the results determined duringnumerical simulation and that obtained in the real run was36 for sample 2 and 269 for sample 3 The difference atthis level was considered to be small Searching for optimalcontrol strategy has not taken into account possible rdquoerrorsrdquowhich could be made by the driver and which result fromthe current situation on the route for example selecting thepath and using the route by other participants in the raceIncluding driver behaviour in the simulation model shouldbe the subject of further work

Figure 19 shows the vehicle velocity together with thecontrol signals recorded during run 2 The black curvesrepresent the real vehicle velocity V119903 and the control signalGreen curves are the optimum control strategy st119880 andthe optimal velocity V119900119901119905 determined by the simulationThe graph shows the entire distance travelled (10 laps) Theanalysis of the graph shows that the driver did not performthe exact planned strategy Errors in the implementationof the strategy are related to the disruptions During thecompetition the driver is not alone on the track in certainsituations the driver cannot overtake other participants andcannot take the optimal path In addition weather conditionsuch as wind has influence on the motion resistance In suchcases the driver has to modify the optimal control strategy

In Figure 20 the velocity recorded during the race V119903(black) and the velocity obtained by the computer simulationV119904119894119898 (red) were shown V119904119894119898 was determined by computersimulation by using real control signal The purpose of thissimulation was to investigate the correctness of identification

VrVopt

Ur Uopt

2000 4000 6000 8000 10000 12000 14000 16000 180000X [m]

05

10152025303540

V [k

mh

]

Figure 19 Comparison of speed and control signal during attempt2

2000 4000 6000 8000 10000 12000 14000 16000 180000x [m]

05

10152025303540

V [k

mh

]

Ur

VrVsim

Figure 20 Comparison of speed registered in real conditions withthe speed determined by computer simulation

of the simulation model and to identify the identificationerror

Compared to the Shell Eco-marathon competitions heldin 2012 and 2013 our performance has improved The resultsin these years were equal to 425 [km kWh] and 454[km kWh] respectively In 2012 and 2013 the controlstrategy was chosen on the basis of the simulation modelbut the model was not adequately identified and the controlstrategy had to be modified In previous editions of therace the implementation of optimal control strategy was notsupported by the visualization system which would informthe driver of the need to take specific actions (pressing orreleasing the accelerator button)

6 Conclusion

The presented method was developed and tested for aprototype electric racing car that has been designed for theShell Eco-marathon race As it was shown the results of thenumerical simulations were very similar to the outcomes ofthe real races in the context of the final result of energyconsumption and the profile of velocity of the car during therace The method has been developed and applied since 2012

Journal of Advanced Transportation 19

and led in 2014 to achieving the optimal result for this type ofthe vehicle

The optimization method was evaluated The resultsachieved during the race attempts where the optimal con-trol strategy was applied (4813 and 4873 kmkWh) werecompared to the result where the strategy was proposed bythe experts (3654 kmkWh) who already had contact withthe results of similar optimization models Optimal attemptswere better by over 30 despite errors in the implementationof the strategy by the driver In the case of experts who did nothave such experiences the differences were even greater

Further improvement of the control strategy is impossiblefor this type of a vehicle and the best way to reduce energyconsumption is by improving the mechanical design It wasthe reason to develop new racing cars for UrbanConceptBattery Electric and Hydrogen competitions The developedresearch methodology for vehicle optimization and controlstrategies has been developed and implemented in the ShellEco-marathon in 2015 which has improved the score to 504km kWhHowever the research has shown that the potentialfor improved performance of the MuSHELLka vehicle hasbeen exhausted No major structural changes in the vehiclecan significantly improve the result so in the followingyears the race was abandoned and the focus was on thedevelopment of the HydroGENIUS the electric vehicle ofUrbanConcept class with fuel cell stack as power sourcewhich eventually scored vice Championship in SEM 2016 Inthe further work it is planned to improve the optimizationresults by using the presented methodology in the case ofthe models of newly constructed vehicles The developmentof the optimization method should take into considerationthe uncertainty resulting from the given velocity strategyconsidering the real conditions of the race It is also possibleto use this method for controlling vehicles in traffic To dothis it is necessary to completely change the way of the routemodelling and the driving conditions modelling as well as todevelop a new optimization method for obtaining results inreal time

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] W Skarka ldquoReducing the Energy Consumption of ElectricVehiclesrdquo in Proceedings of the 22nd ISPE-Inc InternationalConference on Concurrent Engineering Location R Curran NWognumM Borsato et al Eds Advances in TransdisciplinaryEngineering pp 500ndash509 IOS Press Delft Netherlands 2015

[2] R Andrzejewski and J Awrejcewicz Nonlinear Dynamics of aWheeled Vehicle vol 10 Springer-Verlag New York NY USA2005

[3] D W Gao C Mi and A Emadi ldquoModeling and simulation ofelectric and hybrid vehiclesrdquo Proceedings of the IEEE vol 95 no4 pp 729ndash745 2007

[4] ldquoAdvisor documentationrdquo httpadv-vehiclesimsourceforgenet

[5] TMarkel A Brooker THendricks et al ldquoADVISORA systemsanalysis tool for advanced vehicle modelingrdquo Journal of PowerSources vol 110 no 1 pp 255ndash266 2002

[6] K B Wipke M R Cuddy and S D Burch ldquoADVISOR21 a user-friendly advanced powertrain simulation using acombined backwardforward approachrdquo IEEE Transactions onVehicular Technology vol 48 no 6 pp 1751ndash1761 1999

[7] ldquoWebsiterdquo 2014 httpwwwtransportationanlgovmodeling[8] ldquoWebsiterdquo 2014 httpwwwautonomienet[9] K Krykowski J Hetmanczyk Z Gałuszkiewicz and R Mik-

siewicz ldquoComputer analysis of high-speed PM BLDC motorpropertiesrdquo COMPEL - The International Journal for Computa-tion and Mathematics in Electrical and Electronic Engineeringvol 30 no 3 pp 941ndash956 2011

[10] M Vaillant M Eckert and F Gauterin ldquoEnergy managementstrategy to be used in design space exploration for electricpowertrain optimizationrdquo inProceedings of the 2014 9th Interna-tional Conference on Ecological Vehicles and Renewable EnergiesEVER 2014 mco March 2014

[11] A T Nguyen S Reiter and P Rigo ldquoA review on simulation-based optimization methods applied to building performanceanalysisrdquo Applied Energy vol 113 pp 1043ndash1058 2014

[12] W Silka and W Siłka Energy Intensity in the Car Traffic InPolish WNT Warszawa 1997

[13] T J Barlow S Latham I S Mrcrae and P Boulter A referencebook of driving cycles for use in the measurement of roadvehicle emissions TRL 2009 httpswwwgovukgovernmentuploadssystemdata

[14] R N Jazar Vehicle Dynamics Theory and Application SpringerUS Boston MA 2008

[15] MMeywerk ldquoVehicle Dynamicsrdquo inWest Sussex JohnWiley ampSons Lecture Notes to theMOOCVehicle Dynamics of iversity1st edition 2015

[16] MMitschke andHWallentowitzDynamik der KraftfahrzeugeSpringer Berlin Germany 1972

[17] T Stefanski and Ł Zawarczynski ldquoParametric identification ofPM motor mathematical modelsrdquo Przegląd Elektrotechnicznyvol 88 no 4 B pp 224ndash229 2012

[18] A Cameron ldquoMeasuring drive-train efficiencyrdquoHuman Powervol 46

[19] B Rohloff and P Greb ldquoEfficiency measurements of bicycletransmissions a neverending storyrdquo Human Power vol 55 p11 2004

[20] J B Spicer C J K Richardson M J Ehrlich J R BernsteinM Fukuda and M Terada ldquoEffects of frictional loss on bicyclechain drive efficiencyrdquo Journal of Mechanical Design vol 123no 4 pp 598ndash605 2001

[21] K Sternal A Cholewa W Skarka and M Targosz ldquoElec-tric vehicle for the studentsrsquo shell eco-marathon competitionDesign of the car and telemetry systemrdquo Communications inComputer and Information Science vol 329 pp 26ndash33 2012

[22] K Cichonski and W Skarka ldquoInnovative control system forhigh efficiency electric urban vehiclerdquo Communications inComputer and Information Science vol 531 pp 121ndash130 2015

[23] M J Er and R J Oentaryo ldquoComputational IntelligenceMethods andTechniques (Rutkowski L 2008) [BookReview]rdquoIEEE Computational Intelligence Magazine vol 6 no 4 pp 76ndash78 2011

[24] M Targosz M Szumowski W Skarka and P PrzystałkaldquoVelocity Planning of an Electric Vehicle Using an Evolutionary

Journal of Advanced Transportation 11

623

972

1600

2605

Figure 10 Dimensions of the vehicle

(a) DT1 (b) DT2

Figure 11 Maps of the efficiency of tested drivetrain systems

Table 2 The air drag coefficient and frontal area

cx numericalsimulation

cx experimentalresearch Frontal area A [m2]

023 022 0275 0297

53 Determination of Rolling Resistance According to for-mula (7) the rolling resistance depends on the weight of thevehicle (Table 1) the tires rolling resistance coefficient andthe resistance of the bearings Depending on the drive unit(DT1 DT2) used in the vehicle additional resistance has to beadded In theDT1 system there is a one-way clutchwhich alsogenerates some resistance torque The DT2 system cannot bemechanically disconnected and therefore has a higher rollingresistance As a result of the coast down test the total rollingresistance of the vehicle has been identified for the four typesof tiresThe test was performed only with theDT1 system iethe systemwith the clutch Table 3 shows the basic parametersof the tires used in the experiments

The prototype vehicle can be equipped with speciallymanufactured Michelin tires with a low rolling resistantcoefficient of c119903119903 = 00014

In addition to the specialMichelin tires three other typesof tires were tested The identification of rolling resistance

coefficients was also estimated using a coast down test Themeasurements were made as follows

(i) The driver accelerated the vehicle to a fixed speed(ii) At themoment of crossing themarked gate the driver

pressed the marker button to save the flag in theacquired data

(iii) The run continued until free braking after which thedriver switched off the measuring system

(iv) The measurements were made at both directions ofthe road to minimize influence of the wind

(v) Before the attempts wind velocity temperature andatmospheric pressure were measured

(vi) The distance of the road was measured using ameasurement system mounted on the vehicle and itwas also verified using distance measuring wheel

On the basis of the experimental data the total rolling resis-tance coefficient of the vehicle was determined Table 4 showsthe coefficients of rolling resistance of the vehicle dependingon the tire used during the test Total resistance includesthe tire rolling coefficient the bearings resistance and theresistance of the clutch Verification of the data derived fromthe simulation and the experiment was conducted using

12 Journal of Advanced Transportation

Table 3 The types of tires used in the prototype vehicle

Tiresmarker Name of the tire Tirersquos

symbol Shape Type of tread Workingpressure

W1

Michelin ShellEco-marathon 4575R16 Rectangular Slick max500 [kPa]

W2

SchwalbeUl-Termo 23-406 Round Slick 600-1100 [kPa]

W3

Continental SportContact 28-406 Round Slick 600 [kPa]

W4

SchwalbeMarathon 40-406 Round Symmetrical 400-700 [kPa]

Table 4 The total rolling coefficient depending on the tires

Tiresmarker Name of the tire The total rolling coefficient crr mMAPE []

W1 Michelin ShellEco-marathon 00035 784W2 Schwalbe Ultermo 00043 1103W3 Continental SportContact 00058 1252W4 Schwalbe Marathon 00053 445

0

1

2

3

4

5

6

7

8

V [m

s]

100 200 300 400 500 6000x [m]

W1rW1simW2rW2sim

W3rW3simW4rW4sim

Figure 12 Velocity of the vehicle during coast down test

mMAPE (modifiable Mean Absolute Percentage Error) Forvelocity simulationmMAPE can be determined by

119898119872119860119875119864 = 1001119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119881119903 minus 119881119904119894119898119881119898119886119909 minus 119881119898119894119899

10038161003816100381610038161003816100381610038161003816 (29)

Figure 12 shows the experimental data obtained in a coastdown test compared with the results obtained during thecomputer simulation

54 Model of the Race Circuit In accordance with themethodology presented in Section 32 three routes have beendescribed

(i) Route 1 a street race circuit at the Shell Eco-marathoncompetition in Rotterdam

Figure 13 Plan view of the path of the drive on route 1 in Rotterdam

(ii) Routes 2 and 3 on the experimental rides track of theFiat Chrysler Automobiles Poland factory located inTychy in the south of Poland

The Shell Eco-marathon competition is held on a streetcircuit in Rotterdam One lap is 1630 meters long Vehicleshave to cover ten laps in no longer than 39 minutes so suchrequirements impose an averageminimum speed of 25 kmh

The trajectory of the vehicle path was developed usingsatellite images The vehicle trajectory was determined usingthe maximum curvature possible that could be obtained onthe existing roads

Movement of the vehicle in a curved motion causesthe centrifugal force Centrifugal force creates additionalresistance This resistance is inversely proportional to theradius of the path (8) so it is justified to select the largestradius In addition if the centrifugal force exceeds thelimit value it could provide to the side slip of the vehicleAccording to drawings in AutoCAD Civil 3D the lengths ofstraight sections and the lengths and the radius of arcs wereobtained Figure 13 shows a plan view of the path of the drive

Driving the prototype vehicle on public roads is prohib-ited and can be dangerous Vehicle testing was also carried

Journal of Advanced Transportation 13

Table 5 Travel times and total lengths of the routes

Route Length of the lap D [m] The numberof laps The total length of the route Dc [m] Travel time Tmax [s]

Route 1Rotterdam 1630 10 16 300 2340

Route 2Tychy 640 5 3200 460

Route 3Tychy 1000 5 5000 720

Figure 14 Plan view of the path of the drive on route 3 in Tychy

out on the experimental rides track of the Fiat ChryslerAutomobiles Poland factory

For the track in Tychy geodetic measurements weretaken using theDGPS (Differential Global Positioning System)technology The measuring points were collected along theaxis of the road with the distance between points amountingto 10 meters If on the measured route direction or elevationwere changed the frequency of measurement was increasedGeodetic coordinates were also imported intoAutoCADCivil3D and were used to prepare data concerning the route thatwas imported into the simulation environment MATLAB-Simulink Figures 14 and 15 show the path and elevationprofile respectively

Selected routes 2 and 3 have significant differences com-pared to route 1 especially in the height profile This set ofroutes was selected to verify the effect of the route profile onthe achieved results and to verify the proposed optimizationmethods for various road conditions The routes in Tychyare located in an open area there are no large buildingswhich guarantees stability of wind conditions The technicalcondition of the surface on routes 2 and 3 is much worsethan on route 1 which has a significant influence on therolling resistance Rolling resistance was also identified andintroduced into the simulation model For route 2 the c119903119903coefficient was 00056 and for route 3 was 00068

55 Verification of the Simulation Model In order to verifythe compatibility of the identified simulation model a seriesof numerical simulations and experimental tests were per-formed The first experiment consisted of running 300 [m]with a control strategy of 50 [m] with the workingmotor andafter that the vehicle was moving freely for the next 50 [m]The motor is turned on three times Figures 16(a) and 16(b)show the velocity of the vehicle and the power of the motorin function of the distance determined during the experiment

(red curves) and during the numerical simulations (greencurves)

Verification of the data derived from the simulation andthe experimentwas conducted usingmMAPE (29) Formotorpower simulationmMAPE can be determined by

119898119872119860119875119864119875 = 1001119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119875119903 minus 119875119904119894119898119875119898119886119909 minus 119875119898119894119899

10038161003816100381610038161003816100381610038161003816 (30)

where P119903 is the motor power measured during experimentand P119904119894119898 is the motor power conducted in simulation

As a result of the model validation tests estimationerror of the velocity was on level between 235 and 534However the motor power error level was greater It wasbetween 802 and 998

56 Determination of the Optimal Control Strategy Thelength of route 1 and the number of laps are determined bythe organizers of the Shell Eco-marathon competition Thelength of routes 2 and 3 is derived from the existing road planwhere it was possible to carry out trials in real conditionsThenumber of laps for routes 2 and 3 was assumed arbitrarily

The travel time for route 1 is based on the rules of therace which determine the minimum average speed of thevehicle Based on the average speed and the length of routes 2and 3 the travel times for these routes were determined Themaximum travel times and the total length of the route aswell as the number and length of one lap D are summarizedin Table 5

Evolutionary algorithms which are available in theMAT-LAB Global Optimization Toolbox were used From theMATLAB workspace the algorithm ran a simulation modelin a Simulink environment During optimization while usingevolutionary algorithms the maximum number of fitnessfunction evaluations 119873119891V119886119897

is the product of the populationsize 119873119901119900119901 and number of generations 119873119892119890119899

It was assumed that the total number of fitness functionevaluations was equal to 104 therefore should this value beexceeded the calculation would be cancelled Therefore thetotal number of generations 119873119892119890119899 is dependent on the valueof population size 119873119901119900119901

As part of this work phase the vectors st119880 st119881 15 andst119881 10 of the optimum control strategy for an electric vehiclefor routes 1 2 and 3 were determined During evolutionaryoptimization the heuristic method of crossing was usedand the probability of crossing was established on the basisof previous studies at the level of 08 [24 29] At the

14 Journal of Advanced Transportation

0+000

106410

minus164 minus492minus166 minus012 minus018 minus082 minus035 059 031

811

0+100 0+200 0+300 0+400 0+500 0+600 0+700 0+800 0+900 1+000

Figure 15 Profile of the path on route 3 in Tychy

50 100 150 200 250 3000X [m]

0

2

4

6

8

10

V [m

s]

(a) DT1

0

100

200

300

400

500

P [W

]50 100 150 200 250 3000

X [m]

(b) DT1

Figure 16 The velocity and the power determined with used DT1 drive unit

stage of reproduction the elitist succession method wasapplied where the best adapted two individuals in the currentpopulation passed to the next population An adaptivemethod of mutation was used The remaining parameters ofthe algorithm remain the default for the MATLAB GlobalOptimization Toolbox

The first case was the search st119880 vector for route 1Figures 17(a)ndash17(c) show the vehicle velocity V119904119894119898 obtainedby computer simulation The graph of the st119880 control signalis graphically displayed Figure 17 shows the results wherethe optimal control strategy st119880119900119901119905 was used and populationwas 119873119901119900119901=100 and 119873119892119890119899=100 The total energy consumptionwas estimated as r119904119894119898=527633 [km kWh] Figure 17(a) showsthe vehicle speed and control signal st119880 during the first lapwhile Figure 17(b) shows center laps and Figure 17(c) showsthe last lap Figure 17(d) shows the curves of the mean valuesof the fitness functions f 119907119886119897 depending on the number ofcalculations of these functions during the optimization ofthe control strategy There are eight curves in the graph(Figure 17(d)) for each of the 119873119901119900119901 parameters used in thealgorithm

When analyzing the vehicle velocity chart on the last lapof route 1 (Figure 17(c)) it can be seen that according tothe determined control strategy the propulsion system of thevehicle should no longer be used The vehicle should use thestored kinetic energy

The analysis of vehicle velocity V119904119894119898 during the last lapindicates that at the moment of reaching the given distancethe speed was still about 2 [ms] This demonstrates thatthe simulated vehicle has kinetic energy that would haveto be dispersed by the braking system or recovered by the

electric motor Having such a speed does not mean that thereis still possibility for improvement Lower speed at the endof the route has to cause higher speed of the earlier partsof the route This speed is the optimum speed due to thechosen criterion From the analysis of the shape of the fitnessfunction (Figure 17(d)) it can be seen that for route 1 itis preferable to use a smaller population of 119873119901119900119901=25 andincrease the number of 119873119892119890119899=400 The curve shape for thiscase is steep and it falls to the minimum value of the fitnessfunction which may indicate that the algorithm has reacheda convergence

Results of the optimization where B type of coding wasused were analyzed The results obtained as the mean of ther119904119894119898 result together with the standard deviation from all thetests were summarized in Table 6

By analyzing the results in Table 6 it can be seen thatfor route 1 better results were obtained (reduced simulatedtotal energy consumption) using A coding compared to Bespecially for st119881 15 whose results are characterized by thehighest standard deviation For routes 2 and 3 the same as forroute 1 the procedure was followed Optimization strategieshave been optimized for all variants of control vector st119880st119881 15 st10

The results using the control strategy st119881 10 are shownin Figures 18(a)ndash18(c) (119873119901119900119901=100 where r119904119894119898=351795 [km kWh]) Figure 18(d) illustrates the graph of the value of thefitness function

The results obtained for route 2 are presented in Table 7For route 2 compared to route 1 the best results were

achieved using the stV10 vector When using vectors st119880 andstV15 the results were slightly worse Having analyzed the size

Journal of Advanced Transportation 15

0

2

4

6

8

10V

[ms

]

VsimstU

500 1000 15000X [m]

(a) Lap 1

0

2

4

6

8

10

V [m

s]

2500 30002000X [m]

VsimstU

(b) Laps 2-9

0

2

4

6

8

10

V [m

s]

155 1615X [m]

Vsimstu

times104

(c) Lap 10

times10minus3

Npop=25Npop=50Npop=75Npop=100

Npop=125Npop=150Npop=175Npop=200

15

2

25

3

35

4f va

l

2000 4000 6000 8000 100000Nfval

(d) Mean values of the fitness functions

Figure 17 Vehicle speed and control signal st119880 for route 1

Table 6 The results for route 1

The type of coding A The type of coding Bst119880 st11988115 st11988110119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 52465 1459 42845 1741 51569 5477550 52579 10053 44431 22486 51492 3409475 52497 39913 43842 28173 51256 80682100 52589 18128 42232 1797 51166 49379125 52625 13862 42733 39616 51341 70765150 5243 2979 4435 47701 51486 27086175 52513 2511 41428 27299 51838 19358200 52579 19666 42337 25776 51204 78357

16 Journal of Advanced Transportation

100 200 300 400 500 6000X [m]

0

2

4

6

8

10V

[ms

]

VsimstV10

USET

(a) Lap 1

0

2

4

6

8

10

V [m

s]

800 900 1000 1100 1200700X [m]

VsimstV10

USET

(b) Laps 2-4

0

2

4

6

8

10

V [m

s]

2700 2800 2900 3000 3100 32002600X [m]

VsimstV10

USET

(c) Lap 5

times10minus3

Npop=25Npop=50Npop=75Npop=100

Npop=125Npop=150Npop=175Npop=200

275

28

285

29

295

3

305

f val

2000 4000 6000 8000 100000Nfval

(d) Mean values of the fitness functions

Figure 18 Vehicle speed and control signal st11988110 for route 2

of the population used in the optimization process it shouldbe noted that for route 2 it is preferable to use higher value of119873119901119900119901 For all the analyzed cases the best average results for119873119901119900119901=200 were obtained Table 8 summarizes the results forroute 3

For route 3 the average results were reported for a largerpopulation of119873119901119900119901 with B coding In the case of using vectorwith A type coding no characteristic change was notedAs expected comparing the standard deviation betweenalgorithms using B coding the standard deviation is less forthe less variance range

Evolutionary algorithms are not complete search algo-rithms therefore it is not possible to determine whetherthe solution found is best for the chosen criterion and theconstraints assumed

57 Applying the Optimal Control Strategy in Real ConditionsElectric vehicle energy consumption optimization was finallyverified in real conditions at the European edition of the ShellEco-marathon held on 16-18 May 2014 in Rotterdam

Optimal control strategy st119880was displayed by a prototypevisualization system Visualization unit is installed in the

Journal of Advanced Transportation 17

Table 7 The results for route 2

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 34138 66734 34294 23839 34873 5353250 34573 46359 35003 462 3506 3886275 34512 55134 34961 33476 35419 067858100 34836 45332 35253 26117 3544 19295125 34632 52704 35017 49039 35483 14756150 34552 63714 35326 14885 35343 071015175 35063 18728 35274 47141 35564 038022200 35073 14496 3540 13389 35569 14942

Table 8 The results for route 3

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 28071 10173 28643 7323 30994 277650 29346 6142 29581 7894 30874 439975 29711 5002 29217 7367 31141 1856100 29826 3231 29515 7022 30957 4049125 29781 2980 29866 12977 31168 3445150 29453 3346 30217 9623 31288 1249175 29234 2317 30621 6816 31481 1261200 29686 2337 30531 11737 31089 4880

Table 9 Comparison of simulation results with experimental tests

Number of attempts 119903119878119864ndash119898 119903119903 119903119904119894119898 119903119900119901119905 119890119898 119890119894 119890119904119905Attempt 1 3654 3608 - - 125 - -Attempt 2 4813 5082 5148 5265 558 129 36Attempt 3 4873 5127 5198 5265 521 139 269Attempt 4 Failed attempt damaged tires during 1st lap

steering wheel of the vehicle The visualization system showsthe basic data such as instantaneous speed average speedtravel time and distance In addition the visualization systemprovides information on which part of the track the drivershould press the acceleration button to execute the optimalcontrol strategy Measurement of the position on the track iscarried out by the odometrical measuring system Due to thepossibility of accumulating errors in the measurement of theroad the driver will reset the measuring system every timeheshe exceeds the lap line

Table 9 presents the results of all the measurementsconducted during the Shell Eco-marathonThe columns in theTable 9 contain

(i) r119878119864119898 [kmkWh] the result recorded during the raceby the measuring device provided by the organizerthe results are available on the Shell Eco-marathonofficial website

(ii) r119903 [kWkWh] the result based on the indications of aprototypemeasuring system permanently installed inthe vehicle

(iii) r119904119894119898 the result estimated by computer simulationusing recorded real control signal U119903

(iv) r119900119901119905 the result obtained by computer simulation usingthe optimal control strategy U119900119901119905

Table 9 also includes the following

(i) Measurement error

119890119898 = 1003816100381610038161003816119903119878119864119898 minus 1199031199031003816100381610038161003816119903119878119864119898 100 (31)

(ii) Identification error

119890119894 =1003816100381610038161003816119903119903 minus 1199031199041198941198981003816100381610038161003816119903119903 100 (32)

(iii) Strategy implementation error

119890119904119905 =10038161003816100381610038161003816119903119903 minus 11990311990011990111990510038161003816100381610038161003816119903119903 100 (33)

18 Journal of Advanced Transportation

There were four measurement trials available Duringrun 1 a much weaker result was obtained than estimated bysimulation The driver performed run 1 without a definedcontrol strategy As part of the experiment the driver andthe support team were asked to select the optimal tires forthe vehicle and to implement the proposed control strategyDuring run 1 only the travel time of individual laps waschecked According to the choice of the team in run 1 tiresW2 were selected (Table 4) During this test the worst resultwas obtained about 24 and 25 worse than in the othertrials In subsequent runs 2 and 3 the vehicle was equippedwith the best W1 tires (Table 4) The driver has implementedan algorithm-based optimal control strategy Strategy infor-mation was provided by the visualization system During run3 the best result was recorded This result was taken intoaccount in the classification of competitions where the teamplaced in 12 positions out of 28 classified teams Trials 4 dueto damage to the tires were not successful

Measurement error was from 125 to 558 dependingon the sample The measurement system installed perma-nently in the vehicle is a prototype system This systemhas been calibrated using available laboratory equipmentMeasurement errors indicate that other measuring devices ofthe higher accuracy class should be used

Based on the measurement data obtained during testdrives the model was tuned thus reducing the identificationerror The competition took place in stable weather thedivergence of results was small and was about 129 forsample 2 and 139 for sample 3

The difference between the results determined duringnumerical simulation and that obtained in the real run was36 for sample 2 and 269 for sample 3 The difference atthis level was considered to be small Searching for optimalcontrol strategy has not taken into account possible rdquoerrorsrdquowhich could be made by the driver and which result fromthe current situation on the route for example selecting thepath and using the route by other participants in the raceIncluding driver behaviour in the simulation model shouldbe the subject of further work

Figure 19 shows the vehicle velocity together with thecontrol signals recorded during run 2 The black curvesrepresent the real vehicle velocity V119903 and the control signalGreen curves are the optimum control strategy st119880 andthe optimal velocity V119900119901119905 determined by the simulationThe graph shows the entire distance travelled (10 laps) Theanalysis of the graph shows that the driver did not performthe exact planned strategy Errors in the implementationof the strategy are related to the disruptions During thecompetition the driver is not alone on the track in certainsituations the driver cannot overtake other participants andcannot take the optimal path In addition weather conditionsuch as wind has influence on the motion resistance In suchcases the driver has to modify the optimal control strategy

In Figure 20 the velocity recorded during the race V119903(black) and the velocity obtained by the computer simulationV119904119894119898 (red) were shown V119904119894119898 was determined by computersimulation by using real control signal The purpose of thissimulation was to investigate the correctness of identification

VrVopt

Ur Uopt

2000 4000 6000 8000 10000 12000 14000 16000 180000X [m]

05

10152025303540

V [k

mh

]

Figure 19 Comparison of speed and control signal during attempt2

2000 4000 6000 8000 10000 12000 14000 16000 180000x [m]

05

10152025303540

V [k

mh

]

Ur

VrVsim

Figure 20 Comparison of speed registered in real conditions withthe speed determined by computer simulation

of the simulation model and to identify the identificationerror

Compared to the Shell Eco-marathon competitions heldin 2012 and 2013 our performance has improved The resultsin these years were equal to 425 [km kWh] and 454[km kWh] respectively In 2012 and 2013 the controlstrategy was chosen on the basis of the simulation modelbut the model was not adequately identified and the controlstrategy had to be modified In previous editions of therace the implementation of optimal control strategy was notsupported by the visualization system which would informthe driver of the need to take specific actions (pressing orreleasing the accelerator button)

6 Conclusion

The presented method was developed and tested for aprototype electric racing car that has been designed for theShell Eco-marathon race As it was shown the results of thenumerical simulations were very similar to the outcomes ofthe real races in the context of the final result of energyconsumption and the profile of velocity of the car during therace The method has been developed and applied since 2012

Journal of Advanced Transportation 19

and led in 2014 to achieving the optimal result for this type ofthe vehicle

The optimization method was evaluated The resultsachieved during the race attempts where the optimal con-trol strategy was applied (4813 and 4873 kmkWh) werecompared to the result where the strategy was proposed bythe experts (3654 kmkWh) who already had contact withthe results of similar optimization models Optimal attemptswere better by over 30 despite errors in the implementationof the strategy by the driver In the case of experts who did nothave such experiences the differences were even greater

Further improvement of the control strategy is impossiblefor this type of a vehicle and the best way to reduce energyconsumption is by improving the mechanical design It wasthe reason to develop new racing cars for UrbanConceptBattery Electric and Hydrogen competitions The developedresearch methodology for vehicle optimization and controlstrategies has been developed and implemented in the ShellEco-marathon in 2015 which has improved the score to 504km kWhHowever the research has shown that the potentialfor improved performance of the MuSHELLka vehicle hasbeen exhausted No major structural changes in the vehiclecan significantly improve the result so in the followingyears the race was abandoned and the focus was on thedevelopment of the HydroGENIUS the electric vehicle ofUrbanConcept class with fuel cell stack as power sourcewhich eventually scored vice Championship in SEM 2016 Inthe further work it is planned to improve the optimizationresults by using the presented methodology in the case ofthe models of newly constructed vehicles The developmentof the optimization method should take into considerationthe uncertainty resulting from the given velocity strategyconsidering the real conditions of the race It is also possibleto use this method for controlling vehicles in traffic To dothis it is necessary to completely change the way of the routemodelling and the driving conditions modelling as well as todevelop a new optimization method for obtaining results inreal time

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] W Skarka ldquoReducing the Energy Consumption of ElectricVehiclesrdquo in Proceedings of the 22nd ISPE-Inc InternationalConference on Concurrent Engineering Location R Curran NWognumM Borsato et al Eds Advances in TransdisciplinaryEngineering pp 500ndash509 IOS Press Delft Netherlands 2015

[2] R Andrzejewski and J Awrejcewicz Nonlinear Dynamics of aWheeled Vehicle vol 10 Springer-Verlag New York NY USA2005

[3] D W Gao C Mi and A Emadi ldquoModeling and simulation ofelectric and hybrid vehiclesrdquo Proceedings of the IEEE vol 95 no4 pp 729ndash745 2007

[4] ldquoAdvisor documentationrdquo httpadv-vehiclesimsourceforgenet

[5] TMarkel A Brooker THendricks et al ldquoADVISORA systemsanalysis tool for advanced vehicle modelingrdquo Journal of PowerSources vol 110 no 1 pp 255ndash266 2002

[6] K B Wipke M R Cuddy and S D Burch ldquoADVISOR21 a user-friendly advanced powertrain simulation using acombined backwardforward approachrdquo IEEE Transactions onVehicular Technology vol 48 no 6 pp 1751ndash1761 1999

[7] ldquoWebsiterdquo 2014 httpwwwtransportationanlgovmodeling[8] ldquoWebsiterdquo 2014 httpwwwautonomienet[9] K Krykowski J Hetmanczyk Z Gałuszkiewicz and R Mik-

siewicz ldquoComputer analysis of high-speed PM BLDC motorpropertiesrdquo COMPEL - The International Journal for Computa-tion and Mathematics in Electrical and Electronic Engineeringvol 30 no 3 pp 941ndash956 2011

[10] M Vaillant M Eckert and F Gauterin ldquoEnergy managementstrategy to be used in design space exploration for electricpowertrain optimizationrdquo inProceedings of the 2014 9th Interna-tional Conference on Ecological Vehicles and Renewable EnergiesEVER 2014 mco March 2014

[11] A T Nguyen S Reiter and P Rigo ldquoA review on simulation-based optimization methods applied to building performanceanalysisrdquo Applied Energy vol 113 pp 1043ndash1058 2014

[12] W Silka and W Siłka Energy Intensity in the Car Traffic InPolish WNT Warszawa 1997

[13] T J Barlow S Latham I S Mrcrae and P Boulter A referencebook of driving cycles for use in the measurement of roadvehicle emissions TRL 2009 httpswwwgovukgovernmentuploadssystemdata

[14] R N Jazar Vehicle Dynamics Theory and Application SpringerUS Boston MA 2008

[15] MMeywerk ldquoVehicle Dynamicsrdquo inWest Sussex JohnWiley ampSons Lecture Notes to theMOOCVehicle Dynamics of iversity1st edition 2015

[16] MMitschke andHWallentowitzDynamik der KraftfahrzeugeSpringer Berlin Germany 1972

[17] T Stefanski and Ł Zawarczynski ldquoParametric identification ofPM motor mathematical modelsrdquo Przegląd Elektrotechnicznyvol 88 no 4 B pp 224ndash229 2012

[18] A Cameron ldquoMeasuring drive-train efficiencyrdquoHuman Powervol 46

[19] B Rohloff and P Greb ldquoEfficiency measurements of bicycletransmissions a neverending storyrdquo Human Power vol 55 p11 2004

[20] J B Spicer C J K Richardson M J Ehrlich J R BernsteinM Fukuda and M Terada ldquoEffects of frictional loss on bicyclechain drive efficiencyrdquo Journal of Mechanical Design vol 123no 4 pp 598ndash605 2001

[21] K Sternal A Cholewa W Skarka and M Targosz ldquoElec-tric vehicle for the studentsrsquo shell eco-marathon competitionDesign of the car and telemetry systemrdquo Communications inComputer and Information Science vol 329 pp 26ndash33 2012

[22] K Cichonski and W Skarka ldquoInnovative control system forhigh efficiency electric urban vehiclerdquo Communications inComputer and Information Science vol 531 pp 121ndash130 2015

[23] M J Er and R J Oentaryo ldquoComputational IntelligenceMethods andTechniques (Rutkowski L 2008) [BookReview]rdquoIEEE Computational Intelligence Magazine vol 6 no 4 pp 76ndash78 2011

[24] M Targosz M Szumowski W Skarka and P PrzystałkaldquoVelocity Planning of an Electric Vehicle Using an Evolutionary

12 Journal of Advanced Transportation

Table 3 The types of tires used in the prototype vehicle

Tiresmarker Name of the tire Tirersquos

symbol Shape Type of tread Workingpressure

W1

Michelin ShellEco-marathon 4575R16 Rectangular Slick max500 [kPa]

W2

SchwalbeUl-Termo 23-406 Round Slick 600-1100 [kPa]

W3

Continental SportContact 28-406 Round Slick 600 [kPa]

W4

SchwalbeMarathon 40-406 Round Symmetrical 400-700 [kPa]

Table 4 The total rolling coefficient depending on the tires

Tiresmarker Name of the tire The total rolling coefficient crr mMAPE []

W1 Michelin ShellEco-marathon 00035 784W2 Schwalbe Ultermo 00043 1103W3 Continental SportContact 00058 1252W4 Schwalbe Marathon 00053 445

0

1

2

3

4

5

6

7

8

V [m

s]

100 200 300 400 500 6000x [m]

W1rW1simW2rW2sim

W3rW3simW4rW4sim

Figure 12 Velocity of the vehicle during coast down test

mMAPE (modifiable Mean Absolute Percentage Error) Forvelocity simulationmMAPE can be determined by

119898119872119860119875119864 = 1001119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119881119903 minus 119881119904119894119898119881119898119886119909 minus 119881119898119894119899

10038161003816100381610038161003816100381610038161003816 (29)

Figure 12 shows the experimental data obtained in a coastdown test compared with the results obtained during thecomputer simulation

54 Model of the Race Circuit In accordance with themethodology presented in Section 32 three routes have beendescribed

(i) Route 1 a street race circuit at the Shell Eco-marathoncompetition in Rotterdam

Figure 13 Plan view of the path of the drive on route 1 in Rotterdam

(ii) Routes 2 and 3 on the experimental rides track of theFiat Chrysler Automobiles Poland factory located inTychy in the south of Poland

The Shell Eco-marathon competition is held on a streetcircuit in Rotterdam One lap is 1630 meters long Vehicleshave to cover ten laps in no longer than 39 minutes so suchrequirements impose an averageminimum speed of 25 kmh

The trajectory of the vehicle path was developed usingsatellite images The vehicle trajectory was determined usingthe maximum curvature possible that could be obtained onthe existing roads

Movement of the vehicle in a curved motion causesthe centrifugal force Centrifugal force creates additionalresistance This resistance is inversely proportional to theradius of the path (8) so it is justified to select the largestradius In addition if the centrifugal force exceeds thelimit value it could provide to the side slip of the vehicleAccording to drawings in AutoCAD Civil 3D the lengths ofstraight sections and the lengths and the radius of arcs wereobtained Figure 13 shows a plan view of the path of the drive

Driving the prototype vehicle on public roads is prohib-ited and can be dangerous Vehicle testing was also carried

Journal of Advanced Transportation 13

Table 5 Travel times and total lengths of the routes

Route Length of the lap D [m] The numberof laps The total length of the route Dc [m] Travel time Tmax [s]

Route 1Rotterdam 1630 10 16 300 2340

Route 2Tychy 640 5 3200 460

Route 3Tychy 1000 5 5000 720

Figure 14 Plan view of the path of the drive on route 3 in Tychy

out on the experimental rides track of the Fiat ChryslerAutomobiles Poland factory

For the track in Tychy geodetic measurements weretaken using theDGPS (Differential Global Positioning System)technology The measuring points were collected along theaxis of the road with the distance between points amountingto 10 meters If on the measured route direction or elevationwere changed the frequency of measurement was increasedGeodetic coordinates were also imported intoAutoCADCivil3D and were used to prepare data concerning the route thatwas imported into the simulation environment MATLAB-Simulink Figures 14 and 15 show the path and elevationprofile respectively

Selected routes 2 and 3 have significant differences com-pared to route 1 especially in the height profile This set ofroutes was selected to verify the effect of the route profile onthe achieved results and to verify the proposed optimizationmethods for various road conditions The routes in Tychyare located in an open area there are no large buildingswhich guarantees stability of wind conditions The technicalcondition of the surface on routes 2 and 3 is much worsethan on route 1 which has a significant influence on therolling resistance Rolling resistance was also identified andintroduced into the simulation model For route 2 the c119903119903coefficient was 00056 and for route 3 was 00068

55 Verification of the Simulation Model In order to verifythe compatibility of the identified simulation model a seriesof numerical simulations and experimental tests were per-formed The first experiment consisted of running 300 [m]with a control strategy of 50 [m] with the workingmotor andafter that the vehicle was moving freely for the next 50 [m]The motor is turned on three times Figures 16(a) and 16(b)show the velocity of the vehicle and the power of the motorin function of the distance determined during the experiment

(red curves) and during the numerical simulations (greencurves)

Verification of the data derived from the simulation andthe experimentwas conducted usingmMAPE (29) Formotorpower simulationmMAPE can be determined by

119898119872119860119875119864119875 = 1001119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119875119903 minus 119875119904119894119898119875119898119886119909 minus 119875119898119894119899

10038161003816100381610038161003816100381610038161003816 (30)

where P119903 is the motor power measured during experimentand P119904119894119898 is the motor power conducted in simulation

As a result of the model validation tests estimationerror of the velocity was on level between 235 and 534However the motor power error level was greater It wasbetween 802 and 998

56 Determination of the Optimal Control Strategy Thelength of route 1 and the number of laps are determined bythe organizers of the Shell Eco-marathon competition Thelength of routes 2 and 3 is derived from the existing road planwhere it was possible to carry out trials in real conditionsThenumber of laps for routes 2 and 3 was assumed arbitrarily

The travel time for route 1 is based on the rules of therace which determine the minimum average speed of thevehicle Based on the average speed and the length of routes 2and 3 the travel times for these routes were determined Themaximum travel times and the total length of the route aswell as the number and length of one lap D are summarizedin Table 5

Evolutionary algorithms which are available in theMAT-LAB Global Optimization Toolbox were used From theMATLAB workspace the algorithm ran a simulation modelin a Simulink environment During optimization while usingevolutionary algorithms the maximum number of fitnessfunction evaluations 119873119891V119886119897

is the product of the populationsize 119873119901119900119901 and number of generations 119873119892119890119899

It was assumed that the total number of fitness functionevaluations was equal to 104 therefore should this value beexceeded the calculation would be cancelled Therefore thetotal number of generations 119873119892119890119899 is dependent on the valueof population size 119873119901119900119901

As part of this work phase the vectors st119880 st119881 15 andst119881 10 of the optimum control strategy for an electric vehiclefor routes 1 2 and 3 were determined During evolutionaryoptimization the heuristic method of crossing was usedand the probability of crossing was established on the basisof previous studies at the level of 08 [24 29] At the

14 Journal of Advanced Transportation

0+000

106410

minus164 minus492minus166 minus012 minus018 minus082 minus035 059 031

811

0+100 0+200 0+300 0+400 0+500 0+600 0+700 0+800 0+900 1+000

Figure 15 Profile of the path on route 3 in Tychy

50 100 150 200 250 3000X [m]

0

2

4

6

8

10

V [m

s]

(a) DT1

0

100

200

300

400

500

P [W

]50 100 150 200 250 3000

X [m]

(b) DT1

Figure 16 The velocity and the power determined with used DT1 drive unit

stage of reproduction the elitist succession method wasapplied where the best adapted two individuals in the currentpopulation passed to the next population An adaptivemethod of mutation was used The remaining parameters ofthe algorithm remain the default for the MATLAB GlobalOptimization Toolbox

The first case was the search st119880 vector for route 1Figures 17(a)ndash17(c) show the vehicle velocity V119904119894119898 obtainedby computer simulation The graph of the st119880 control signalis graphically displayed Figure 17 shows the results wherethe optimal control strategy st119880119900119901119905 was used and populationwas 119873119901119900119901=100 and 119873119892119890119899=100 The total energy consumptionwas estimated as r119904119894119898=527633 [km kWh] Figure 17(a) showsthe vehicle speed and control signal st119880 during the first lapwhile Figure 17(b) shows center laps and Figure 17(c) showsthe last lap Figure 17(d) shows the curves of the mean valuesof the fitness functions f 119907119886119897 depending on the number ofcalculations of these functions during the optimization ofthe control strategy There are eight curves in the graph(Figure 17(d)) for each of the 119873119901119900119901 parameters used in thealgorithm

When analyzing the vehicle velocity chart on the last lapof route 1 (Figure 17(c)) it can be seen that according tothe determined control strategy the propulsion system of thevehicle should no longer be used The vehicle should use thestored kinetic energy

The analysis of vehicle velocity V119904119894119898 during the last lapindicates that at the moment of reaching the given distancethe speed was still about 2 [ms] This demonstrates thatthe simulated vehicle has kinetic energy that would haveto be dispersed by the braking system or recovered by the

electric motor Having such a speed does not mean that thereis still possibility for improvement Lower speed at the endof the route has to cause higher speed of the earlier partsof the route This speed is the optimum speed due to thechosen criterion From the analysis of the shape of the fitnessfunction (Figure 17(d)) it can be seen that for route 1 itis preferable to use a smaller population of 119873119901119900119901=25 andincrease the number of 119873119892119890119899=400 The curve shape for thiscase is steep and it falls to the minimum value of the fitnessfunction which may indicate that the algorithm has reacheda convergence

Results of the optimization where B type of coding wasused were analyzed The results obtained as the mean of ther119904119894119898 result together with the standard deviation from all thetests were summarized in Table 6

By analyzing the results in Table 6 it can be seen thatfor route 1 better results were obtained (reduced simulatedtotal energy consumption) using A coding compared to Bespecially for st119881 15 whose results are characterized by thehighest standard deviation For routes 2 and 3 the same as forroute 1 the procedure was followed Optimization strategieshave been optimized for all variants of control vector st119880st119881 15 st10

The results using the control strategy st119881 10 are shownin Figures 18(a)ndash18(c) (119873119901119900119901=100 where r119904119894119898=351795 [km kWh]) Figure 18(d) illustrates the graph of the value of thefitness function

The results obtained for route 2 are presented in Table 7For route 2 compared to route 1 the best results were

achieved using the stV10 vector When using vectors st119880 andstV15 the results were slightly worse Having analyzed the size

Journal of Advanced Transportation 15

0

2

4

6

8

10V

[ms

]

VsimstU

500 1000 15000X [m]

(a) Lap 1

0

2

4

6

8

10

V [m

s]

2500 30002000X [m]

VsimstU

(b) Laps 2-9

0

2

4

6

8

10

V [m

s]

155 1615X [m]

Vsimstu

times104

(c) Lap 10

times10minus3

Npop=25Npop=50Npop=75Npop=100

Npop=125Npop=150Npop=175Npop=200

15

2

25

3

35

4f va

l

2000 4000 6000 8000 100000Nfval

(d) Mean values of the fitness functions

Figure 17 Vehicle speed and control signal st119880 for route 1

Table 6 The results for route 1

The type of coding A The type of coding Bst119880 st11988115 st11988110119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 52465 1459 42845 1741 51569 5477550 52579 10053 44431 22486 51492 3409475 52497 39913 43842 28173 51256 80682100 52589 18128 42232 1797 51166 49379125 52625 13862 42733 39616 51341 70765150 5243 2979 4435 47701 51486 27086175 52513 2511 41428 27299 51838 19358200 52579 19666 42337 25776 51204 78357

16 Journal of Advanced Transportation

100 200 300 400 500 6000X [m]

0

2

4

6

8

10V

[ms

]

VsimstV10

USET

(a) Lap 1

0

2

4

6

8

10

V [m

s]

800 900 1000 1100 1200700X [m]

VsimstV10

USET

(b) Laps 2-4

0

2

4

6

8

10

V [m

s]

2700 2800 2900 3000 3100 32002600X [m]

VsimstV10

USET

(c) Lap 5

times10minus3

Npop=25Npop=50Npop=75Npop=100

Npop=125Npop=150Npop=175Npop=200

275

28

285

29

295

3

305

f val

2000 4000 6000 8000 100000Nfval

(d) Mean values of the fitness functions

Figure 18 Vehicle speed and control signal st11988110 for route 2

of the population used in the optimization process it shouldbe noted that for route 2 it is preferable to use higher value of119873119901119900119901 For all the analyzed cases the best average results for119873119901119900119901=200 were obtained Table 8 summarizes the results forroute 3

For route 3 the average results were reported for a largerpopulation of119873119901119900119901 with B coding In the case of using vectorwith A type coding no characteristic change was notedAs expected comparing the standard deviation betweenalgorithms using B coding the standard deviation is less forthe less variance range

Evolutionary algorithms are not complete search algo-rithms therefore it is not possible to determine whetherthe solution found is best for the chosen criterion and theconstraints assumed

57 Applying the Optimal Control Strategy in Real ConditionsElectric vehicle energy consumption optimization was finallyverified in real conditions at the European edition of the ShellEco-marathon held on 16-18 May 2014 in Rotterdam

Optimal control strategy st119880was displayed by a prototypevisualization system Visualization unit is installed in the

Journal of Advanced Transportation 17

Table 7 The results for route 2

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 34138 66734 34294 23839 34873 5353250 34573 46359 35003 462 3506 3886275 34512 55134 34961 33476 35419 067858100 34836 45332 35253 26117 3544 19295125 34632 52704 35017 49039 35483 14756150 34552 63714 35326 14885 35343 071015175 35063 18728 35274 47141 35564 038022200 35073 14496 3540 13389 35569 14942

Table 8 The results for route 3

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 28071 10173 28643 7323 30994 277650 29346 6142 29581 7894 30874 439975 29711 5002 29217 7367 31141 1856100 29826 3231 29515 7022 30957 4049125 29781 2980 29866 12977 31168 3445150 29453 3346 30217 9623 31288 1249175 29234 2317 30621 6816 31481 1261200 29686 2337 30531 11737 31089 4880

Table 9 Comparison of simulation results with experimental tests

Number of attempts 119903119878119864ndash119898 119903119903 119903119904119894119898 119903119900119901119905 119890119898 119890119894 119890119904119905Attempt 1 3654 3608 - - 125 - -Attempt 2 4813 5082 5148 5265 558 129 36Attempt 3 4873 5127 5198 5265 521 139 269Attempt 4 Failed attempt damaged tires during 1st lap

steering wheel of the vehicle The visualization system showsthe basic data such as instantaneous speed average speedtravel time and distance In addition the visualization systemprovides information on which part of the track the drivershould press the acceleration button to execute the optimalcontrol strategy Measurement of the position on the track iscarried out by the odometrical measuring system Due to thepossibility of accumulating errors in the measurement of theroad the driver will reset the measuring system every timeheshe exceeds the lap line

Table 9 presents the results of all the measurementsconducted during the Shell Eco-marathonThe columns in theTable 9 contain

(i) r119878119864119898 [kmkWh] the result recorded during the raceby the measuring device provided by the organizerthe results are available on the Shell Eco-marathonofficial website

(ii) r119903 [kWkWh] the result based on the indications of aprototypemeasuring system permanently installed inthe vehicle

(iii) r119904119894119898 the result estimated by computer simulationusing recorded real control signal U119903

(iv) r119900119901119905 the result obtained by computer simulation usingthe optimal control strategy U119900119901119905

Table 9 also includes the following

(i) Measurement error

119890119898 = 1003816100381610038161003816119903119878119864119898 minus 1199031199031003816100381610038161003816119903119878119864119898 100 (31)

(ii) Identification error

119890119894 =1003816100381610038161003816119903119903 minus 1199031199041198941198981003816100381610038161003816119903119903 100 (32)

(iii) Strategy implementation error

119890119904119905 =10038161003816100381610038161003816119903119903 minus 11990311990011990111990510038161003816100381610038161003816119903119903 100 (33)

18 Journal of Advanced Transportation

There were four measurement trials available Duringrun 1 a much weaker result was obtained than estimated bysimulation The driver performed run 1 without a definedcontrol strategy As part of the experiment the driver andthe support team were asked to select the optimal tires forthe vehicle and to implement the proposed control strategyDuring run 1 only the travel time of individual laps waschecked According to the choice of the team in run 1 tiresW2 were selected (Table 4) During this test the worst resultwas obtained about 24 and 25 worse than in the othertrials In subsequent runs 2 and 3 the vehicle was equippedwith the best W1 tires (Table 4) The driver has implementedan algorithm-based optimal control strategy Strategy infor-mation was provided by the visualization system During run3 the best result was recorded This result was taken intoaccount in the classification of competitions where the teamplaced in 12 positions out of 28 classified teams Trials 4 dueto damage to the tires were not successful

Measurement error was from 125 to 558 dependingon the sample The measurement system installed perma-nently in the vehicle is a prototype system This systemhas been calibrated using available laboratory equipmentMeasurement errors indicate that other measuring devices ofthe higher accuracy class should be used

Based on the measurement data obtained during testdrives the model was tuned thus reducing the identificationerror The competition took place in stable weather thedivergence of results was small and was about 129 forsample 2 and 139 for sample 3

The difference between the results determined duringnumerical simulation and that obtained in the real run was36 for sample 2 and 269 for sample 3 The difference atthis level was considered to be small Searching for optimalcontrol strategy has not taken into account possible rdquoerrorsrdquowhich could be made by the driver and which result fromthe current situation on the route for example selecting thepath and using the route by other participants in the raceIncluding driver behaviour in the simulation model shouldbe the subject of further work

Figure 19 shows the vehicle velocity together with thecontrol signals recorded during run 2 The black curvesrepresent the real vehicle velocity V119903 and the control signalGreen curves are the optimum control strategy st119880 andthe optimal velocity V119900119901119905 determined by the simulationThe graph shows the entire distance travelled (10 laps) Theanalysis of the graph shows that the driver did not performthe exact planned strategy Errors in the implementationof the strategy are related to the disruptions During thecompetition the driver is not alone on the track in certainsituations the driver cannot overtake other participants andcannot take the optimal path In addition weather conditionsuch as wind has influence on the motion resistance In suchcases the driver has to modify the optimal control strategy

In Figure 20 the velocity recorded during the race V119903(black) and the velocity obtained by the computer simulationV119904119894119898 (red) were shown V119904119894119898 was determined by computersimulation by using real control signal The purpose of thissimulation was to investigate the correctness of identification

VrVopt

Ur Uopt

2000 4000 6000 8000 10000 12000 14000 16000 180000X [m]

05

10152025303540

V [k

mh

]

Figure 19 Comparison of speed and control signal during attempt2

2000 4000 6000 8000 10000 12000 14000 16000 180000x [m]

05

10152025303540

V [k

mh

]

Ur

VrVsim

Figure 20 Comparison of speed registered in real conditions withthe speed determined by computer simulation

of the simulation model and to identify the identificationerror

Compared to the Shell Eco-marathon competitions heldin 2012 and 2013 our performance has improved The resultsin these years were equal to 425 [km kWh] and 454[km kWh] respectively In 2012 and 2013 the controlstrategy was chosen on the basis of the simulation modelbut the model was not adequately identified and the controlstrategy had to be modified In previous editions of therace the implementation of optimal control strategy was notsupported by the visualization system which would informthe driver of the need to take specific actions (pressing orreleasing the accelerator button)

6 Conclusion

The presented method was developed and tested for aprototype electric racing car that has been designed for theShell Eco-marathon race As it was shown the results of thenumerical simulations were very similar to the outcomes ofthe real races in the context of the final result of energyconsumption and the profile of velocity of the car during therace The method has been developed and applied since 2012

Journal of Advanced Transportation 19

and led in 2014 to achieving the optimal result for this type ofthe vehicle

The optimization method was evaluated The resultsachieved during the race attempts where the optimal con-trol strategy was applied (4813 and 4873 kmkWh) werecompared to the result where the strategy was proposed bythe experts (3654 kmkWh) who already had contact withthe results of similar optimization models Optimal attemptswere better by over 30 despite errors in the implementationof the strategy by the driver In the case of experts who did nothave such experiences the differences were even greater

Further improvement of the control strategy is impossiblefor this type of a vehicle and the best way to reduce energyconsumption is by improving the mechanical design It wasthe reason to develop new racing cars for UrbanConceptBattery Electric and Hydrogen competitions The developedresearch methodology for vehicle optimization and controlstrategies has been developed and implemented in the ShellEco-marathon in 2015 which has improved the score to 504km kWhHowever the research has shown that the potentialfor improved performance of the MuSHELLka vehicle hasbeen exhausted No major structural changes in the vehiclecan significantly improve the result so in the followingyears the race was abandoned and the focus was on thedevelopment of the HydroGENIUS the electric vehicle ofUrbanConcept class with fuel cell stack as power sourcewhich eventually scored vice Championship in SEM 2016 Inthe further work it is planned to improve the optimizationresults by using the presented methodology in the case ofthe models of newly constructed vehicles The developmentof the optimization method should take into considerationthe uncertainty resulting from the given velocity strategyconsidering the real conditions of the race It is also possibleto use this method for controlling vehicles in traffic To dothis it is necessary to completely change the way of the routemodelling and the driving conditions modelling as well as todevelop a new optimization method for obtaining results inreal time

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] W Skarka ldquoReducing the Energy Consumption of ElectricVehiclesrdquo in Proceedings of the 22nd ISPE-Inc InternationalConference on Concurrent Engineering Location R Curran NWognumM Borsato et al Eds Advances in TransdisciplinaryEngineering pp 500ndash509 IOS Press Delft Netherlands 2015

[2] R Andrzejewski and J Awrejcewicz Nonlinear Dynamics of aWheeled Vehicle vol 10 Springer-Verlag New York NY USA2005

[3] D W Gao C Mi and A Emadi ldquoModeling and simulation ofelectric and hybrid vehiclesrdquo Proceedings of the IEEE vol 95 no4 pp 729ndash745 2007

[4] ldquoAdvisor documentationrdquo httpadv-vehiclesimsourceforgenet

[5] TMarkel A Brooker THendricks et al ldquoADVISORA systemsanalysis tool for advanced vehicle modelingrdquo Journal of PowerSources vol 110 no 1 pp 255ndash266 2002

[6] K B Wipke M R Cuddy and S D Burch ldquoADVISOR21 a user-friendly advanced powertrain simulation using acombined backwardforward approachrdquo IEEE Transactions onVehicular Technology vol 48 no 6 pp 1751ndash1761 1999

[7] ldquoWebsiterdquo 2014 httpwwwtransportationanlgovmodeling[8] ldquoWebsiterdquo 2014 httpwwwautonomienet[9] K Krykowski J Hetmanczyk Z Gałuszkiewicz and R Mik-

siewicz ldquoComputer analysis of high-speed PM BLDC motorpropertiesrdquo COMPEL - The International Journal for Computa-tion and Mathematics in Electrical and Electronic Engineeringvol 30 no 3 pp 941ndash956 2011

[10] M Vaillant M Eckert and F Gauterin ldquoEnergy managementstrategy to be used in design space exploration for electricpowertrain optimizationrdquo inProceedings of the 2014 9th Interna-tional Conference on Ecological Vehicles and Renewable EnergiesEVER 2014 mco March 2014

[11] A T Nguyen S Reiter and P Rigo ldquoA review on simulation-based optimization methods applied to building performanceanalysisrdquo Applied Energy vol 113 pp 1043ndash1058 2014

[12] W Silka and W Siłka Energy Intensity in the Car Traffic InPolish WNT Warszawa 1997

[13] T J Barlow S Latham I S Mrcrae and P Boulter A referencebook of driving cycles for use in the measurement of roadvehicle emissions TRL 2009 httpswwwgovukgovernmentuploadssystemdata

[14] R N Jazar Vehicle Dynamics Theory and Application SpringerUS Boston MA 2008

[15] MMeywerk ldquoVehicle Dynamicsrdquo inWest Sussex JohnWiley ampSons Lecture Notes to theMOOCVehicle Dynamics of iversity1st edition 2015

[16] MMitschke andHWallentowitzDynamik der KraftfahrzeugeSpringer Berlin Germany 1972

[17] T Stefanski and Ł Zawarczynski ldquoParametric identification ofPM motor mathematical modelsrdquo Przegląd Elektrotechnicznyvol 88 no 4 B pp 224ndash229 2012

[18] A Cameron ldquoMeasuring drive-train efficiencyrdquoHuman Powervol 46

[19] B Rohloff and P Greb ldquoEfficiency measurements of bicycletransmissions a neverending storyrdquo Human Power vol 55 p11 2004

[20] J B Spicer C J K Richardson M J Ehrlich J R BernsteinM Fukuda and M Terada ldquoEffects of frictional loss on bicyclechain drive efficiencyrdquo Journal of Mechanical Design vol 123no 4 pp 598ndash605 2001

[21] K Sternal A Cholewa W Skarka and M Targosz ldquoElec-tric vehicle for the studentsrsquo shell eco-marathon competitionDesign of the car and telemetry systemrdquo Communications inComputer and Information Science vol 329 pp 26ndash33 2012

[22] K Cichonski and W Skarka ldquoInnovative control system forhigh efficiency electric urban vehiclerdquo Communications inComputer and Information Science vol 531 pp 121ndash130 2015

[23] M J Er and R J Oentaryo ldquoComputational IntelligenceMethods andTechniques (Rutkowski L 2008) [BookReview]rdquoIEEE Computational Intelligence Magazine vol 6 no 4 pp 76ndash78 2011

[24] M Targosz M Szumowski W Skarka and P PrzystałkaldquoVelocity Planning of an Electric Vehicle Using an Evolutionary

Journal of Advanced Transportation 13

Table 5 Travel times and total lengths of the routes

Route Length of the lap D [m] The numberof laps The total length of the route Dc [m] Travel time Tmax [s]

Route 1Rotterdam 1630 10 16 300 2340

Route 2Tychy 640 5 3200 460

Route 3Tychy 1000 5 5000 720

Figure 14 Plan view of the path of the drive on route 3 in Tychy

out on the experimental rides track of the Fiat ChryslerAutomobiles Poland factory

For the track in Tychy geodetic measurements weretaken using theDGPS (Differential Global Positioning System)technology The measuring points were collected along theaxis of the road with the distance between points amountingto 10 meters If on the measured route direction or elevationwere changed the frequency of measurement was increasedGeodetic coordinates were also imported intoAutoCADCivil3D and were used to prepare data concerning the route thatwas imported into the simulation environment MATLAB-Simulink Figures 14 and 15 show the path and elevationprofile respectively

Selected routes 2 and 3 have significant differences com-pared to route 1 especially in the height profile This set ofroutes was selected to verify the effect of the route profile onthe achieved results and to verify the proposed optimizationmethods for various road conditions The routes in Tychyare located in an open area there are no large buildingswhich guarantees stability of wind conditions The technicalcondition of the surface on routes 2 and 3 is much worsethan on route 1 which has a significant influence on therolling resistance Rolling resistance was also identified andintroduced into the simulation model For route 2 the c119903119903coefficient was 00056 and for route 3 was 00068

55 Verification of the Simulation Model In order to verifythe compatibility of the identified simulation model a seriesof numerical simulations and experimental tests were per-formed The first experiment consisted of running 300 [m]with a control strategy of 50 [m] with the workingmotor andafter that the vehicle was moving freely for the next 50 [m]The motor is turned on three times Figures 16(a) and 16(b)show the velocity of the vehicle and the power of the motorin function of the distance determined during the experiment

(red curves) and during the numerical simulations (greencurves)

Verification of the data derived from the simulation andthe experimentwas conducted usingmMAPE (29) Formotorpower simulationmMAPE can be determined by

119898119872119860119875119864119875 = 1001119899119899sum119894=1

10038161003816100381610038161003816100381610038161003816119875119903 minus 119875119904119894119898119875119898119886119909 minus 119875119898119894119899

10038161003816100381610038161003816100381610038161003816 (30)

where P119903 is the motor power measured during experimentand P119904119894119898 is the motor power conducted in simulation

As a result of the model validation tests estimationerror of the velocity was on level between 235 and 534However the motor power error level was greater It wasbetween 802 and 998

56 Determination of the Optimal Control Strategy Thelength of route 1 and the number of laps are determined bythe organizers of the Shell Eco-marathon competition Thelength of routes 2 and 3 is derived from the existing road planwhere it was possible to carry out trials in real conditionsThenumber of laps for routes 2 and 3 was assumed arbitrarily

The travel time for route 1 is based on the rules of therace which determine the minimum average speed of thevehicle Based on the average speed and the length of routes 2and 3 the travel times for these routes were determined Themaximum travel times and the total length of the route aswell as the number and length of one lap D are summarizedin Table 5

Evolutionary algorithms which are available in theMAT-LAB Global Optimization Toolbox were used From theMATLAB workspace the algorithm ran a simulation modelin a Simulink environment During optimization while usingevolutionary algorithms the maximum number of fitnessfunction evaluations 119873119891V119886119897

is the product of the populationsize 119873119901119900119901 and number of generations 119873119892119890119899

It was assumed that the total number of fitness functionevaluations was equal to 104 therefore should this value beexceeded the calculation would be cancelled Therefore thetotal number of generations 119873119892119890119899 is dependent on the valueof population size 119873119901119900119901

As part of this work phase the vectors st119880 st119881 15 andst119881 10 of the optimum control strategy for an electric vehiclefor routes 1 2 and 3 were determined During evolutionaryoptimization the heuristic method of crossing was usedand the probability of crossing was established on the basisof previous studies at the level of 08 [24 29] At the

14 Journal of Advanced Transportation

0+000

106410

minus164 minus492minus166 minus012 minus018 minus082 minus035 059 031

811

0+100 0+200 0+300 0+400 0+500 0+600 0+700 0+800 0+900 1+000

Figure 15 Profile of the path on route 3 in Tychy

50 100 150 200 250 3000X [m]

0

2

4

6

8

10

V [m

s]

(a) DT1

0

100

200

300

400

500

P [W

]50 100 150 200 250 3000

X [m]

(b) DT1

Figure 16 The velocity and the power determined with used DT1 drive unit

stage of reproduction the elitist succession method wasapplied where the best adapted two individuals in the currentpopulation passed to the next population An adaptivemethod of mutation was used The remaining parameters ofthe algorithm remain the default for the MATLAB GlobalOptimization Toolbox

The first case was the search st119880 vector for route 1Figures 17(a)ndash17(c) show the vehicle velocity V119904119894119898 obtainedby computer simulation The graph of the st119880 control signalis graphically displayed Figure 17 shows the results wherethe optimal control strategy st119880119900119901119905 was used and populationwas 119873119901119900119901=100 and 119873119892119890119899=100 The total energy consumptionwas estimated as r119904119894119898=527633 [km kWh] Figure 17(a) showsthe vehicle speed and control signal st119880 during the first lapwhile Figure 17(b) shows center laps and Figure 17(c) showsthe last lap Figure 17(d) shows the curves of the mean valuesof the fitness functions f 119907119886119897 depending on the number ofcalculations of these functions during the optimization ofthe control strategy There are eight curves in the graph(Figure 17(d)) for each of the 119873119901119900119901 parameters used in thealgorithm

When analyzing the vehicle velocity chart on the last lapof route 1 (Figure 17(c)) it can be seen that according tothe determined control strategy the propulsion system of thevehicle should no longer be used The vehicle should use thestored kinetic energy

The analysis of vehicle velocity V119904119894119898 during the last lapindicates that at the moment of reaching the given distancethe speed was still about 2 [ms] This demonstrates thatthe simulated vehicle has kinetic energy that would haveto be dispersed by the braking system or recovered by the

electric motor Having such a speed does not mean that thereis still possibility for improvement Lower speed at the endof the route has to cause higher speed of the earlier partsof the route This speed is the optimum speed due to thechosen criterion From the analysis of the shape of the fitnessfunction (Figure 17(d)) it can be seen that for route 1 itis preferable to use a smaller population of 119873119901119900119901=25 andincrease the number of 119873119892119890119899=400 The curve shape for thiscase is steep and it falls to the minimum value of the fitnessfunction which may indicate that the algorithm has reacheda convergence

Results of the optimization where B type of coding wasused were analyzed The results obtained as the mean of ther119904119894119898 result together with the standard deviation from all thetests were summarized in Table 6

By analyzing the results in Table 6 it can be seen thatfor route 1 better results were obtained (reduced simulatedtotal energy consumption) using A coding compared to Bespecially for st119881 15 whose results are characterized by thehighest standard deviation For routes 2 and 3 the same as forroute 1 the procedure was followed Optimization strategieshave been optimized for all variants of control vector st119880st119881 15 st10

The results using the control strategy st119881 10 are shownin Figures 18(a)ndash18(c) (119873119901119900119901=100 where r119904119894119898=351795 [km kWh]) Figure 18(d) illustrates the graph of the value of thefitness function

The results obtained for route 2 are presented in Table 7For route 2 compared to route 1 the best results were

achieved using the stV10 vector When using vectors st119880 andstV15 the results were slightly worse Having analyzed the size

Journal of Advanced Transportation 15

0

2

4

6

8

10V

[ms

]

VsimstU

500 1000 15000X [m]

(a) Lap 1

0

2

4

6

8

10

V [m

s]

2500 30002000X [m]

VsimstU

(b) Laps 2-9

0

2

4

6

8

10

V [m

s]

155 1615X [m]

Vsimstu

times104

(c) Lap 10

times10minus3

Npop=25Npop=50Npop=75Npop=100

Npop=125Npop=150Npop=175Npop=200

15

2

25

3

35

4f va

l

2000 4000 6000 8000 100000Nfval

(d) Mean values of the fitness functions

Figure 17 Vehicle speed and control signal st119880 for route 1

Table 6 The results for route 1

The type of coding A The type of coding Bst119880 st11988115 st11988110119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 52465 1459 42845 1741 51569 5477550 52579 10053 44431 22486 51492 3409475 52497 39913 43842 28173 51256 80682100 52589 18128 42232 1797 51166 49379125 52625 13862 42733 39616 51341 70765150 5243 2979 4435 47701 51486 27086175 52513 2511 41428 27299 51838 19358200 52579 19666 42337 25776 51204 78357

16 Journal of Advanced Transportation

100 200 300 400 500 6000X [m]

0

2

4

6

8

10V

[ms

]

VsimstV10

USET

(a) Lap 1

0

2

4

6

8

10

V [m

s]

800 900 1000 1100 1200700X [m]

VsimstV10

USET

(b) Laps 2-4

0

2

4

6

8

10

V [m

s]

2700 2800 2900 3000 3100 32002600X [m]

VsimstV10

USET

(c) Lap 5

times10minus3

Npop=25Npop=50Npop=75Npop=100

Npop=125Npop=150Npop=175Npop=200

275

28

285

29

295

3

305

f val

2000 4000 6000 8000 100000Nfval

(d) Mean values of the fitness functions

Figure 18 Vehicle speed and control signal st11988110 for route 2

of the population used in the optimization process it shouldbe noted that for route 2 it is preferable to use higher value of119873119901119900119901 For all the analyzed cases the best average results for119873119901119900119901=200 were obtained Table 8 summarizes the results forroute 3

For route 3 the average results were reported for a largerpopulation of119873119901119900119901 with B coding In the case of using vectorwith A type coding no characteristic change was notedAs expected comparing the standard deviation betweenalgorithms using B coding the standard deviation is less forthe less variance range

Evolutionary algorithms are not complete search algo-rithms therefore it is not possible to determine whetherthe solution found is best for the chosen criterion and theconstraints assumed

57 Applying the Optimal Control Strategy in Real ConditionsElectric vehicle energy consumption optimization was finallyverified in real conditions at the European edition of the ShellEco-marathon held on 16-18 May 2014 in Rotterdam

Optimal control strategy st119880was displayed by a prototypevisualization system Visualization unit is installed in the

Journal of Advanced Transportation 17

Table 7 The results for route 2

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 34138 66734 34294 23839 34873 5353250 34573 46359 35003 462 3506 3886275 34512 55134 34961 33476 35419 067858100 34836 45332 35253 26117 3544 19295125 34632 52704 35017 49039 35483 14756150 34552 63714 35326 14885 35343 071015175 35063 18728 35274 47141 35564 038022200 35073 14496 3540 13389 35569 14942

Table 8 The results for route 3

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 28071 10173 28643 7323 30994 277650 29346 6142 29581 7894 30874 439975 29711 5002 29217 7367 31141 1856100 29826 3231 29515 7022 30957 4049125 29781 2980 29866 12977 31168 3445150 29453 3346 30217 9623 31288 1249175 29234 2317 30621 6816 31481 1261200 29686 2337 30531 11737 31089 4880

Table 9 Comparison of simulation results with experimental tests

Number of attempts 119903119878119864ndash119898 119903119903 119903119904119894119898 119903119900119901119905 119890119898 119890119894 119890119904119905Attempt 1 3654 3608 - - 125 - -Attempt 2 4813 5082 5148 5265 558 129 36Attempt 3 4873 5127 5198 5265 521 139 269Attempt 4 Failed attempt damaged tires during 1st lap

steering wheel of the vehicle The visualization system showsthe basic data such as instantaneous speed average speedtravel time and distance In addition the visualization systemprovides information on which part of the track the drivershould press the acceleration button to execute the optimalcontrol strategy Measurement of the position on the track iscarried out by the odometrical measuring system Due to thepossibility of accumulating errors in the measurement of theroad the driver will reset the measuring system every timeheshe exceeds the lap line

Table 9 presents the results of all the measurementsconducted during the Shell Eco-marathonThe columns in theTable 9 contain

(i) r119878119864119898 [kmkWh] the result recorded during the raceby the measuring device provided by the organizerthe results are available on the Shell Eco-marathonofficial website

(ii) r119903 [kWkWh] the result based on the indications of aprototypemeasuring system permanently installed inthe vehicle

(iii) r119904119894119898 the result estimated by computer simulationusing recorded real control signal U119903

(iv) r119900119901119905 the result obtained by computer simulation usingthe optimal control strategy U119900119901119905

Table 9 also includes the following

(i) Measurement error

119890119898 = 1003816100381610038161003816119903119878119864119898 minus 1199031199031003816100381610038161003816119903119878119864119898 100 (31)

(ii) Identification error

119890119894 =1003816100381610038161003816119903119903 minus 1199031199041198941198981003816100381610038161003816119903119903 100 (32)

(iii) Strategy implementation error

119890119904119905 =10038161003816100381610038161003816119903119903 minus 11990311990011990111990510038161003816100381610038161003816119903119903 100 (33)

18 Journal of Advanced Transportation

There were four measurement trials available Duringrun 1 a much weaker result was obtained than estimated bysimulation The driver performed run 1 without a definedcontrol strategy As part of the experiment the driver andthe support team were asked to select the optimal tires forthe vehicle and to implement the proposed control strategyDuring run 1 only the travel time of individual laps waschecked According to the choice of the team in run 1 tiresW2 were selected (Table 4) During this test the worst resultwas obtained about 24 and 25 worse than in the othertrials In subsequent runs 2 and 3 the vehicle was equippedwith the best W1 tires (Table 4) The driver has implementedan algorithm-based optimal control strategy Strategy infor-mation was provided by the visualization system During run3 the best result was recorded This result was taken intoaccount in the classification of competitions where the teamplaced in 12 positions out of 28 classified teams Trials 4 dueto damage to the tires were not successful

Measurement error was from 125 to 558 dependingon the sample The measurement system installed perma-nently in the vehicle is a prototype system This systemhas been calibrated using available laboratory equipmentMeasurement errors indicate that other measuring devices ofthe higher accuracy class should be used

Based on the measurement data obtained during testdrives the model was tuned thus reducing the identificationerror The competition took place in stable weather thedivergence of results was small and was about 129 forsample 2 and 139 for sample 3

The difference between the results determined duringnumerical simulation and that obtained in the real run was36 for sample 2 and 269 for sample 3 The difference atthis level was considered to be small Searching for optimalcontrol strategy has not taken into account possible rdquoerrorsrdquowhich could be made by the driver and which result fromthe current situation on the route for example selecting thepath and using the route by other participants in the raceIncluding driver behaviour in the simulation model shouldbe the subject of further work

Figure 19 shows the vehicle velocity together with thecontrol signals recorded during run 2 The black curvesrepresent the real vehicle velocity V119903 and the control signalGreen curves are the optimum control strategy st119880 andthe optimal velocity V119900119901119905 determined by the simulationThe graph shows the entire distance travelled (10 laps) Theanalysis of the graph shows that the driver did not performthe exact planned strategy Errors in the implementationof the strategy are related to the disruptions During thecompetition the driver is not alone on the track in certainsituations the driver cannot overtake other participants andcannot take the optimal path In addition weather conditionsuch as wind has influence on the motion resistance In suchcases the driver has to modify the optimal control strategy

In Figure 20 the velocity recorded during the race V119903(black) and the velocity obtained by the computer simulationV119904119894119898 (red) were shown V119904119894119898 was determined by computersimulation by using real control signal The purpose of thissimulation was to investigate the correctness of identification

VrVopt

Ur Uopt

2000 4000 6000 8000 10000 12000 14000 16000 180000X [m]

05

10152025303540

V [k

mh

]

Figure 19 Comparison of speed and control signal during attempt2

2000 4000 6000 8000 10000 12000 14000 16000 180000x [m]

05

10152025303540

V [k

mh

]

Ur

VrVsim

Figure 20 Comparison of speed registered in real conditions withthe speed determined by computer simulation

of the simulation model and to identify the identificationerror

Compared to the Shell Eco-marathon competitions heldin 2012 and 2013 our performance has improved The resultsin these years were equal to 425 [km kWh] and 454[km kWh] respectively In 2012 and 2013 the controlstrategy was chosen on the basis of the simulation modelbut the model was not adequately identified and the controlstrategy had to be modified In previous editions of therace the implementation of optimal control strategy was notsupported by the visualization system which would informthe driver of the need to take specific actions (pressing orreleasing the accelerator button)

6 Conclusion

The presented method was developed and tested for aprototype electric racing car that has been designed for theShell Eco-marathon race As it was shown the results of thenumerical simulations were very similar to the outcomes ofthe real races in the context of the final result of energyconsumption and the profile of velocity of the car during therace The method has been developed and applied since 2012

Journal of Advanced Transportation 19

and led in 2014 to achieving the optimal result for this type ofthe vehicle

The optimization method was evaluated The resultsachieved during the race attempts where the optimal con-trol strategy was applied (4813 and 4873 kmkWh) werecompared to the result where the strategy was proposed bythe experts (3654 kmkWh) who already had contact withthe results of similar optimization models Optimal attemptswere better by over 30 despite errors in the implementationof the strategy by the driver In the case of experts who did nothave such experiences the differences were even greater

Further improvement of the control strategy is impossiblefor this type of a vehicle and the best way to reduce energyconsumption is by improving the mechanical design It wasthe reason to develop new racing cars for UrbanConceptBattery Electric and Hydrogen competitions The developedresearch methodology for vehicle optimization and controlstrategies has been developed and implemented in the ShellEco-marathon in 2015 which has improved the score to 504km kWhHowever the research has shown that the potentialfor improved performance of the MuSHELLka vehicle hasbeen exhausted No major structural changes in the vehiclecan significantly improve the result so in the followingyears the race was abandoned and the focus was on thedevelopment of the HydroGENIUS the electric vehicle ofUrbanConcept class with fuel cell stack as power sourcewhich eventually scored vice Championship in SEM 2016 Inthe further work it is planned to improve the optimizationresults by using the presented methodology in the case ofthe models of newly constructed vehicles The developmentof the optimization method should take into considerationthe uncertainty resulting from the given velocity strategyconsidering the real conditions of the race It is also possibleto use this method for controlling vehicles in traffic To dothis it is necessary to completely change the way of the routemodelling and the driving conditions modelling as well as todevelop a new optimization method for obtaining results inreal time

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] W Skarka ldquoReducing the Energy Consumption of ElectricVehiclesrdquo in Proceedings of the 22nd ISPE-Inc InternationalConference on Concurrent Engineering Location R Curran NWognumM Borsato et al Eds Advances in TransdisciplinaryEngineering pp 500ndash509 IOS Press Delft Netherlands 2015

[2] R Andrzejewski and J Awrejcewicz Nonlinear Dynamics of aWheeled Vehicle vol 10 Springer-Verlag New York NY USA2005

[3] D W Gao C Mi and A Emadi ldquoModeling and simulation ofelectric and hybrid vehiclesrdquo Proceedings of the IEEE vol 95 no4 pp 729ndash745 2007

[4] ldquoAdvisor documentationrdquo httpadv-vehiclesimsourceforgenet

[5] TMarkel A Brooker THendricks et al ldquoADVISORA systemsanalysis tool for advanced vehicle modelingrdquo Journal of PowerSources vol 110 no 1 pp 255ndash266 2002

[6] K B Wipke M R Cuddy and S D Burch ldquoADVISOR21 a user-friendly advanced powertrain simulation using acombined backwardforward approachrdquo IEEE Transactions onVehicular Technology vol 48 no 6 pp 1751ndash1761 1999

[7] ldquoWebsiterdquo 2014 httpwwwtransportationanlgovmodeling[8] ldquoWebsiterdquo 2014 httpwwwautonomienet[9] K Krykowski J Hetmanczyk Z Gałuszkiewicz and R Mik-

siewicz ldquoComputer analysis of high-speed PM BLDC motorpropertiesrdquo COMPEL - The International Journal for Computa-tion and Mathematics in Electrical and Electronic Engineeringvol 30 no 3 pp 941ndash956 2011

[10] M Vaillant M Eckert and F Gauterin ldquoEnergy managementstrategy to be used in design space exploration for electricpowertrain optimizationrdquo inProceedings of the 2014 9th Interna-tional Conference on Ecological Vehicles and Renewable EnergiesEVER 2014 mco March 2014

[11] A T Nguyen S Reiter and P Rigo ldquoA review on simulation-based optimization methods applied to building performanceanalysisrdquo Applied Energy vol 113 pp 1043ndash1058 2014

[12] W Silka and W Siłka Energy Intensity in the Car Traffic InPolish WNT Warszawa 1997

[13] T J Barlow S Latham I S Mrcrae and P Boulter A referencebook of driving cycles for use in the measurement of roadvehicle emissions TRL 2009 httpswwwgovukgovernmentuploadssystemdata

[14] R N Jazar Vehicle Dynamics Theory and Application SpringerUS Boston MA 2008

[15] MMeywerk ldquoVehicle Dynamicsrdquo inWest Sussex JohnWiley ampSons Lecture Notes to theMOOCVehicle Dynamics of iversity1st edition 2015

[16] MMitschke andHWallentowitzDynamik der KraftfahrzeugeSpringer Berlin Germany 1972

[17] T Stefanski and Ł Zawarczynski ldquoParametric identification ofPM motor mathematical modelsrdquo Przegląd Elektrotechnicznyvol 88 no 4 B pp 224ndash229 2012

[18] A Cameron ldquoMeasuring drive-train efficiencyrdquoHuman Powervol 46

[19] B Rohloff and P Greb ldquoEfficiency measurements of bicycletransmissions a neverending storyrdquo Human Power vol 55 p11 2004

[20] J B Spicer C J K Richardson M J Ehrlich J R BernsteinM Fukuda and M Terada ldquoEffects of frictional loss on bicyclechain drive efficiencyrdquo Journal of Mechanical Design vol 123no 4 pp 598ndash605 2001

[21] K Sternal A Cholewa W Skarka and M Targosz ldquoElec-tric vehicle for the studentsrsquo shell eco-marathon competitionDesign of the car and telemetry systemrdquo Communications inComputer and Information Science vol 329 pp 26ndash33 2012

[22] K Cichonski and W Skarka ldquoInnovative control system forhigh efficiency electric urban vehiclerdquo Communications inComputer and Information Science vol 531 pp 121ndash130 2015

[23] M J Er and R J Oentaryo ldquoComputational IntelligenceMethods andTechniques (Rutkowski L 2008) [BookReview]rdquoIEEE Computational Intelligence Magazine vol 6 no 4 pp 76ndash78 2011

[24] M Targosz M Szumowski W Skarka and P PrzystałkaldquoVelocity Planning of an Electric Vehicle Using an Evolutionary

14 Journal of Advanced Transportation

0+000

106410

minus164 minus492minus166 minus012 minus018 minus082 minus035 059 031

811

0+100 0+200 0+300 0+400 0+500 0+600 0+700 0+800 0+900 1+000

Figure 15 Profile of the path on route 3 in Tychy

50 100 150 200 250 3000X [m]

0

2

4

6

8

10

V [m

s]

(a) DT1

0

100

200

300

400

500

P [W

]50 100 150 200 250 3000

X [m]

(b) DT1

Figure 16 The velocity and the power determined with used DT1 drive unit

stage of reproduction the elitist succession method wasapplied where the best adapted two individuals in the currentpopulation passed to the next population An adaptivemethod of mutation was used The remaining parameters ofthe algorithm remain the default for the MATLAB GlobalOptimization Toolbox

The first case was the search st119880 vector for route 1Figures 17(a)ndash17(c) show the vehicle velocity V119904119894119898 obtainedby computer simulation The graph of the st119880 control signalis graphically displayed Figure 17 shows the results wherethe optimal control strategy st119880119900119901119905 was used and populationwas 119873119901119900119901=100 and 119873119892119890119899=100 The total energy consumptionwas estimated as r119904119894119898=527633 [km kWh] Figure 17(a) showsthe vehicle speed and control signal st119880 during the first lapwhile Figure 17(b) shows center laps and Figure 17(c) showsthe last lap Figure 17(d) shows the curves of the mean valuesof the fitness functions f 119907119886119897 depending on the number ofcalculations of these functions during the optimization ofthe control strategy There are eight curves in the graph(Figure 17(d)) for each of the 119873119901119900119901 parameters used in thealgorithm

When analyzing the vehicle velocity chart on the last lapof route 1 (Figure 17(c)) it can be seen that according tothe determined control strategy the propulsion system of thevehicle should no longer be used The vehicle should use thestored kinetic energy

The analysis of vehicle velocity V119904119894119898 during the last lapindicates that at the moment of reaching the given distancethe speed was still about 2 [ms] This demonstrates thatthe simulated vehicle has kinetic energy that would haveto be dispersed by the braking system or recovered by the

electric motor Having such a speed does not mean that thereis still possibility for improvement Lower speed at the endof the route has to cause higher speed of the earlier partsof the route This speed is the optimum speed due to thechosen criterion From the analysis of the shape of the fitnessfunction (Figure 17(d)) it can be seen that for route 1 itis preferable to use a smaller population of 119873119901119900119901=25 andincrease the number of 119873119892119890119899=400 The curve shape for thiscase is steep and it falls to the minimum value of the fitnessfunction which may indicate that the algorithm has reacheda convergence

Results of the optimization where B type of coding wasused were analyzed The results obtained as the mean of ther119904119894119898 result together with the standard deviation from all thetests were summarized in Table 6

By analyzing the results in Table 6 it can be seen thatfor route 1 better results were obtained (reduced simulatedtotal energy consumption) using A coding compared to Bespecially for st119881 15 whose results are characterized by thehighest standard deviation For routes 2 and 3 the same as forroute 1 the procedure was followed Optimization strategieshave been optimized for all variants of control vector st119880st119881 15 st10

The results using the control strategy st119881 10 are shownin Figures 18(a)ndash18(c) (119873119901119900119901=100 where r119904119894119898=351795 [km kWh]) Figure 18(d) illustrates the graph of the value of thefitness function

The results obtained for route 2 are presented in Table 7For route 2 compared to route 1 the best results were

achieved using the stV10 vector When using vectors st119880 andstV15 the results were slightly worse Having analyzed the size

Journal of Advanced Transportation 15

0

2

4

6

8

10V

[ms

]

VsimstU

500 1000 15000X [m]

(a) Lap 1

0

2

4

6

8

10

V [m

s]

2500 30002000X [m]

VsimstU

(b) Laps 2-9

0

2

4

6

8

10

V [m

s]

155 1615X [m]

Vsimstu

times104

(c) Lap 10

times10minus3

Npop=25Npop=50Npop=75Npop=100

Npop=125Npop=150Npop=175Npop=200

15

2

25

3

35

4f va

l

2000 4000 6000 8000 100000Nfval

(d) Mean values of the fitness functions

Figure 17 Vehicle speed and control signal st119880 for route 1

Table 6 The results for route 1

The type of coding A The type of coding Bst119880 st11988115 st11988110119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 52465 1459 42845 1741 51569 5477550 52579 10053 44431 22486 51492 3409475 52497 39913 43842 28173 51256 80682100 52589 18128 42232 1797 51166 49379125 52625 13862 42733 39616 51341 70765150 5243 2979 4435 47701 51486 27086175 52513 2511 41428 27299 51838 19358200 52579 19666 42337 25776 51204 78357

16 Journal of Advanced Transportation

100 200 300 400 500 6000X [m]

0

2

4

6

8

10V

[ms

]

VsimstV10

USET

(a) Lap 1

0

2

4

6

8

10

V [m

s]

800 900 1000 1100 1200700X [m]

VsimstV10

USET

(b) Laps 2-4

0

2

4

6

8

10

V [m

s]

2700 2800 2900 3000 3100 32002600X [m]

VsimstV10

USET

(c) Lap 5

times10minus3

Npop=25Npop=50Npop=75Npop=100

Npop=125Npop=150Npop=175Npop=200

275

28

285

29

295

3

305

f val

2000 4000 6000 8000 100000Nfval

(d) Mean values of the fitness functions

Figure 18 Vehicle speed and control signal st11988110 for route 2

of the population used in the optimization process it shouldbe noted that for route 2 it is preferable to use higher value of119873119901119900119901 For all the analyzed cases the best average results for119873119901119900119901=200 were obtained Table 8 summarizes the results forroute 3

For route 3 the average results were reported for a largerpopulation of119873119901119900119901 with B coding In the case of using vectorwith A type coding no characteristic change was notedAs expected comparing the standard deviation betweenalgorithms using B coding the standard deviation is less forthe less variance range

Evolutionary algorithms are not complete search algo-rithms therefore it is not possible to determine whetherthe solution found is best for the chosen criterion and theconstraints assumed

57 Applying the Optimal Control Strategy in Real ConditionsElectric vehicle energy consumption optimization was finallyverified in real conditions at the European edition of the ShellEco-marathon held on 16-18 May 2014 in Rotterdam

Optimal control strategy st119880was displayed by a prototypevisualization system Visualization unit is installed in the

Journal of Advanced Transportation 17

Table 7 The results for route 2

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 34138 66734 34294 23839 34873 5353250 34573 46359 35003 462 3506 3886275 34512 55134 34961 33476 35419 067858100 34836 45332 35253 26117 3544 19295125 34632 52704 35017 49039 35483 14756150 34552 63714 35326 14885 35343 071015175 35063 18728 35274 47141 35564 038022200 35073 14496 3540 13389 35569 14942

Table 8 The results for route 3

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 28071 10173 28643 7323 30994 277650 29346 6142 29581 7894 30874 439975 29711 5002 29217 7367 31141 1856100 29826 3231 29515 7022 30957 4049125 29781 2980 29866 12977 31168 3445150 29453 3346 30217 9623 31288 1249175 29234 2317 30621 6816 31481 1261200 29686 2337 30531 11737 31089 4880

Table 9 Comparison of simulation results with experimental tests

Number of attempts 119903119878119864ndash119898 119903119903 119903119904119894119898 119903119900119901119905 119890119898 119890119894 119890119904119905Attempt 1 3654 3608 - - 125 - -Attempt 2 4813 5082 5148 5265 558 129 36Attempt 3 4873 5127 5198 5265 521 139 269Attempt 4 Failed attempt damaged tires during 1st lap

steering wheel of the vehicle The visualization system showsthe basic data such as instantaneous speed average speedtravel time and distance In addition the visualization systemprovides information on which part of the track the drivershould press the acceleration button to execute the optimalcontrol strategy Measurement of the position on the track iscarried out by the odometrical measuring system Due to thepossibility of accumulating errors in the measurement of theroad the driver will reset the measuring system every timeheshe exceeds the lap line

Table 9 presents the results of all the measurementsconducted during the Shell Eco-marathonThe columns in theTable 9 contain

(i) r119878119864119898 [kmkWh] the result recorded during the raceby the measuring device provided by the organizerthe results are available on the Shell Eco-marathonofficial website

(ii) r119903 [kWkWh] the result based on the indications of aprototypemeasuring system permanently installed inthe vehicle

(iii) r119904119894119898 the result estimated by computer simulationusing recorded real control signal U119903

(iv) r119900119901119905 the result obtained by computer simulation usingthe optimal control strategy U119900119901119905

Table 9 also includes the following

(i) Measurement error

119890119898 = 1003816100381610038161003816119903119878119864119898 minus 1199031199031003816100381610038161003816119903119878119864119898 100 (31)

(ii) Identification error

119890119894 =1003816100381610038161003816119903119903 minus 1199031199041198941198981003816100381610038161003816119903119903 100 (32)

(iii) Strategy implementation error

119890119904119905 =10038161003816100381610038161003816119903119903 minus 11990311990011990111990510038161003816100381610038161003816119903119903 100 (33)

18 Journal of Advanced Transportation

There were four measurement trials available Duringrun 1 a much weaker result was obtained than estimated bysimulation The driver performed run 1 without a definedcontrol strategy As part of the experiment the driver andthe support team were asked to select the optimal tires forthe vehicle and to implement the proposed control strategyDuring run 1 only the travel time of individual laps waschecked According to the choice of the team in run 1 tiresW2 were selected (Table 4) During this test the worst resultwas obtained about 24 and 25 worse than in the othertrials In subsequent runs 2 and 3 the vehicle was equippedwith the best W1 tires (Table 4) The driver has implementedan algorithm-based optimal control strategy Strategy infor-mation was provided by the visualization system During run3 the best result was recorded This result was taken intoaccount in the classification of competitions where the teamplaced in 12 positions out of 28 classified teams Trials 4 dueto damage to the tires were not successful

Measurement error was from 125 to 558 dependingon the sample The measurement system installed perma-nently in the vehicle is a prototype system This systemhas been calibrated using available laboratory equipmentMeasurement errors indicate that other measuring devices ofthe higher accuracy class should be used

Based on the measurement data obtained during testdrives the model was tuned thus reducing the identificationerror The competition took place in stable weather thedivergence of results was small and was about 129 forsample 2 and 139 for sample 3

The difference between the results determined duringnumerical simulation and that obtained in the real run was36 for sample 2 and 269 for sample 3 The difference atthis level was considered to be small Searching for optimalcontrol strategy has not taken into account possible rdquoerrorsrdquowhich could be made by the driver and which result fromthe current situation on the route for example selecting thepath and using the route by other participants in the raceIncluding driver behaviour in the simulation model shouldbe the subject of further work

Figure 19 shows the vehicle velocity together with thecontrol signals recorded during run 2 The black curvesrepresent the real vehicle velocity V119903 and the control signalGreen curves are the optimum control strategy st119880 andthe optimal velocity V119900119901119905 determined by the simulationThe graph shows the entire distance travelled (10 laps) Theanalysis of the graph shows that the driver did not performthe exact planned strategy Errors in the implementationof the strategy are related to the disruptions During thecompetition the driver is not alone on the track in certainsituations the driver cannot overtake other participants andcannot take the optimal path In addition weather conditionsuch as wind has influence on the motion resistance In suchcases the driver has to modify the optimal control strategy

In Figure 20 the velocity recorded during the race V119903(black) and the velocity obtained by the computer simulationV119904119894119898 (red) were shown V119904119894119898 was determined by computersimulation by using real control signal The purpose of thissimulation was to investigate the correctness of identification

VrVopt

Ur Uopt

2000 4000 6000 8000 10000 12000 14000 16000 180000X [m]

05

10152025303540

V [k

mh

]

Figure 19 Comparison of speed and control signal during attempt2

2000 4000 6000 8000 10000 12000 14000 16000 180000x [m]

05

10152025303540

V [k

mh

]

Ur

VrVsim

Figure 20 Comparison of speed registered in real conditions withthe speed determined by computer simulation

of the simulation model and to identify the identificationerror

Compared to the Shell Eco-marathon competitions heldin 2012 and 2013 our performance has improved The resultsin these years were equal to 425 [km kWh] and 454[km kWh] respectively In 2012 and 2013 the controlstrategy was chosen on the basis of the simulation modelbut the model was not adequately identified and the controlstrategy had to be modified In previous editions of therace the implementation of optimal control strategy was notsupported by the visualization system which would informthe driver of the need to take specific actions (pressing orreleasing the accelerator button)

6 Conclusion

The presented method was developed and tested for aprototype electric racing car that has been designed for theShell Eco-marathon race As it was shown the results of thenumerical simulations were very similar to the outcomes ofthe real races in the context of the final result of energyconsumption and the profile of velocity of the car during therace The method has been developed and applied since 2012

Journal of Advanced Transportation 19

and led in 2014 to achieving the optimal result for this type ofthe vehicle

The optimization method was evaluated The resultsachieved during the race attempts where the optimal con-trol strategy was applied (4813 and 4873 kmkWh) werecompared to the result where the strategy was proposed bythe experts (3654 kmkWh) who already had contact withthe results of similar optimization models Optimal attemptswere better by over 30 despite errors in the implementationof the strategy by the driver In the case of experts who did nothave such experiences the differences were even greater

Further improvement of the control strategy is impossiblefor this type of a vehicle and the best way to reduce energyconsumption is by improving the mechanical design It wasthe reason to develop new racing cars for UrbanConceptBattery Electric and Hydrogen competitions The developedresearch methodology for vehicle optimization and controlstrategies has been developed and implemented in the ShellEco-marathon in 2015 which has improved the score to 504km kWhHowever the research has shown that the potentialfor improved performance of the MuSHELLka vehicle hasbeen exhausted No major structural changes in the vehiclecan significantly improve the result so in the followingyears the race was abandoned and the focus was on thedevelopment of the HydroGENIUS the electric vehicle ofUrbanConcept class with fuel cell stack as power sourcewhich eventually scored vice Championship in SEM 2016 Inthe further work it is planned to improve the optimizationresults by using the presented methodology in the case ofthe models of newly constructed vehicles The developmentof the optimization method should take into considerationthe uncertainty resulting from the given velocity strategyconsidering the real conditions of the race It is also possibleto use this method for controlling vehicles in traffic To dothis it is necessary to completely change the way of the routemodelling and the driving conditions modelling as well as todevelop a new optimization method for obtaining results inreal time

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] W Skarka ldquoReducing the Energy Consumption of ElectricVehiclesrdquo in Proceedings of the 22nd ISPE-Inc InternationalConference on Concurrent Engineering Location R Curran NWognumM Borsato et al Eds Advances in TransdisciplinaryEngineering pp 500ndash509 IOS Press Delft Netherlands 2015

[2] R Andrzejewski and J Awrejcewicz Nonlinear Dynamics of aWheeled Vehicle vol 10 Springer-Verlag New York NY USA2005

[3] D W Gao C Mi and A Emadi ldquoModeling and simulation ofelectric and hybrid vehiclesrdquo Proceedings of the IEEE vol 95 no4 pp 729ndash745 2007

[4] ldquoAdvisor documentationrdquo httpadv-vehiclesimsourceforgenet

[5] TMarkel A Brooker THendricks et al ldquoADVISORA systemsanalysis tool for advanced vehicle modelingrdquo Journal of PowerSources vol 110 no 1 pp 255ndash266 2002

[6] K B Wipke M R Cuddy and S D Burch ldquoADVISOR21 a user-friendly advanced powertrain simulation using acombined backwardforward approachrdquo IEEE Transactions onVehicular Technology vol 48 no 6 pp 1751ndash1761 1999

[7] ldquoWebsiterdquo 2014 httpwwwtransportationanlgovmodeling[8] ldquoWebsiterdquo 2014 httpwwwautonomienet[9] K Krykowski J Hetmanczyk Z Gałuszkiewicz and R Mik-

siewicz ldquoComputer analysis of high-speed PM BLDC motorpropertiesrdquo COMPEL - The International Journal for Computa-tion and Mathematics in Electrical and Electronic Engineeringvol 30 no 3 pp 941ndash956 2011

[10] M Vaillant M Eckert and F Gauterin ldquoEnergy managementstrategy to be used in design space exploration for electricpowertrain optimizationrdquo inProceedings of the 2014 9th Interna-tional Conference on Ecological Vehicles and Renewable EnergiesEVER 2014 mco March 2014

[11] A T Nguyen S Reiter and P Rigo ldquoA review on simulation-based optimization methods applied to building performanceanalysisrdquo Applied Energy vol 113 pp 1043ndash1058 2014

[12] W Silka and W Siłka Energy Intensity in the Car Traffic InPolish WNT Warszawa 1997

[13] T J Barlow S Latham I S Mrcrae and P Boulter A referencebook of driving cycles for use in the measurement of roadvehicle emissions TRL 2009 httpswwwgovukgovernmentuploadssystemdata

[14] R N Jazar Vehicle Dynamics Theory and Application SpringerUS Boston MA 2008

[15] MMeywerk ldquoVehicle Dynamicsrdquo inWest Sussex JohnWiley ampSons Lecture Notes to theMOOCVehicle Dynamics of iversity1st edition 2015

[16] MMitschke andHWallentowitzDynamik der KraftfahrzeugeSpringer Berlin Germany 1972

[17] T Stefanski and Ł Zawarczynski ldquoParametric identification ofPM motor mathematical modelsrdquo Przegląd Elektrotechnicznyvol 88 no 4 B pp 224ndash229 2012

[18] A Cameron ldquoMeasuring drive-train efficiencyrdquoHuman Powervol 46

[19] B Rohloff and P Greb ldquoEfficiency measurements of bicycletransmissions a neverending storyrdquo Human Power vol 55 p11 2004

[20] J B Spicer C J K Richardson M J Ehrlich J R BernsteinM Fukuda and M Terada ldquoEffects of frictional loss on bicyclechain drive efficiencyrdquo Journal of Mechanical Design vol 123no 4 pp 598ndash605 2001

[21] K Sternal A Cholewa W Skarka and M Targosz ldquoElec-tric vehicle for the studentsrsquo shell eco-marathon competitionDesign of the car and telemetry systemrdquo Communications inComputer and Information Science vol 329 pp 26ndash33 2012

[22] K Cichonski and W Skarka ldquoInnovative control system forhigh efficiency electric urban vehiclerdquo Communications inComputer and Information Science vol 531 pp 121ndash130 2015

[23] M J Er and R J Oentaryo ldquoComputational IntelligenceMethods andTechniques (Rutkowski L 2008) [BookReview]rdquoIEEE Computational Intelligence Magazine vol 6 no 4 pp 76ndash78 2011

[24] M Targosz M Szumowski W Skarka and P PrzystałkaldquoVelocity Planning of an Electric Vehicle Using an Evolutionary

Journal of Advanced Transportation 15

0

2

4

6

8

10V

[ms

]

VsimstU

500 1000 15000X [m]

(a) Lap 1

0

2

4

6

8

10

V [m

s]

2500 30002000X [m]

VsimstU

(b) Laps 2-9

0

2

4

6

8

10

V [m

s]

155 1615X [m]

Vsimstu

times104

(c) Lap 10

times10minus3

Npop=25Npop=50Npop=75Npop=100

Npop=125Npop=150Npop=175Npop=200

15

2

25

3

35

4f va

l

2000 4000 6000 8000 100000Nfval

(d) Mean values of the fitness functions

Figure 17 Vehicle speed and control signal st119880 for route 1

Table 6 The results for route 1

The type of coding A The type of coding Bst119880 st11988115 st11988110119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 52465 1459 42845 1741 51569 5477550 52579 10053 44431 22486 51492 3409475 52497 39913 43842 28173 51256 80682100 52589 18128 42232 1797 51166 49379125 52625 13862 42733 39616 51341 70765150 5243 2979 4435 47701 51486 27086175 52513 2511 41428 27299 51838 19358200 52579 19666 42337 25776 51204 78357

16 Journal of Advanced Transportation

100 200 300 400 500 6000X [m]

0

2

4

6

8

10V

[ms

]

VsimstV10

USET

(a) Lap 1

0

2

4

6

8

10

V [m

s]

800 900 1000 1100 1200700X [m]

VsimstV10

USET

(b) Laps 2-4

0

2

4

6

8

10

V [m

s]

2700 2800 2900 3000 3100 32002600X [m]

VsimstV10

USET

(c) Lap 5

times10minus3

Npop=25Npop=50Npop=75Npop=100

Npop=125Npop=150Npop=175Npop=200

275

28

285

29

295

3

305

f val

2000 4000 6000 8000 100000Nfval

(d) Mean values of the fitness functions

Figure 18 Vehicle speed and control signal st11988110 for route 2

of the population used in the optimization process it shouldbe noted that for route 2 it is preferable to use higher value of119873119901119900119901 For all the analyzed cases the best average results for119873119901119900119901=200 were obtained Table 8 summarizes the results forroute 3

For route 3 the average results were reported for a largerpopulation of119873119901119900119901 with B coding In the case of using vectorwith A type coding no characteristic change was notedAs expected comparing the standard deviation betweenalgorithms using B coding the standard deviation is less forthe less variance range

Evolutionary algorithms are not complete search algo-rithms therefore it is not possible to determine whetherthe solution found is best for the chosen criterion and theconstraints assumed

57 Applying the Optimal Control Strategy in Real ConditionsElectric vehicle energy consumption optimization was finallyverified in real conditions at the European edition of the ShellEco-marathon held on 16-18 May 2014 in Rotterdam

Optimal control strategy st119880was displayed by a prototypevisualization system Visualization unit is installed in the

Journal of Advanced Transportation 17

Table 7 The results for route 2

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 34138 66734 34294 23839 34873 5353250 34573 46359 35003 462 3506 3886275 34512 55134 34961 33476 35419 067858100 34836 45332 35253 26117 3544 19295125 34632 52704 35017 49039 35483 14756150 34552 63714 35326 14885 35343 071015175 35063 18728 35274 47141 35564 038022200 35073 14496 3540 13389 35569 14942

Table 8 The results for route 3

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 28071 10173 28643 7323 30994 277650 29346 6142 29581 7894 30874 439975 29711 5002 29217 7367 31141 1856100 29826 3231 29515 7022 30957 4049125 29781 2980 29866 12977 31168 3445150 29453 3346 30217 9623 31288 1249175 29234 2317 30621 6816 31481 1261200 29686 2337 30531 11737 31089 4880

Table 9 Comparison of simulation results with experimental tests

Number of attempts 119903119878119864ndash119898 119903119903 119903119904119894119898 119903119900119901119905 119890119898 119890119894 119890119904119905Attempt 1 3654 3608 - - 125 - -Attempt 2 4813 5082 5148 5265 558 129 36Attempt 3 4873 5127 5198 5265 521 139 269Attempt 4 Failed attempt damaged tires during 1st lap

steering wheel of the vehicle The visualization system showsthe basic data such as instantaneous speed average speedtravel time and distance In addition the visualization systemprovides information on which part of the track the drivershould press the acceleration button to execute the optimalcontrol strategy Measurement of the position on the track iscarried out by the odometrical measuring system Due to thepossibility of accumulating errors in the measurement of theroad the driver will reset the measuring system every timeheshe exceeds the lap line

Table 9 presents the results of all the measurementsconducted during the Shell Eco-marathonThe columns in theTable 9 contain

(i) r119878119864119898 [kmkWh] the result recorded during the raceby the measuring device provided by the organizerthe results are available on the Shell Eco-marathonofficial website

(ii) r119903 [kWkWh] the result based on the indications of aprototypemeasuring system permanently installed inthe vehicle

(iii) r119904119894119898 the result estimated by computer simulationusing recorded real control signal U119903

(iv) r119900119901119905 the result obtained by computer simulation usingthe optimal control strategy U119900119901119905

Table 9 also includes the following

(i) Measurement error

119890119898 = 1003816100381610038161003816119903119878119864119898 minus 1199031199031003816100381610038161003816119903119878119864119898 100 (31)

(ii) Identification error

119890119894 =1003816100381610038161003816119903119903 minus 1199031199041198941198981003816100381610038161003816119903119903 100 (32)

(iii) Strategy implementation error

119890119904119905 =10038161003816100381610038161003816119903119903 minus 11990311990011990111990510038161003816100381610038161003816119903119903 100 (33)

18 Journal of Advanced Transportation

There were four measurement trials available Duringrun 1 a much weaker result was obtained than estimated bysimulation The driver performed run 1 without a definedcontrol strategy As part of the experiment the driver andthe support team were asked to select the optimal tires forthe vehicle and to implement the proposed control strategyDuring run 1 only the travel time of individual laps waschecked According to the choice of the team in run 1 tiresW2 were selected (Table 4) During this test the worst resultwas obtained about 24 and 25 worse than in the othertrials In subsequent runs 2 and 3 the vehicle was equippedwith the best W1 tires (Table 4) The driver has implementedan algorithm-based optimal control strategy Strategy infor-mation was provided by the visualization system During run3 the best result was recorded This result was taken intoaccount in the classification of competitions where the teamplaced in 12 positions out of 28 classified teams Trials 4 dueto damage to the tires were not successful

Measurement error was from 125 to 558 dependingon the sample The measurement system installed perma-nently in the vehicle is a prototype system This systemhas been calibrated using available laboratory equipmentMeasurement errors indicate that other measuring devices ofthe higher accuracy class should be used

Based on the measurement data obtained during testdrives the model was tuned thus reducing the identificationerror The competition took place in stable weather thedivergence of results was small and was about 129 forsample 2 and 139 for sample 3

The difference between the results determined duringnumerical simulation and that obtained in the real run was36 for sample 2 and 269 for sample 3 The difference atthis level was considered to be small Searching for optimalcontrol strategy has not taken into account possible rdquoerrorsrdquowhich could be made by the driver and which result fromthe current situation on the route for example selecting thepath and using the route by other participants in the raceIncluding driver behaviour in the simulation model shouldbe the subject of further work

Figure 19 shows the vehicle velocity together with thecontrol signals recorded during run 2 The black curvesrepresent the real vehicle velocity V119903 and the control signalGreen curves are the optimum control strategy st119880 andthe optimal velocity V119900119901119905 determined by the simulationThe graph shows the entire distance travelled (10 laps) Theanalysis of the graph shows that the driver did not performthe exact planned strategy Errors in the implementationof the strategy are related to the disruptions During thecompetition the driver is not alone on the track in certainsituations the driver cannot overtake other participants andcannot take the optimal path In addition weather conditionsuch as wind has influence on the motion resistance In suchcases the driver has to modify the optimal control strategy

In Figure 20 the velocity recorded during the race V119903(black) and the velocity obtained by the computer simulationV119904119894119898 (red) were shown V119904119894119898 was determined by computersimulation by using real control signal The purpose of thissimulation was to investigate the correctness of identification

VrVopt

Ur Uopt

2000 4000 6000 8000 10000 12000 14000 16000 180000X [m]

05

10152025303540

V [k

mh

]

Figure 19 Comparison of speed and control signal during attempt2

2000 4000 6000 8000 10000 12000 14000 16000 180000x [m]

05

10152025303540

V [k

mh

]

Ur

VrVsim

Figure 20 Comparison of speed registered in real conditions withthe speed determined by computer simulation

of the simulation model and to identify the identificationerror

Compared to the Shell Eco-marathon competitions heldin 2012 and 2013 our performance has improved The resultsin these years were equal to 425 [km kWh] and 454[km kWh] respectively In 2012 and 2013 the controlstrategy was chosen on the basis of the simulation modelbut the model was not adequately identified and the controlstrategy had to be modified In previous editions of therace the implementation of optimal control strategy was notsupported by the visualization system which would informthe driver of the need to take specific actions (pressing orreleasing the accelerator button)

6 Conclusion

The presented method was developed and tested for aprototype electric racing car that has been designed for theShell Eco-marathon race As it was shown the results of thenumerical simulations were very similar to the outcomes ofthe real races in the context of the final result of energyconsumption and the profile of velocity of the car during therace The method has been developed and applied since 2012

Journal of Advanced Transportation 19

and led in 2014 to achieving the optimal result for this type ofthe vehicle

The optimization method was evaluated The resultsachieved during the race attempts where the optimal con-trol strategy was applied (4813 and 4873 kmkWh) werecompared to the result where the strategy was proposed bythe experts (3654 kmkWh) who already had contact withthe results of similar optimization models Optimal attemptswere better by over 30 despite errors in the implementationof the strategy by the driver In the case of experts who did nothave such experiences the differences were even greater

Further improvement of the control strategy is impossiblefor this type of a vehicle and the best way to reduce energyconsumption is by improving the mechanical design It wasthe reason to develop new racing cars for UrbanConceptBattery Electric and Hydrogen competitions The developedresearch methodology for vehicle optimization and controlstrategies has been developed and implemented in the ShellEco-marathon in 2015 which has improved the score to 504km kWhHowever the research has shown that the potentialfor improved performance of the MuSHELLka vehicle hasbeen exhausted No major structural changes in the vehiclecan significantly improve the result so in the followingyears the race was abandoned and the focus was on thedevelopment of the HydroGENIUS the electric vehicle ofUrbanConcept class with fuel cell stack as power sourcewhich eventually scored vice Championship in SEM 2016 Inthe further work it is planned to improve the optimizationresults by using the presented methodology in the case ofthe models of newly constructed vehicles The developmentof the optimization method should take into considerationthe uncertainty resulting from the given velocity strategyconsidering the real conditions of the race It is also possibleto use this method for controlling vehicles in traffic To dothis it is necessary to completely change the way of the routemodelling and the driving conditions modelling as well as todevelop a new optimization method for obtaining results inreal time

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] W Skarka ldquoReducing the Energy Consumption of ElectricVehiclesrdquo in Proceedings of the 22nd ISPE-Inc InternationalConference on Concurrent Engineering Location R Curran NWognumM Borsato et al Eds Advances in TransdisciplinaryEngineering pp 500ndash509 IOS Press Delft Netherlands 2015

[2] R Andrzejewski and J Awrejcewicz Nonlinear Dynamics of aWheeled Vehicle vol 10 Springer-Verlag New York NY USA2005

[3] D W Gao C Mi and A Emadi ldquoModeling and simulation ofelectric and hybrid vehiclesrdquo Proceedings of the IEEE vol 95 no4 pp 729ndash745 2007

[4] ldquoAdvisor documentationrdquo httpadv-vehiclesimsourceforgenet

[5] TMarkel A Brooker THendricks et al ldquoADVISORA systemsanalysis tool for advanced vehicle modelingrdquo Journal of PowerSources vol 110 no 1 pp 255ndash266 2002

[6] K B Wipke M R Cuddy and S D Burch ldquoADVISOR21 a user-friendly advanced powertrain simulation using acombined backwardforward approachrdquo IEEE Transactions onVehicular Technology vol 48 no 6 pp 1751ndash1761 1999

[7] ldquoWebsiterdquo 2014 httpwwwtransportationanlgovmodeling[8] ldquoWebsiterdquo 2014 httpwwwautonomienet[9] K Krykowski J Hetmanczyk Z Gałuszkiewicz and R Mik-

siewicz ldquoComputer analysis of high-speed PM BLDC motorpropertiesrdquo COMPEL - The International Journal for Computa-tion and Mathematics in Electrical and Electronic Engineeringvol 30 no 3 pp 941ndash956 2011

[10] M Vaillant M Eckert and F Gauterin ldquoEnergy managementstrategy to be used in design space exploration for electricpowertrain optimizationrdquo inProceedings of the 2014 9th Interna-tional Conference on Ecological Vehicles and Renewable EnergiesEVER 2014 mco March 2014

[11] A T Nguyen S Reiter and P Rigo ldquoA review on simulation-based optimization methods applied to building performanceanalysisrdquo Applied Energy vol 113 pp 1043ndash1058 2014

[12] W Silka and W Siłka Energy Intensity in the Car Traffic InPolish WNT Warszawa 1997

[13] T J Barlow S Latham I S Mrcrae and P Boulter A referencebook of driving cycles for use in the measurement of roadvehicle emissions TRL 2009 httpswwwgovukgovernmentuploadssystemdata

[14] R N Jazar Vehicle Dynamics Theory and Application SpringerUS Boston MA 2008

[15] MMeywerk ldquoVehicle Dynamicsrdquo inWest Sussex JohnWiley ampSons Lecture Notes to theMOOCVehicle Dynamics of iversity1st edition 2015

[16] MMitschke andHWallentowitzDynamik der KraftfahrzeugeSpringer Berlin Germany 1972

[17] T Stefanski and Ł Zawarczynski ldquoParametric identification ofPM motor mathematical modelsrdquo Przegląd Elektrotechnicznyvol 88 no 4 B pp 224ndash229 2012

[18] A Cameron ldquoMeasuring drive-train efficiencyrdquoHuman Powervol 46

[19] B Rohloff and P Greb ldquoEfficiency measurements of bicycletransmissions a neverending storyrdquo Human Power vol 55 p11 2004

[20] J B Spicer C J K Richardson M J Ehrlich J R BernsteinM Fukuda and M Terada ldquoEffects of frictional loss on bicyclechain drive efficiencyrdquo Journal of Mechanical Design vol 123no 4 pp 598ndash605 2001

[21] K Sternal A Cholewa W Skarka and M Targosz ldquoElec-tric vehicle for the studentsrsquo shell eco-marathon competitionDesign of the car and telemetry systemrdquo Communications inComputer and Information Science vol 329 pp 26ndash33 2012

[22] K Cichonski and W Skarka ldquoInnovative control system forhigh efficiency electric urban vehiclerdquo Communications inComputer and Information Science vol 531 pp 121ndash130 2015

[23] M J Er and R J Oentaryo ldquoComputational IntelligenceMethods andTechniques (Rutkowski L 2008) [BookReview]rdquoIEEE Computational Intelligence Magazine vol 6 no 4 pp 76ndash78 2011

[24] M Targosz M Szumowski W Skarka and P PrzystałkaldquoVelocity Planning of an Electric Vehicle Using an Evolutionary

16 Journal of Advanced Transportation

100 200 300 400 500 6000X [m]

0

2

4

6

8

10V

[ms

]

VsimstV10

USET

(a) Lap 1

0

2

4

6

8

10

V [m

s]

800 900 1000 1100 1200700X [m]

VsimstV10

USET

(b) Laps 2-4

0

2

4

6

8

10

V [m

s]

2700 2800 2900 3000 3100 32002600X [m]

VsimstV10

USET

(c) Lap 5

times10minus3

Npop=25Npop=50Npop=75Npop=100

Npop=125Npop=150Npop=175Npop=200

275

28

285

29

295

3

305

f val

2000 4000 6000 8000 100000Nfval

(d) Mean values of the fitness functions

Figure 18 Vehicle speed and control signal st11988110 for route 2

of the population used in the optimization process it shouldbe noted that for route 2 it is preferable to use higher value of119873119901119900119901 For all the analyzed cases the best average results for119873119901119900119901=200 were obtained Table 8 summarizes the results forroute 3

For route 3 the average results were reported for a largerpopulation of119873119901119900119901 with B coding In the case of using vectorwith A type coding no characteristic change was notedAs expected comparing the standard deviation betweenalgorithms using B coding the standard deviation is less forthe less variance range

Evolutionary algorithms are not complete search algo-rithms therefore it is not possible to determine whetherthe solution found is best for the chosen criterion and theconstraints assumed

57 Applying the Optimal Control Strategy in Real ConditionsElectric vehicle energy consumption optimization was finallyverified in real conditions at the European edition of the ShellEco-marathon held on 16-18 May 2014 in Rotterdam

Optimal control strategy st119880was displayed by a prototypevisualization system Visualization unit is installed in the

Journal of Advanced Transportation 17

Table 7 The results for route 2

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 34138 66734 34294 23839 34873 5353250 34573 46359 35003 462 3506 3886275 34512 55134 34961 33476 35419 067858100 34836 45332 35253 26117 3544 19295125 34632 52704 35017 49039 35483 14756150 34552 63714 35326 14885 35343 071015175 35063 18728 35274 47141 35564 038022200 35073 14496 3540 13389 35569 14942

Table 8 The results for route 3

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 28071 10173 28643 7323 30994 277650 29346 6142 29581 7894 30874 439975 29711 5002 29217 7367 31141 1856100 29826 3231 29515 7022 30957 4049125 29781 2980 29866 12977 31168 3445150 29453 3346 30217 9623 31288 1249175 29234 2317 30621 6816 31481 1261200 29686 2337 30531 11737 31089 4880

Table 9 Comparison of simulation results with experimental tests

Number of attempts 119903119878119864ndash119898 119903119903 119903119904119894119898 119903119900119901119905 119890119898 119890119894 119890119904119905Attempt 1 3654 3608 - - 125 - -Attempt 2 4813 5082 5148 5265 558 129 36Attempt 3 4873 5127 5198 5265 521 139 269Attempt 4 Failed attempt damaged tires during 1st lap

steering wheel of the vehicle The visualization system showsthe basic data such as instantaneous speed average speedtravel time and distance In addition the visualization systemprovides information on which part of the track the drivershould press the acceleration button to execute the optimalcontrol strategy Measurement of the position on the track iscarried out by the odometrical measuring system Due to thepossibility of accumulating errors in the measurement of theroad the driver will reset the measuring system every timeheshe exceeds the lap line

Table 9 presents the results of all the measurementsconducted during the Shell Eco-marathonThe columns in theTable 9 contain

(i) r119878119864119898 [kmkWh] the result recorded during the raceby the measuring device provided by the organizerthe results are available on the Shell Eco-marathonofficial website

(ii) r119903 [kWkWh] the result based on the indications of aprototypemeasuring system permanently installed inthe vehicle

(iii) r119904119894119898 the result estimated by computer simulationusing recorded real control signal U119903

(iv) r119900119901119905 the result obtained by computer simulation usingthe optimal control strategy U119900119901119905

Table 9 also includes the following

(i) Measurement error

119890119898 = 1003816100381610038161003816119903119878119864119898 minus 1199031199031003816100381610038161003816119903119878119864119898 100 (31)

(ii) Identification error

119890119894 =1003816100381610038161003816119903119903 minus 1199031199041198941198981003816100381610038161003816119903119903 100 (32)

(iii) Strategy implementation error

119890119904119905 =10038161003816100381610038161003816119903119903 minus 11990311990011990111990510038161003816100381610038161003816119903119903 100 (33)

18 Journal of Advanced Transportation

There were four measurement trials available Duringrun 1 a much weaker result was obtained than estimated bysimulation The driver performed run 1 without a definedcontrol strategy As part of the experiment the driver andthe support team were asked to select the optimal tires forthe vehicle and to implement the proposed control strategyDuring run 1 only the travel time of individual laps waschecked According to the choice of the team in run 1 tiresW2 were selected (Table 4) During this test the worst resultwas obtained about 24 and 25 worse than in the othertrials In subsequent runs 2 and 3 the vehicle was equippedwith the best W1 tires (Table 4) The driver has implementedan algorithm-based optimal control strategy Strategy infor-mation was provided by the visualization system During run3 the best result was recorded This result was taken intoaccount in the classification of competitions where the teamplaced in 12 positions out of 28 classified teams Trials 4 dueto damage to the tires were not successful

Measurement error was from 125 to 558 dependingon the sample The measurement system installed perma-nently in the vehicle is a prototype system This systemhas been calibrated using available laboratory equipmentMeasurement errors indicate that other measuring devices ofthe higher accuracy class should be used

Based on the measurement data obtained during testdrives the model was tuned thus reducing the identificationerror The competition took place in stable weather thedivergence of results was small and was about 129 forsample 2 and 139 for sample 3

The difference between the results determined duringnumerical simulation and that obtained in the real run was36 for sample 2 and 269 for sample 3 The difference atthis level was considered to be small Searching for optimalcontrol strategy has not taken into account possible rdquoerrorsrdquowhich could be made by the driver and which result fromthe current situation on the route for example selecting thepath and using the route by other participants in the raceIncluding driver behaviour in the simulation model shouldbe the subject of further work

Figure 19 shows the vehicle velocity together with thecontrol signals recorded during run 2 The black curvesrepresent the real vehicle velocity V119903 and the control signalGreen curves are the optimum control strategy st119880 andthe optimal velocity V119900119901119905 determined by the simulationThe graph shows the entire distance travelled (10 laps) Theanalysis of the graph shows that the driver did not performthe exact planned strategy Errors in the implementationof the strategy are related to the disruptions During thecompetition the driver is not alone on the track in certainsituations the driver cannot overtake other participants andcannot take the optimal path In addition weather conditionsuch as wind has influence on the motion resistance In suchcases the driver has to modify the optimal control strategy

In Figure 20 the velocity recorded during the race V119903(black) and the velocity obtained by the computer simulationV119904119894119898 (red) were shown V119904119894119898 was determined by computersimulation by using real control signal The purpose of thissimulation was to investigate the correctness of identification

VrVopt

Ur Uopt

2000 4000 6000 8000 10000 12000 14000 16000 180000X [m]

05

10152025303540

V [k

mh

]

Figure 19 Comparison of speed and control signal during attempt2

2000 4000 6000 8000 10000 12000 14000 16000 180000x [m]

05

10152025303540

V [k

mh

]

Ur

VrVsim

Figure 20 Comparison of speed registered in real conditions withthe speed determined by computer simulation

of the simulation model and to identify the identificationerror

Compared to the Shell Eco-marathon competitions heldin 2012 and 2013 our performance has improved The resultsin these years were equal to 425 [km kWh] and 454[km kWh] respectively In 2012 and 2013 the controlstrategy was chosen on the basis of the simulation modelbut the model was not adequately identified and the controlstrategy had to be modified In previous editions of therace the implementation of optimal control strategy was notsupported by the visualization system which would informthe driver of the need to take specific actions (pressing orreleasing the accelerator button)

6 Conclusion

The presented method was developed and tested for aprototype electric racing car that has been designed for theShell Eco-marathon race As it was shown the results of thenumerical simulations were very similar to the outcomes ofthe real races in the context of the final result of energyconsumption and the profile of velocity of the car during therace The method has been developed and applied since 2012

Journal of Advanced Transportation 19

and led in 2014 to achieving the optimal result for this type ofthe vehicle

The optimization method was evaluated The resultsachieved during the race attempts where the optimal con-trol strategy was applied (4813 and 4873 kmkWh) werecompared to the result where the strategy was proposed bythe experts (3654 kmkWh) who already had contact withthe results of similar optimization models Optimal attemptswere better by over 30 despite errors in the implementationof the strategy by the driver In the case of experts who did nothave such experiences the differences were even greater

Further improvement of the control strategy is impossiblefor this type of a vehicle and the best way to reduce energyconsumption is by improving the mechanical design It wasthe reason to develop new racing cars for UrbanConceptBattery Electric and Hydrogen competitions The developedresearch methodology for vehicle optimization and controlstrategies has been developed and implemented in the ShellEco-marathon in 2015 which has improved the score to 504km kWhHowever the research has shown that the potentialfor improved performance of the MuSHELLka vehicle hasbeen exhausted No major structural changes in the vehiclecan significantly improve the result so in the followingyears the race was abandoned and the focus was on thedevelopment of the HydroGENIUS the electric vehicle ofUrbanConcept class with fuel cell stack as power sourcewhich eventually scored vice Championship in SEM 2016 Inthe further work it is planned to improve the optimizationresults by using the presented methodology in the case ofthe models of newly constructed vehicles The developmentof the optimization method should take into considerationthe uncertainty resulting from the given velocity strategyconsidering the real conditions of the race It is also possibleto use this method for controlling vehicles in traffic To dothis it is necessary to completely change the way of the routemodelling and the driving conditions modelling as well as todevelop a new optimization method for obtaining results inreal time

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] W Skarka ldquoReducing the Energy Consumption of ElectricVehiclesrdquo in Proceedings of the 22nd ISPE-Inc InternationalConference on Concurrent Engineering Location R Curran NWognumM Borsato et al Eds Advances in TransdisciplinaryEngineering pp 500ndash509 IOS Press Delft Netherlands 2015

[2] R Andrzejewski and J Awrejcewicz Nonlinear Dynamics of aWheeled Vehicle vol 10 Springer-Verlag New York NY USA2005

[3] D W Gao C Mi and A Emadi ldquoModeling and simulation ofelectric and hybrid vehiclesrdquo Proceedings of the IEEE vol 95 no4 pp 729ndash745 2007

[4] ldquoAdvisor documentationrdquo httpadv-vehiclesimsourceforgenet

[5] TMarkel A Brooker THendricks et al ldquoADVISORA systemsanalysis tool for advanced vehicle modelingrdquo Journal of PowerSources vol 110 no 1 pp 255ndash266 2002

[6] K B Wipke M R Cuddy and S D Burch ldquoADVISOR21 a user-friendly advanced powertrain simulation using acombined backwardforward approachrdquo IEEE Transactions onVehicular Technology vol 48 no 6 pp 1751ndash1761 1999

[7] ldquoWebsiterdquo 2014 httpwwwtransportationanlgovmodeling[8] ldquoWebsiterdquo 2014 httpwwwautonomienet[9] K Krykowski J Hetmanczyk Z Gałuszkiewicz and R Mik-

siewicz ldquoComputer analysis of high-speed PM BLDC motorpropertiesrdquo COMPEL - The International Journal for Computa-tion and Mathematics in Electrical and Electronic Engineeringvol 30 no 3 pp 941ndash956 2011

[10] M Vaillant M Eckert and F Gauterin ldquoEnergy managementstrategy to be used in design space exploration for electricpowertrain optimizationrdquo inProceedings of the 2014 9th Interna-tional Conference on Ecological Vehicles and Renewable EnergiesEVER 2014 mco March 2014

[11] A T Nguyen S Reiter and P Rigo ldquoA review on simulation-based optimization methods applied to building performanceanalysisrdquo Applied Energy vol 113 pp 1043ndash1058 2014

[12] W Silka and W Siłka Energy Intensity in the Car Traffic InPolish WNT Warszawa 1997

[13] T J Barlow S Latham I S Mrcrae and P Boulter A referencebook of driving cycles for use in the measurement of roadvehicle emissions TRL 2009 httpswwwgovukgovernmentuploadssystemdata

[14] R N Jazar Vehicle Dynamics Theory and Application SpringerUS Boston MA 2008

[15] MMeywerk ldquoVehicle Dynamicsrdquo inWest Sussex JohnWiley ampSons Lecture Notes to theMOOCVehicle Dynamics of iversity1st edition 2015

[16] MMitschke andHWallentowitzDynamik der KraftfahrzeugeSpringer Berlin Germany 1972

[17] T Stefanski and Ł Zawarczynski ldquoParametric identification ofPM motor mathematical modelsrdquo Przegląd Elektrotechnicznyvol 88 no 4 B pp 224ndash229 2012

[18] A Cameron ldquoMeasuring drive-train efficiencyrdquoHuman Powervol 46

[19] B Rohloff and P Greb ldquoEfficiency measurements of bicycletransmissions a neverending storyrdquo Human Power vol 55 p11 2004

[20] J B Spicer C J K Richardson M J Ehrlich J R BernsteinM Fukuda and M Terada ldquoEffects of frictional loss on bicyclechain drive efficiencyrdquo Journal of Mechanical Design vol 123no 4 pp 598ndash605 2001

[21] K Sternal A Cholewa W Skarka and M Targosz ldquoElec-tric vehicle for the studentsrsquo shell eco-marathon competitionDesign of the car and telemetry systemrdquo Communications inComputer and Information Science vol 329 pp 26ndash33 2012

[22] K Cichonski and W Skarka ldquoInnovative control system forhigh efficiency electric urban vehiclerdquo Communications inComputer and Information Science vol 531 pp 121ndash130 2015

[23] M J Er and R J Oentaryo ldquoComputational IntelligenceMethods andTechniques (Rutkowski L 2008) [BookReview]rdquoIEEE Computational Intelligence Magazine vol 6 no 4 pp 76ndash78 2011

[24] M Targosz M Szumowski W Skarka and P PrzystałkaldquoVelocity Planning of an Electric Vehicle Using an Evolutionary

Journal of Advanced Transportation 17

Table 7 The results for route 2

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 34138 66734 34294 23839 34873 5353250 34573 46359 35003 462 3506 3886275 34512 55134 34961 33476 35419 067858100 34836 45332 35253 26117 3544 19295125 34632 52704 35017 49039 35483 14756150 34552 63714 35326 14885 35343 071015175 35063 18728 35274 47141 35564 038022200 35073 14496 3540 13389 35569 14942

Table 8 The results for route 3

The type of coding A The type of coding Bst119880 st119881 15 st119881 10119873119901119900119901 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std 119903119904119894119898 [kmkWh] std

25 28071 10173 28643 7323 30994 277650 29346 6142 29581 7894 30874 439975 29711 5002 29217 7367 31141 1856100 29826 3231 29515 7022 30957 4049125 29781 2980 29866 12977 31168 3445150 29453 3346 30217 9623 31288 1249175 29234 2317 30621 6816 31481 1261200 29686 2337 30531 11737 31089 4880

Table 9 Comparison of simulation results with experimental tests

Number of attempts 119903119878119864ndash119898 119903119903 119903119904119894119898 119903119900119901119905 119890119898 119890119894 119890119904119905Attempt 1 3654 3608 - - 125 - -Attempt 2 4813 5082 5148 5265 558 129 36Attempt 3 4873 5127 5198 5265 521 139 269Attempt 4 Failed attempt damaged tires during 1st lap

steering wheel of the vehicle The visualization system showsthe basic data such as instantaneous speed average speedtravel time and distance In addition the visualization systemprovides information on which part of the track the drivershould press the acceleration button to execute the optimalcontrol strategy Measurement of the position on the track iscarried out by the odometrical measuring system Due to thepossibility of accumulating errors in the measurement of theroad the driver will reset the measuring system every timeheshe exceeds the lap line

Table 9 presents the results of all the measurementsconducted during the Shell Eco-marathonThe columns in theTable 9 contain

(i) r119878119864119898 [kmkWh] the result recorded during the raceby the measuring device provided by the organizerthe results are available on the Shell Eco-marathonofficial website

(ii) r119903 [kWkWh] the result based on the indications of aprototypemeasuring system permanently installed inthe vehicle

(iii) r119904119894119898 the result estimated by computer simulationusing recorded real control signal U119903

(iv) r119900119901119905 the result obtained by computer simulation usingthe optimal control strategy U119900119901119905

Table 9 also includes the following

(i) Measurement error

119890119898 = 1003816100381610038161003816119903119878119864119898 minus 1199031199031003816100381610038161003816119903119878119864119898 100 (31)

(ii) Identification error

119890119894 =1003816100381610038161003816119903119903 minus 1199031199041198941198981003816100381610038161003816119903119903 100 (32)

(iii) Strategy implementation error

119890119904119905 =10038161003816100381610038161003816119903119903 minus 11990311990011990111990510038161003816100381610038161003816119903119903 100 (33)

18 Journal of Advanced Transportation

There were four measurement trials available Duringrun 1 a much weaker result was obtained than estimated bysimulation The driver performed run 1 without a definedcontrol strategy As part of the experiment the driver andthe support team were asked to select the optimal tires forthe vehicle and to implement the proposed control strategyDuring run 1 only the travel time of individual laps waschecked According to the choice of the team in run 1 tiresW2 were selected (Table 4) During this test the worst resultwas obtained about 24 and 25 worse than in the othertrials In subsequent runs 2 and 3 the vehicle was equippedwith the best W1 tires (Table 4) The driver has implementedan algorithm-based optimal control strategy Strategy infor-mation was provided by the visualization system During run3 the best result was recorded This result was taken intoaccount in the classification of competitions where the teamplaced in 12 positions out of 28 classified teams Trials 4 dueto damage to the tires were not successful

Measurement error was from 125 to 558 dependingon the sample The measurement system installed perma-nently in the vehicle is a prototype system This systemhas been calibrated using available laboratory equipmentMeasurement errors indicate that other measuring devices ofthe higher accuracy class should be used

Based on the measurement data obtained during testdrives the model was tuned thus reducing the identificationerror The competition took place in stable weather thedivergence of results was small and was about 129 forsample 2 and 139 for sample 3

The difference between the results determined duringnumerical simulation and that obtained in the real run was36 for sample 2 and 269 for sample 3 The difference atthis level was considered to be small Searching for optimalcontrol strategy has not taken into account possible rdquoerrorsrdquowhich could be made by the driver and which result fromthe current situation on the route for example selecting thepath and using the route by other participants in the raceIncluding driver behaviour in the simulation model shouldbe the subject of further work

Figure 19 shows the vehicle velocity together with thecontrol signals recorded during run 2 The black curvesrepresent the real vehicle velocity V119903 and the control signalGreen curves are the optimum control strategy st119880 andthe optimal velocity V119900119901119905 determined by the simulationThe graph shows the entire distance travelled (10 laps) Theanalysis of the graph shows that the driver did not performthe exact planned strategy Errors in the implementationof the strategy are related to the disruptions During thecompetition the driver is not alone on the track in certainsituations the driver cannot overtake other participants andcannot take the optimal path In addition weather conditionsuch as wind has influence on the motion resistance In suchcases the driver has to modify the optimal control strategy

In Figure 20 the velocity recorded during the race V119903(black) and the velocity obtained by the computer simulationV119904119894119898 (red) were shown V119904119894119898 was determined by computersimulation by using real control signal The purpose of thissimulation was to investigate the correctness of identification

VrVopt

Ur Uopt

2000 4000 6000 8000 10000 12000 14000 16000 180000X [m]

05

10152025303540

V [k

mh

]

Figure 19 Comparison of speed and control signal during attempt2

2000 4000 6000 8000 10000 12000 14000 16000 180000x [m]

05

10152025303540

V [k

mh

]

Ur

VrVsim

Figure 20 Comparison of speed registered in real conditions withthe speed determined by computer simulation

of the simulation model and to identify the identificationerror

Compared to the Shell Eco-marathon competitions heldin 2012 and 2013 our performance has improved The resultsin these years were equal to 425 [km kWh] and 454[km kWh] respectively In 2012 and 2013 the controlstrategy was chosen on the basis of the simulation modelbut the model was not adequately identified and the controlstrategy had to be modified In previous editions of therace the implementation of optimal control strategy was notsupported by the visualization system which would informthe driver of the need to take specific actions (pressing orreleasing the accelerator button)

6 Conclusion

The presented method was developed and tested for aprototype electric racing car that has been designed for theShell Eco-marathon race As it was shown the results of thenumerical simulations were very similar to the outcomes ofthe real races in the context of the final result of energyconsumption and the profile of velocity of the car during therace The method has been developed and applied since 2012

Journal of Advanced Transportation 19

and led in 2014 to achieving the optimal result for this type ofthe vehicle

The optimization method was evaluated The resultsachieved during the race attempts where the optimal con-trol strategy was applied (4813 and 4873 kmkWh) werecompared to the result where the strategy was proposed bythe experts (3654 kmkWh) who already had contact withthe results of similar optimization models Optimal attemptswere better by over 30 despite errors in the implementationof the strategy by the driver In the case of experts who did nothave such experiences the differences were even greater

Further improvement of the control strategy is impossiblefor this type of a vehicle and the best way to reduce energyconsumption is by improving the mechanical design It wasthe reason to develop new racing cars for UrbanConceptBattery Electric and Hydrogen competitions The developedresearch methodology for vehicle optimization and controlstrategies has been developed and implemented in the ShellEco-marathon in 2015 which has improved the score to 504km kWhHowever the research has shown that the potentialfor improved performance of the MuSHELLka vehicle hasbeen exhausted No major structural changes in the vehiclecan significantly improve the result so in the followingyears the race was abandoned and the focus was on thedevelopment of the HydroGENIUS the electric vehicle ofUrbanConcept class with fuel cell stack as power sourcewhich eventually scored vice Championship in SEM 2016 Inthe further work it is planned to improve the optimizationresults by using the presented methodology in the case ofthe models of newly constructed vehicles The developmentof the optimization method should take into considerationthe uncertainty resulting from the given velocity strategyconsidering the real conditions of the race It is also possibleto use this method for controlling vehicles in traffic To dothis it is necessary to completely change the way of the routemodelling and the driving conditions modelling as well as todevelop a new optimization method for obtaining results inreal time

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] W Skarka ldquoReducing the Energy Consumption of ElectricVehiclesrdquo in Proceedings of the 22nd ISPE-Inc InternationalConference on Concurrent Engineering Location R Curran NWognumM Borsato et al Eds Advances in TransdisciplinaryEngineering pp 500ndash509 IOS Press Delft Netherlands 2015

[2] R Andrzejewski and J Awrejcewicz Nonlinear Dynamics of aWheeled Vehicle vol 10 Springer-Verlag New York NY USA2005

[3] D W Gao C Mi and A Emadi ldquoModeling and simulation ofelectric and hybrid vehiclesrdquo Proceedings of the IEEE vol 95 no4 pp 729ndash745 2007

[4] ldquoAdvisor documentationrdquo httpadv-vehiclesimsourceforgenet

[5] TMarkel A Brooker THendricks et al ldquoADVISORA systemsanalysis tool for advanced vehicle modelingrdquo Journal of PowerSources vol 110 no 1 pp 255ndash266 2002

[6] K B Wipke M R Cuddy and S D Burch ldquoADVISOR21 a user-friendly advanced powertrain simulation using acombined backwardforward approachrdquo IEEE Transactions onVehicular Technology vol 48 no 6 pp 1751ndash1761 1999

[7] ldquoWebsiterdquo 2014 httpwwwtransportationanlgovmodeling[8] ldquoWebsiterdquo 2014 httpwwwautonomienet[9] K Krykowski J Hetmanczyk Z Gałuszkiewicz and R Mik-

siewicz ldquoComputer analysis of high-speed PM BLDC motorpropertiesrdquo COMPEL - The International Journal for Computa-tion and Mathematics in Electrical and Electronic Engineeringvol 30 no 3 pp 941ndash956 2011

[10] M Vaillant M Eckert and F Gauterin ldquoEnergy managementstrategy to be used in design space exploration for electricpowertrain optimizationrdquo inProceedings of the 2014 9th Interna-tional Conference on Ecological Vehicles and Renewable EnergiesEVER 2014 mco March 2014

[11] A T Nguyen S Reiter and P Rigo ldquoA review on simulation-based optimization methods applied to building performanceanalysisrdquo Applied Energy vol 113 pp 1043ndash1058 2014

[12] W Silka and W Siłka Energy Intensity in the Car Traffic InPolish WNT Warszawa 1997

[13] T J Barlow S Latham I S Mrcrae and P Boulter A referencebook of driving cycles for use in the measurement of roadvehicle emissions TRL 2009 httpswwwgovukgovernmentuploadssystemdata

[14] R N Jazar Vehicle Dynamics Theory and Application SpringerUS Boston MA 2008

[15] MMeywerk ldquoVehicle Dynamicsrdquo inWest Sussex JohnWiley ampSons Lecture Notes to theMOOCVehicle Dynamics of iversity1st edition 2015

[16] MMitschke andHWallentowitzDynamik der KraftfahrzeugeSpringer Berlin Germany 1972

[17] T Stefanski and Ł Zawarczynski ldquoParametric identification ofPM motor mathematical modelsrdquo Przegląd Elektrotechnicznyvol 88 no 4 B pp 224ndash229 2012

[18] A Cameron ldquoMeasuring drive-train efficiencyrdquoHuman Powervol 46

[19] B Rohloff and P Greb ldquoEfficiency measurements of bicycletransmissions a neverending storyrdquo Human Power vol 55 p11 2004

[20] J B Spicer C J K Richardson M J Ehrlich J R BernsteinM Fukuda and M Terada ldquoEffects of frictional loss on bicyclechain drive efficiencyrdquo Journal of Mechanical Design vol 123no 4 pp 598ndash605 2001

[21] K Sternal A Cholewa W Skarka and M Targosz ldquoElec-tric vehicle for the studentsrsquo shell eco-marathon competitionDesign of the car and telemetry systemrdquo Communications inComputer and Information Science vol 329 pp 26ndash33 2012

[22] K Cichonski and W Skarka ldquoInnovative control system forhigh efficiency electric urban vehiclerdquo Communications inComputer and Information Science vol 531 pp 121ndash130 2015

[23] M J Er and R J Oentaryo ldquoComputational IntelligenceMethods andTechniques (Rutkowski L 2008) [BookReview]rdquoIEEE Computational Intelligence Magazine vol 6 no 4 pp 76ndash78 2011

[24] M Targosz M Szumowski W Skarka and P PrzystałkaldquoVelocity Planning of an Electric Vehicle Using an Evolutionary

18 Journal of Advanced Transportation

There were four measurement trials available Duringrun 1 a much weaker result was obtained than estimated bysimulation The driver performed run 1 without a definedcontrol strategy As part of the experiment the driver andthe support team were asked to select the optimal tires forthe vehicle and to implement the proposed control strategyDuring run 1 only the travel time of individual laps waschecked According to the choice of the team in run 1 tiresW2 were selected (Table 4) During this test the worst resultwas obtained about 24 and 25 worse than in the othertrials In subsequent runs 2 and 3 the vehicle was equippedwith the best W1 tires (Table 4) The driver has implementedan algorithm-based optimal control strategy Strategy infor-mation was provided by the visualization system During run3 the best result was recorded This result was taken intoaccount in the classification of competitions where the teamplaced in 12 positions out of 28 classified teams Trials 4 dueto damage to the tires were not successful

Measurement error was from 125 to 558 dependingon the sample The measurement system installed perma-nently in the vehicle is a prototype system This systemhas been calibrated using available laboratory equipmentMeasurement errors indicate that other measuring devices ofthe higher accuracy class should be used

Based on the measurement data obtained during testdrives the model was tuned thus reducing the identificationerror The competition took place in stable weather thedivergence of results was small and was about 129 forsample 2 and 139 for sample 3

The difference between the results determined duringnumerical simulation and that obtained in the real run was36 for sample 2 and 269 for sample 3 The difference atthis level was considered to be small Searching for optimalcontrol strategy has not taken into account possible rdquoerrorsrdquowhich could be made by the driver and which result fromthe current situation on the route for example selecting thepath and using the route by other participants in the raceIncluding driver behaviour in the simulation model shouldbe the subject of further work

Figure 19 shows the vehicle velocity together with thecontrol signals recorded during run 2 The black curvesrepresent the real vehicle velocity V119903 and the control signalGreen curves are the optimum control strategy st119880 andthe optimal velocity V119900119901119905 determined by the simulationThe graph shows the entire distance travelled (10 laps) Theanalysis of the graph shows that the driver did not performthe exact planned strategy Errors in the implementationof the strategy are related to the disruptions During thecompetition the driver is not alone on the track in certainsituations the driver cannot overtake other participants andcannot take the optimal path In addition weather conditionsuch as wind has influence on the motion resistance In suchcases the driver has to modify the optimal control strategy

In Figure 20 the velocity recorded during the race V119903(black) and the velocity obtained by the computer simulationV119904119894119898 (red) were shown V119904119894119898 was determined by computersimulation by using real control signal The purpose of thissimulation was to investigate the correctness of identification

VrVopt

Ur Uopt

2000 4000 6000 8000 10000 12000 14000 16000 180000X [m]

05

10152025303540

V [k

mh

]

Figure 19 Comparison of speed and control signal during attempt2

2000 4000 6000 8000 10000 12000 14000 16000 180000x [m]

05

10152025303540

V [k

mh

]

Ur

VrVsim

Figure 20 Comparison of speed registered in real conditions withthe speed determined by computer simulation

of the simulation model and to identify the identificationerror

Compared to the Shell Eco-marathon competitions heldin 2012 and 2013 our performance has improved The resultsin these years were equal to 425 [km kWh] and 454[km kWh] respectively In 2012 and 2013 the controlstrategy was chosen on the basis of the simulation modelbut the model was not adequately identified and the controlstrategy had to be modified In previous editions of therace the implementation of optimal control strategy was notsupported by the visualization system which would informthe driver of the need to take specific actions (pressing orreleasing the accelerator button)

6 Conclusion

The presented method was developed and tested for aprototype electric racing car that has been designed for theShell Eco-marathon race As it was shown the results of thenumerical simulations were very similar to the outcomes ofthe real races in the context of the final result of energyconsumption and the profile of velocity of the car during therace The method has been developed and applied since 2012

Journal of Advanced Transportation 19

and led in 2014 to achieving the optimal result for this type ofthe vehicle

The optimization method was evaluated The resultsachieved during the race attempts where the optimal con-trol strategy was applied (4813 and 4873 kmkWh) werecompared to the result where the strategy was proposed bythe experts (3654 kmkWh) who already had contact withthe results of similar optimization models Optimal attemptswere better by over 30 despite errors in the implementationof the strategy by the driver In the case of experts who did nothave such experiences the differences were even greater

Further improvement of the control strategy is impossiblefor this type of a vehicle and the best way to reduce energyconsumption is by improving the mechanical design It wasthe reason to develop new racing cars for UrbanConceptBattery Electric and Hydrogen competitions The developedresearch methodology for vehicle optimization and controlstrategies has been developed and implemented in the ShellEco-marathon in 2015 which has improved the score to 504km kWhHowever the research has shown that the potentialfor improved performance of the MuSHELLka vehicle hasbeen exhausted No major structural changes in the vehiclecan significantly improve the result so in the followingyears the race was abandoned and the focus was on thedevelopment of the HydroGENIUS the electric vehicle ofUrbanConcept class with fuel cell stack as power sourcewhich eventually scored vice Championship in SEM 2016 Inthe further work it is planned to improve the optimizationresults by using the presented methodology in the case ofthe models of newly constructed vehicles The developmentof the optimization method should take into considerationthe uncertainty resulting from the given velocity strategyconsidering the real conditions of the race It is also possibleto use this method for controlling vehicles in traffic To dothis it is necessary to completely change the way of the routemodelling and the driving conditions modelling as well as todevelop a new optimization method for obtaining results inreal time

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] W Skarka ldquoReducing the Energy Consumption of ElectricVehiclesrdquo in Proceedings of the 22nd ISPE-Inc InternationalConference on Concurrent Engineering Location R Curran NWognumM Borsato et al Eds Advances in TransdisciplinaryEngineering pp 500ndash509 IOS Press Delft Netherlands 2015

[2] R Andrzejewski and J Awrejcewicz Nonlinear Dynamics of aWheeled Vehicle vol 10 Springer-Verlag New York NY USA2005

[3] D W Gao C Mi and A Emadi ldquoModeling and simulation ofelectric and hybrid vehiclesrdquo Proceedings of the IEEE vol 95 no4 pp 729ndash745 2007

[4] ldquoAdvisor documentationrdquo httpadv-vehiclesimsourceforgenet

[5] TMarkel A Brooker THendricks et al ldquoADVISORA systemsanalysis tool for advanced vehicle modelingrdquo Journal of PowerSources vol 110 no 1 pp 255ndash266 2002

[6] K B Wipke M R Cuddy and S D Burch ldquoADVISOR21 a user-friendly advanced powertrain simulation using acombined backwardforward approachrdquo IEEE Transactions onVehicular Technology vol 48 no 6 pp 1751ndash1761 1999

[7] ldquoWebsiterdquo 2014 httpwwwtransportationanlgovmodeling[8] ldquoWebsiterdquo 2014 httpwwwautonomienet[9] K Krykowski J Hetmanczyk Z Gałuszkiewicz and R Mik-

siewicz ldquoComputer analysis of high-speed PM BLDC motorpropertiesrdquo COMPEL - The International Journal for Computa-tion and Mathematics in Electrical and Electronic Engineeringvol 30 no 3 pp 941ndash956 2011

[10] M Vaillant M Eckert and F Gauterin ldquoEnergy managementstrategy to be used in design space exploration for electricpowertrain optimizationrdquo inProceedings of the 2014 9th Interna-tional Conference on Ecological Vehicles and Renewable EnergiesEVER 2014 mco March 2014

[11] A T Nguyen S Reiter and P Rigo ldquoA review on simulation-based optimization methods applied to building performanceanalysisrdquo Applied Energy vol 113 pp 1043ndash1058 2014

[12] W Silka and W Siłka Energy Intensity in the Car Traffic InPolish WNT Warszawa 1997

[13] T J Barlow S Latham I S Mrcrae and P Boulter A referencebook of driving cycles for use in the measurement of roadvehicle emissions TRL 2009 httpswwwgovukgovernmentuploadssystemdata

[14] R N Jazar Vehicle Dynamics Theory and Application SpringerUS Boston MA 2008

[15] MMeywerk ldquoVehicle Dynamicsrdquo inWest Sussex JohnWiley ampSons Lecture Notes to theMOOCVehicle Dynamics of iversity1st edition 2015

[16] MMitschke andHWallentowitzDynamik der KraftfahrzeugeSpringer Berlin Germany 1972

[17] T Stefanski and Ł Zawarczynski ldquoParametric identification ofPM motor mathematical modelsrdquo Przegląd Elektrotechnicznyvol 88 no 4 B pp 224ndash229 2012

[18] A Cameron ldquoMeasuring drive-train efficiencyrdquoHuman Powervol 46

[19] B Rohloff and P Greb ldquoEfficiency measurements of bicycletransmissions a neverending storyrdquo Human Power vol 55 p11 2004

[20] J B Spicer C J K Richardson M J Ehrlich J R BernsteinM Fukuda and M Terada ldquoEffects of frictional loss on bicyclechain drive efficiencyrdquo Journal of Mechanical Design vol 123no 4 pp 598ndash605 2001

[21] K Sternal A Cholewa W Skarka and M Targosz ldquoElec-tric vehicle for the studentsrsquo shell eco-marathon competitionDesign of the car and telemetry systemrdquo Communications inComputer and Information Science vol 329 pp 26ndash33 2012

[22] K Cichonski and W Skarka ldquoInnovative control system forhigh efficiency electric urban vehiclerdquo Communications inComputer and Information Science vol 531 pp 121ndash130 2015

[23] M J Er and R J Oentaryo ldquoComputational IntelligenceMethods andTechniques (Rutkowski L 2008) [BookReview]rdquoIEEE Computational Intelligence Magazine vol 6 no 4 pp 76ndash78 2011

[24] M Targosz M Szumowski W Skarka and P PrzystałkaldquoVelocity Planning of an Electric Vehicle Using an Evolutionary

Journal of Advanced Transportation 19

and led in 2014 to achieving the optimal result for this type ofthe vehicle

The optimization method was evaluated The resultsachieved during the race attempts where the optimal con-trol strategy was applied (4813 and 4873 kmkWh) werecompared to the result where the strategy was proposed bythe experts (3654 kmkWh) who already had contact withthe results of similar optimization models Optimal attemptswere better by over 30 despite errors in the implementationof the strategy by the driver In the case of experts who did nothave such experiences the differences were even greater

Further improvement of the control strategy is impossiblefor this type of a vehicle and the best way to reduce energyconsumption is by improving the mechanical design It wasthe reason to develop new racing cars for UrbanConceptBattery Electric and Hydrogen competitions The developedresearch methodology for vehicle optimization and controlstrategies has been developed and implemented in the ShellEco-marathon in 2015 which has improved the score to 504km kWhHowever the research has shown that the potentialfor improved performance of the MuSHELLka vehicle hasbeen exhausted No major structural changes in the vehiclecan significantly improve the result so in the followingyears the race was abandoned and the focus was on thedevelopment of the HydroGENIUS the electric vehicle ofUrbanConcept class with fuel cell stack as power sourcewhich eventually scored vice Championship in SEM 2016 Inthe further work it is planned to improve the optimizationresults by using the presented methodology in the case ofthe models of newly constructed vehicles The developmentof the optimization method should take into considerationthe uncertainty resulting from the given velocity strategyconsidering the real conditions of the race It is also possibleto use this method for controlling vehicles in traffic To dothis it is necessary to completely change the way of the routemodelling and the driving conditions modelling as well as todevelop a new optimization method for obtaining results inreal time

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] W Skarka ldquoReducing the Energy Consumption of ElectricVehiclesrdquo in Proceedings of the 22nd ISPE-Inc InternationalConference on Concurrent Engineering Location R Curran NWognumM Borsato et al Eds Advances in TransdisciplinaryEngineering pp 500ndash509 IOS Press Delft Netherlands 2015

[2] R Andrzejewski and J Awrejcewicz Nonlinear Dynamics of aWheeled Vehicle vol 10 Springer-Verlag New York NY USA2005

[3] D W Gao C Mi and A Emadi ldquoModeling and simulation ofelectric and hybrid vehiclesrdquo Proceedings of the IEEE vol 95 no4 pp 729ndash745 2007

[4] ldquoAdvisor documentationrdquo httpadv-vehiclesimsourceforgenet

[5] TMarkel A Brooker THendricks et al ldquoADVISORA systemsanalysis tool for advanced vehicle modelingrdquo Journal of PowerSources vol 110 no 1 pp 255ndash266 2002

[6] K B Wipke M R Cuddy and S D Burch ldquoADVISOR21 a user-friendly advanced powertrain simulation using acombined backwardforward approachrdquo IEEE Transactions onVehicular Technology vol 48 no 6 pp 1751ndash1761 1999

[7] ldquoWebsiterdquo 2014 httpwwwtransportationanlgovmodeling[8] ldquoWebsiterdquo 2014 httpwwwautonomienet[9] K Krykowski J Hetmanczyk Z Gałuszkiewicz and R Mik-

siewicz ldquoComputer analysis of high-speed PM BLDC motorpropertiesrdquo COMPEL - The International Journal for Computa-tion and Mathematics in Electrical and Electronic Engineeringvol 30 no 3 pp 941ndash956 2011

[10] M Vaillant M Eckert and F Gauterin ldquoEnergy managementstrategy to be used in design space exploration for electricpowertrain optimizationrdquo inProceedings of the 2014 9th Interna-tional Conference on Ecological Vehicles and Renewable EnergiesEVER 2014 mco March 2014

[11] A T Nguyen S Reiter and P Rigo ldquoA review on simulation-based optimization methods applied to building performanceanalysisrdquo Applied Energy vol 113 pp 1043ndash1058 2014

[12] W Silka and W Siłka Energy Intensity in the Car Traffic InPolish WNT Warszawa 1997

[13] T J Barlow S Latham I S Mrcrae and P Boulter A referencebook of driving cycles for use in the measurement of roadvehicle emissions TRL 2009 httpswwwgovukgovernmentuploadssystemdata

[14] R N Jazar Vehicle Dynamics Theory and Application SpringerUS Boston MA 2008

[15] MMeywerk ldquoVehicle Dynamicsrdquo inWest Sussex JohnWiley ampSons Lecture Notes to theMOOCVehicle Dynamics of iversity1st edition 2015

[16] MMitschke andHWallentowitzDynamik der KraftfahrzeugeSpringer Berlin Germany 1972

[17] T Stefanski and Ł Zawarczynski ldquoParametric identification ofPM motor mathematical modelsrdquo Przegląd Elektrotechnicznyvol 88 no 4 B pp 224ndash229 2012

[18] A Cameron ldquoMeasuring drive-train efficiencyrdquoHuman Powervol 46

[19] B Rohloff and P Greb ldquoEfficiency measurements of bicycletransmissions a neverending storyrdquo Human Power vol 55 p11 2004

[20] J B Spicer C J K Richardson M J Ehrlich J R BernsteinM Fukuda and M Terada ldquoEffects of frictional loss on bicyclechain drive efficiencyrdquo Journal of Mechanical Design vol 123no 4 pp 598ndash605 2001

[21] K Sternal A Cholewa W Skarka and M Targosz ldquoElec-tric vehicle for the studentsrsquo shell eco-marathon competitionDesign of the car and telemetry systemrdquo Communications inComputer and Information Science vol 329 pp 26ndash33 2012

[22] K Cichonski and W Skarka ldquoInnovative control system forhigh efficiency electric urban vehiclerdquo Communications inComputer and Information Science vol 531 pp 121ndash130 2015

[23] M J Er and R J Oentaryo ldquoComputational IntelligenceMethods andTechniques (Rutkowski L 2008) [BookReview]rdquoIEEE Computational Intelligence Magazine vol 6 no 4 pp 76ndash78 2011

[24] M Targosz M Szumowski W Skarka and P PrzystałkaldquoVelocity Planning of an Electric Vehicle Using an Evolutionary

20 Journal of Advanced Transportation

Algorithmrdquo Communications in Computer and InformationScience vol 395 pp 171ndash177 2013

[25] M S Ismail M Moghavvemi and T M I Mahlia ldquoGeneticalgorithmbased optimization onmodeling anddesign of hybridrenewable energy systemsrdquo Energy Conversion and Manage-ment vol 85 pp 120ndash130 2014

[26] Z Michalewicz ldquoEvolutionary algorithms for constrainedparameter optimization problemsrdquo Evolutionary Computationvol 4 no 1 pp 1ndash32 1996

[27] M Targosz ldquoTest bench for efficiency evaluation of belt andchain transmissionsrdquo in Proceedings of the Conference Proceed-ings XII International Technical System Degradation Confer-ences Liptovsky Mikulas 2013

[28] M Targosz K Cichonski M Glen A Szymon K CichonskiandM Glen ldquoAn experimental investigation of the energy con-sumption for lightweight electric vehiclerdquo in Proceedings of the13th International Technical Systems Degradation Conference2014

[29] M TargoszW Skarka P Przystalka and P Przystałka ldquoSimula-tion and optimization methodology of prototype electric vehi-clerdquo in Proceedings of the 13th International Design ConferenceDESIGN 2014 D Marjanovic M Storga N Pavkovic and NBojcetic Eds pp 2014-1349 Croatia 2014

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom