Research Article Adaptive Hybrid Control of Vehicle

Research ArticleAdaptive Hybrid Control of Vehicle Semiactive SuspensionBased on Road Profile Estimation

Yechen Qin1 Mingming Dong1 Reza Langari2 Liang Gu1 and Jifu Guan1

1School of Mechanical Engineering Beijing Institute of Technology Beijing 100081 China2Department of Mechanical Engineering Texas AampM University College Station TX 77840 USA

Correspondence should be addressed to Liang Gu guliangbiteducn

Received 24 January 2015 Accepted 30 April 2015

Academic Editor Mickael Lallart

Copyright copy 2015 Yechen Qin et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A new road estimation based suspension hybrid control strategy is proposed Its aim is to adaptively change control gains to improveboth ride comfort and road handling with the constraint of rattle space To achieve this analytical expressions for ride comfort roadhandling and rattle space with respect to road input are derived based on the hybrid control and the problem is transformed into aMOOP (Multiobjective Optimization Problem) and has been solved by NSGA-II (Nondominated Sorting Genetic Algorithm-II)A new road estimation and classification method which is based on ANFIS (Adaptive Neurofuzzy Inference System) and wavelettransforms is then presented as a means of detecting the road profile level and a Kalman filter is designed for observing unknownstates The results of simulations conducted with random road excitation show that the efficiency of the proposed control strategycompares favourably to that of a passive system

1 Introduction

The increasing demands of the market have led to theemergence of different types of vehicle suspension systemsIn terms of energy consumption vehicle suspension canbe divided into three types passive suspension semiactivesuspension and active suspension Passive suspension isthe most popular form and through careful selection ofspring and damper coefficients a compromise solution isderived for ride comfort and road handling Due to theconflicting of these two criterions the optimal performanceof a passive suspension system can only be achieved in acertain frequency range [1 2] Active suspension systemhas thus emerged to overcome this disadvantage showingimproved performance across a wider frequency range [3ndash5] The defects of active suspension system however suchas inherent stability problems high energy costs and extrapower source requirements restrict its application in com-mercial vehicles [6] Semiactive suspension system has hencebeen created to address this offering a compromise betweenperformance and cost [7 8] Semiactive suspension systemtypically equips a controllable damper with an extra energyinput of only few Watts and their control bandwidth is even

higher than that of active suspension systems [6] Semiactivesuspension system can be further divided into two partsthe first is adaptive semiactive suspension system whichcan slowly change damping coefficient according to roadconditions and has been applied in new Audi A6 AllroadQuattro As for the second one the semiactive suspensionsystem it can rapidly change damping coefficient accordingto states feedback Since the first semiactive suspensioncontrol strategy skyhook control which was proposed inthe 1970s a large number of innovative control strategieshave been proposed to improve the criterions mentionedabove Prominent examples of such strategies include thegroundhook [9 10] robust control [11] and MPC (ModelPredictive Control) [12 13] To evaluate the performance ofa vehicle suspension system three criterions are widely used[6 14ndash17]

(1) Ride comfort To isolate the vehicle body and pas-sengers from road disturbances the performance interms of two frequency ranges needs to be improvedthe natural frequency for the vehicle body (1ndash15Hz)and the frequency range to which humans are sensi-tive (4ndash8Hz) [18] To simplify the calculation process

Hindawi Publishing CorporationShock and VibrationVolume 2015 Article ID 636739 13 pageshttpdxdoiorg1011552015636739

2 Shock and Vibration

the acceleration of the sprung mass is typically usedas the metric upon which comparison is based [1 47 15ndash17 19]

(2) Road handling This criterion measures the abilityof a suspension system to maintain contact with theroad surface [6] Generally speaking tyre force or tyredeflection is normally chosen for use as a comparisonmetric [1 15] In order to obtain better accelerationbraking and steering ability when driving in worseroad conditions the tyre force or deflection shouldbe small

(3) Rattle space (working space) The rattle space repre-sents the distance between the sprung and unsprungmass This is a constraint for the suspension systemand under the assumption that the road input isa Gaussian distribution process [20] and the wholesystem is linear the variance of rattle space should bedesigned not to exceed plusmn13 of the constraint valueThis will ensure that the rattle space remains withinthe constraint range 997 of the time [3 4]

To combine the merits of both skyhook and groundhooksuspension systems for ride comfort and road handlingrespectively the hybrid control is proposed [19 21 22] Thehybrid control is a typical semiactive suspension controlstrategy since it can rapidly adjust damping coefficientaccording to system states feedback By adjusting the weight-ing of hybrid control rule operators can change the sus-pensionrsquos operating characteristics from being ride comfortoriented to being road handling oriented to suit whateversuspension performance they most desire at that time

For the suspension hybrid control that have beenexplored in the literatures little focus has been given to thechoice of damping coefficients for hybrid control systems andhow to cooperate this strategy with varying road conditionTo address this a road estimation based semiactive suspen-sion hybrid control strategy is proposed in this paper Themain contributions and innovations of this paper are as fol-lows Firstly the analytical expressions for three performancecriterions with respect to road excitation are derived and thechoice of damping coefficients is transformed into a MOOP(Multiobjective Optimization Problem) which is solved byNSGA-II (Nondominated Sorting Genetic Algorithm-II) [2324] Secondly the cooperation between hybrid control androad estimation is built A new road classification methodbased on ANFIS (Adaptive Neurofuzzy Inference System)and wavelet transform is presented for estimating the roadprofile level [25] so that the damping coefficients can adap-tively vary according to road condition and the accordingsolution of MOOP

This paper proceeds as follows Section 2 briefly intro-duces the road model and its generation in the time domainSection 3 presents the quarter vehicle model and the controlstrategy Section 4 illustrates the calculation of dampingcoefficients with NSGA-II Section 5 discusses road profileestimation and classification Section 6 describes the designof observer Section 7 contains numerical simulations fordifferent road levels and a conclusion is drawn at last

2 Road Model

The distance between the road surface and the base plateis typically defined as a function of road irregularitiesOften the road profile is assumed to be a homogeneousand isotropic Gaussian random process and its statisticalcharacteristics can be described by Power Spectral Density(PSD) [20] According to ISO 8601 [26] the PSD of roadroughness can be defined as

119866119902 (119899) = 119866119902 (1198990) (119899

1198990)

minus119882

(1)

where 119899 is spatial frequency in mminus1 and 1198990 is reference spatialfrequency with value of 01mminus1 119866119902(1198990) is the PSD value inthe reference spatial frequency in m3 and increasing valuesof 119866119902(1198990) are assigned for different road levels ranging fromA (very good) to H (very poor) 119882 is termed wavinessand reflects the approximate frequency structure of the roadprofile commonly taken as 119882 = 2 During the applicationprocess some researchers have however noted two problemswith (1)

(1) When the spatial frequency approximates zero thePSD of the road profile will approach infinity [20 27]

(2) According to actual roadmeasurements the PSD cal-culated by (1) will always overestimate the amplitudeof the road in the low frequency sections [4 20]

Because of this another formulation for calculating roadprofile PSD has been suggested by [17 28] and is used hereas shown in the following

119866119902 (119899) =120572120588

2

120587 (1205722+ 119899

2)

(2)

where 120572 is the road characteristic parameter in mminus1 and120588 is the road variance in m The values of both 120572 and 120588

are presented in Table 1 [29] It should be noted that thevalues in Table 1 have been carefully validated according tothe standard road level defined by the ISO The road profilein the time domain can be modelled as a first order linearprocess by [2 16 28]

119902 (119905) = minus 120572V119902 (119905) +119908 (119905) (3)

where 119902(119905) is road unevenness inm V is the vehicle velocity inkmh and119908(119905) is a white noise series with covariance shownas follows

cov [119908 (119905)] = 119864 [119908 (119905) 119908 (119905 + 120591)] = 21205882119886V120575 (120591) (4)

where 120575(sdot) is the Dirac delta function

3 Quarter Vehicle Model

In this section the hybrid control strategy and correspondingquarter vehicle model are created and analytical expressionsfor sprung mass acceleration tyre force and rattle space withrespect to road excitation are derived

Shock and Vibration 3

Table 1 Values of road model parameters

Road level 120572mminus1 120588mA 0111 00377B 0111 00754C 0111 0151D 0111 0302E 0111 0603F 0111 1206G 0111 2413H 0111 4825

31 Hybrid Control

311 Skyhook Control The purpose of skyhook control is toisolate the sprung mass from external vibration In this casea virtual damper is installed between the sprung mass andinertial inference For practical implementation howeveran equivalent damper is designed between the sprung andunsprung mass In order to mimic the behaviour of idealskyhook damping the following control rules are needed tobe satisfied [7]

119865sky =

119888sky (119887) if (119887 minus 119908) sdot 119887 ge 0

119888min (119887 minus 119908) if (119887 minus 119908) sdot 119887 lt 0(5)

312 Groundhook Control To improve road handling agroundhook control may be utilised [9] Similar to theskyhook control a virtual damper is placed between theunsprung mass and inertial interference The control algo-rithm can be expressed as [30 31]

119865grd =

119888grd (119908) if minus (119887 minus 119908) sdot 119908 ge 0

119888min (119887 minus 119908) if minus (119887 minus 119908) sdot 119908 lt 0(6)

313 Hybrid Control In order to combine the advantagesof the above two strategies the concept of hybrid control isproposed Hybrid control can be described as a linear com-bination of both skyhook and groundhook control strategiesA typical expression of hybrid control is [19 21 22]

119865119889 = 120578119865sky minus (1minus 120578) 119865grd (7)

where 120578 isin [0 1] is the weight factor for the hybrid controlThe value of 120578 can be adjusted subjectively by operator todecide which part is more important during driving processA value of 120578 = 02 for example can be used if the operatordesires to achieve better road handling performance at theexpense of ride comfort

For individual skyhook and groundhook control theproblem of how to choose the damping coefficients is well-studied in previous research [1 32 33] For hybrid controlhowever the matter becomes more complicated since thechoice of damping coefficients for each individual controlstrategy will affect the other and to the authorsrsquo best knowl-edge little research has been done to the choice of damping

coefficients for hybrid control This paper hence proposes anew method for solving the problem deriving the analyticalexpressions for different criterions and calculating the damp-ing coefficients for both the skyhook and the groundhookcontrol with MOOP

32 System Model and Response to Road Excitation Thestructure of an ideal hybrid control model is shown inFigure 1(a)

Since the structure in Figure 1(a) cannot be realised froma practical viewpoint an equivalent alternative model isshown in Figure 1(b) where 119865119889 represents the controllabledamping force As the purpose of this paper is to calculate thedamping coefficients for different road levels 119865119889 is expressedas

119865119889 = 119888sky sdot 119887 minus 119888grd sdot 119908 (8)

Due to the limitations of actual dampers that is thelimited output force a constraint rule is applied here

119865output119889

=

119865max119889

if 119865119889 gt 119865max119889

119865119889 if 119865max119889

gt 119865119889 gt 119865min119889

119865min119889

if 119865min119889

gt 119865119889

(9)

The dynamic equations of themodel shown in Figure 1(b)are hence given by

119898119887119887 + 119896119904 (119909119887 minus119909119908) + 119865119889 = 0

119898119908119908 + 119896119904 (119909119908 minus119909119887) + 119896119905 (119909119908 minus119909119903) + 119888119905 (119908 minus 119903)

minus 119865119889 = 0

(10)

Taking Laplace transforms for (10) transfer functions forthe acceleration of sprung mass displacement of unsprungmass tyre force and rattle space with respect to road inputcan be expressed as follows

119867(119904) 119909119887sim119909119903=119883119887 (119904)

119883119903 (119904)

=

119888grd1198881199051199044+ (119888grd119896119905 + 119888119905119896119904) 119904

3+ 119896119904119896119905119904

2

119860

119867 (119904)119909119908sim119909119903

=119883119908 (119904)

119883119903 (119904)

=

1198881199051198981198871199043+ (119898119887119896119905 + 119888sky119888119905) 119904

2+ (119888sky119896119905 + 119888119905119896119904) 119904 + 119896119904119896119905

119860

119867 (119904)119891119863sim119909119903= 119896119905 (

119883119908 (119904)

119883119903 (119904)

minus 1) = 119896119905

119863

119860

119867 (119904)(119909119887minus119909119908)sim119909119903

=119883119908 (119904)

119883119903 (119904)

=

minus1198881199051198981198871199043+ (119888grd119888119905 minus 119898119887119896119905 minus 119888sky119888119905) 119904

2+ (119888grd119896119905 minus 119888sky119896119905) 119904

119860

(11)


csky

cgrd ct

ks

kt

mb

mw

xb

xw

xr

(a)

ct

ks

kt

mb

mw

xb

xw

xr

xb minus xwFd

Tyre

Unsprung mass

Suspension

Sprung mass

Rattle space

(b)

Figure 1 Ideal and equivalent models (a) Ideal hybrid suspension system (b) equivalent hybrid suspension system

where

119860 = 1198981199081198981198871199044+ (119888grd119898119887 + 119888sky119898119908 + 119888119905119898119887) 119904

3

+ (119898119908119896119904 +119898119887119896119904 +119898119887119896119905 + 119888sky119888119905) 1199042

+ (119888sky119896119905 + 119888119905119896119904) 119904 + 119896119905119896119904

119863 = minus1198981198871198981199081199044minus (119888grd119898119887 + 119888sky119898119908) 119904

3

minus (119898119887119896119904 +119898119908119896119904) 1199042

(12)

For a stationary and ergodic stochastic process thevariance of a random variable can be described as [34]

1205902119901=

12120587

int

infin

minusinfin

119878119901 (120596) 119889120596 (13)

The Power Spectral Density (PSD) of the output can becomputed as

119878119901 (120596) =10038161003816100381610038161003816119867 (119895120596)

119901sim119909119903

10038161003816100381610038161003816

2119878119909119903

(119895120596) (14)

where 119901 = 1 2 3 4 represent the four translation functionsshown in (11)

Previous research has shown that if 119878119901(120596) can beexpressed as (15) then an analytical solution for1205902

119901exists [35]

119878119901 (120596) =

119873119896minus1 (119895120596)119873119896minus1 (minus119895120596)

119863119896 (119895120596)119863119896 (minus119895120596)

(15)

where119863119896 is a polynomial of degree 119896 and119873119896minus1 is a polynomialof degree 119896 minus 1119863119896 and119873119896minus1 can be expressed as

119863119896 (119895120596) = 119889119896 (119895120596)119896+119889119896minus1 (119895120596)

119896minus1+ sdot sdot sdot + 1198890

119873119896minus1 (119895120596) = 119899119896minus1 (119895120596)119896minus1

+ 119899119896minus2 (119895120596)119896minus2

+ sdot sdot sdot + 1198990

(16)

In order to express 119878119901(120596) in the form of (15) according to(2) the PSD of the road input and translation functions canbe expressed as

119866119902 (119891) =119886V1205882

120587 [(119886V)2 + 1198912]

997888rarr 119878119909119903(119895120596) =

119886V1205882

120587

1(119886V + 119895120596)

1(119886V minus 119895120596)

(17)

The transformation function of (11) can also be expressedas

10038161003816100381610038161003816119867 (119895120596)

119901sim119909119903

10038161003816100381610038161003816

2= 119867 (119895120596)

119901sim119909119903119867(minus119895120596)

119901sim119909119903 (18)

For this problem the value of 119896 can be easily calculated119896 = 5The analytical solution of 1205902

119901can hence be expressed as

[16]1205902

=

(119899241198881198980 + (119899

23 minus 211989921198994) 1198881198981 + 11989911989801198881198982 + (119899

21 minus 211989901198992) 1198881198983 + 119899

201198881198984)

21198890 (11988911198881198984 minus 11988931198881198983 + 11988951198881198982)

(19)

where 1198990 1198994 and 1198890 1198895 stand for the numeratorand denominator items shown in (16) and 1198991198980 1198881198980 1198881198984represent the intermediate variables shown below

1198991198980 = 11989922 minus 211989911198993 + 211989901198994

1198881198980 =11988931198881198981 minus 11988911198881198982

1198895

1198881198981 = minus11988901198893 +11988911198892

1198881198982 = minus11988901198895 +11988911198894

1198881198983 =11988921198881198982 minus 11988941198881198981

1198890

1198881198984 =11988921198881198983 minus 11988941198881198982

1198890

(20)


In thismanner the analytical expressions for determiningthe acceleration of sprung mass the tyre force and the rattlespacewith respect to road excitation are derivedDue to spacelimitations the detailed expressions cannot be representedhere Similar deduction of the analytical expressions forpassive and skyhook control has been successfully applied byValasek et al [16] and Hurmuzlu and Nwokah [17]

4 Damping Coefficients Calculation

In this section a brief introduction ofMOOP (MultiobjectiveOptimization Problems) is presented and the calculation ofdamping coefficients for different road levels is described

Optimization problems are of great importance in engi-neering design decision making and experimentationWhen an optimization problem includes more than oneobjective function it may be treated as MOOP

Multiple different methods are available for solvingMOOP such as direct methods and gradient-based methods[36] These classical methods do however have some limita-tions in common [24]

(1) The initial solutions for the objective functions deter-mine their convergence to the optimal solutions

(2) An algorithm derived by these methods may belimited in certain scope and unable to be used toeffectively solve other types of problems

(3) These classical methods can only obtain one solutionper iteration

To better understand the MOOP the concept of ldquoParetooptimal solutionsrdquo is illustrated here The solutions in thePareto optimal solution set possess the property that thereare no other feasible solutions that can decrease one criterionwithout causing an increase in any other criterions [37] Tobe specific the solution obtained by classical methods withinone iteration is one solution in the Pareto optimal solutionset Evolutionary algorithms have thus been proposed toovercome the above limitations [24] Genetic algorithm isone such that algorithm starts from random initial solutionsapplying operations of selection crossover and mutation toobtain Pareto optimal solutions The criterion for selectionis the fitness function which is always set as the objectivefunctions

Since the analytical expressions for ride comfort roadhandling and rattle space have been derived the choice ofdamping coefficients transforms into MOOP In this paperthe NSGA-II method is applied to solve this problem [23]The flow chart of NSGA-II is shown in Figure 2

The NSGA-II procedure can be briefly described asfollows

(1) Initialise the population The parameters of NSGA-IIare chosen at this step such as the number of elitesand the population size

(2) Generate solutions Random initial solutions are gen-erated at this step

Initializepopulation

Generatesolutions

Non-dominated

sorting

Calculatecrowingdistance

Tournamentselection

CrossovermutationCease

Combine

offspringparent and

Yes

No

OutputPareto

solution

Gen + 1

Figure 2 Flow chart of NSGA-II

(3) Achieve nondominated sorting The values of thefitness function are calculated for each solution anddifferent fronts are assigned after comparison

(4) Calculate crowding distance In order to ensure thediversity of the solution set crowding distances mustbe calculated and solutions with higher crowdingdistance must have a greater probability of beingselected

(5) For selection crossover and mutation new solutionsare generated after these three steps

(6) Combine parent andoffspringA combination of boththe parent and the offspring generations is formedand the best solutions with a predefined populationsize are chosen

(7) Cease When the number of generations or the varia-tion of the fitness function reaches a predefined valuethe procedure stops and Pareto optimal solutions aregenerated

TheMOOP dealt with in this paper can thus be expressedas follows

min 1198911 (119888sky 119888grd) = 1205902119909119887

1198912 (119888sky 119888grd) = 1205902119891119863

subject to 6 sdot 10038161003816100381610038161003816120590119909119887minus11990911990810038161003816100381610038161003816le lim (119909119887 minus119909119908)

500 (Nsm) le 119888sky le 5000 (Nsm)

500 (Nsm) le 119888grd le 5000 (Nsm)

(21)


2 3 4 5 6 7 8 9 10 11 1208

085

09

095

10

11

11

Objective function valuePareto optimal solution

f2(c s

kyc

grd)

(N)

f1(csky cgrd) (ms2)

times106

Figure 3Objective space andPareto optimal solutions for road levelD 40 kmh

where 1205902119909119887and 120590

2119891119863

stand for the variances of the sprungmass acceleration and tyre force respectively as derivedin Section 3 and lim(119909119887 minus 119909119908) represents the rattle spaceconstraint the value of which is taken as 120mm in thispaper and it assumes that the bounce and rebound limitare equal in simulation It should be noted that 1198911 and 1198912are functions of both road level and velocity In order toillustrate the properties of Pareto optimal solutions and thechoice of control gains the MOOP shown in (21) is solvedfor road level D with a velocity of 40 kmh as an exampleThe parameters of NSGA-II are set as follows populationsize is 100 the optimal solution number in the first Paretofront is 50 and the maximum generation is 200 The Paretooptimal solution set and objective area are shown in Figure 3It can be seen that the Pareto optimal solution set whichis represented as circles is located at the bottom left of theobjective areaThese circles are believed to be equal solutionsif we do not specify the orientation of the suspension systemThe results in Figure 3 show that the Pareto optimal solutionsare widely distributed along the Pareto optimal front whichmeans that although the locations of initial solutions andthe corresponding final solutions are random the differencebetween solutions for different runs is still acceptable in termsof the value of the objective function For different road leveland velocity the Pareto optimal solutions can be calculatedoff-line and prestored in the controller for further application

5 Road Estimation

According to the analysis conducted in Section 4 both1198911 and1198912 are functions of both road level and velocity The velocityof a vehicle can be obtained through the CAN bus howeverit should be noted that there might be message delays whenthere is a message collision during the application of CAN

bus Since the road estimation interval is 05 s we assumethat the velocity of vehicle is constant during this intervalThe road level must be updated continuously during drivingin order to successfully realise suspension control In thissection a review of road estimation techniques is presented atfirst and a newmethod for road estimation and classificationis then introduced

During the past fewdecades a significant number of stud-ies have been conducted on road estimation and reproduc-tion Previous research can be divided into three categories

(1) Direct measurement This method generally utilisesprofilometers to measure the amplitude of the roadprofile It has been proven to be very precise howeverthe structure of the instruments restricts its applica-tion in commercial vehicles [38 39]

(2) Road estimation based on vehicle response Thismethod utilises multiple different sensors such asacceleration sensors for sprung or unsprungmass andLVDT for rattle space along with a system model toestimate the road profile This method is the mostpopular and has attracted much research attention[40ndash42]

(3) Noncontact measurement This method uses laser(light ultrasonic) transceivers to measure the roadprofile in a relatively accurate manner howeverthe cost of the instruments and kinds of complexaccessory equipment limit its business application[43]

This paper requires the road estimation method used tointeroperate effectively with the suspension system controlin order to ensure suspension system performance Thisintroduces two general requirements that must be fulfilled

(1) Accuracy As different control gains are assigned todifferent road levels (the principles on which gainchoice is based are shown in the simulation section)the estimated road level needs to be accurate other-wise degradation of road handling may occur duringpoor road conditions which may cause braking andsteering force reduction or even lead to the vehiclesystem becoming out of control

(2) Real time Since the level of the road changes ran-domly the proposed estimationmethod is required tobe able to respond to changes in the road level withoutlarge time lag

Because of this rather than utilising the conventionalmethods mentioned above a new method for road level esti-mation is proposed involving two steps Firstly the amplitudeof the road profile is estimated according to the vehicle systemresponse and then a wavelet transform is applied and theroad level is classified based on the detail components (highfrequency sections) calculated by the wavelet transform

The basic methodology for road profile estimation can bedescribed as follows reverse the vehicle suspension systemand apply the system response to estimate the road profile in


Nonlinear

vehicle modelWhite noisesignal

Inverse

model

quarternonlinear

vehicle model

Inverse

quarter

ANFIS

xr

xr

xb minus xwFdxw

+

minus xr

e

sum

xw

Figure 4 Structure of road estimation with ANFIS

the time domainwith an inverseANFISmodel To be specificaccording to (10) the road input can be expressed as

119909119903 = 119891 (119908 119909119908 (119909119908 minus119909119887) 119865119889) (22)

which means that the road profile can be expressed asa function of four items acceleration of unsprung massdisplacement of unsprung mass rattle space and the controlforce Once the values of these four items are obtained wecan calculate the road profile with the function shown in (22)In this paper the function is replaced by an inverse ANFISmodel and after proper training the road profile is calculatedaccording to the well-trained inverse ANFIS model It shouldbe noted that it is important to ensure the completeness ofthe training signal otherwise large identification errors mayappear In this case a white noise signal with amplitude of025m and an upper cut-off frequency of 30Hz is appliedto train the inverse ANFIS model [25] The structure of theinverse ANFIS model training process is shown in Figure 4For more information about road profile estimation in thetime domain with ANFIS readers are invited to refer to [25]

After the estimated road profile 119909119903 is derived wavelettransform is used for 119909119903 and the value of the RMS (root meansquare) of the detail components that is the high frequencysection of road profile is applied for classification A wavelettransform based method is utilised for the following reasons

(1) Since the excitation energy will rise as the roadlevel increases a higher level road will always beassociated with a PSD higher amplitude across thewhole frequency domain

(2) As the slope of the road PSD is negative according toits ISO definition as shown in (1) the PSD amplitudeof the lower frequency section must be much largerthan that of the high frequency section In order tofulfil the real-time requirementmentioned earlier theslowly changing components of the road that is thelower frequency part must be removed or reduced

It should be noted that wavelet transform is not theonly possible choice for road classification Several othermethods for time-frequency domain analysis can also beapplied such as EMD (empirical mode decomposition) or asimple high pass filter All three methods have been tested forthis problem with the results showing that both the wavelettransformand the EMD(1st order IMF)methods have similar

accuracy Due to phase shifting and the difficulty of choosingthe upper cut-off frequency the high pass filter methodproduces inaccurate results and hence is not recommendedIn the following simulation section wavelet transform ischosen as the classification method and the wavelet base ischosen as ldquodb3rdquo

6 State Observer Design

According to the analysis in Section 5 in order to estimate theroad profile it is necessary to know the value of four variablesthe acceleration of the unsprung mass displacement of theunsprung mass rattle space and control force The accelera-tion of the unsprung mass can be measured directly with anacceleration sensor and the control force can be calculatedaccording to the control strategy shown in Section 3 Therattle space can be measured with a LVDT embedded in thedamper however as the sensor is not connected directly tothe sprung and unsprung mass the difference between themeasured and actual values of the rattle space cannot beignored As indicated in previous research the displacementof the unsprung mass can be calculated by a band pass filter[2] Due to the existence of theDCoffset and phase shift of thefilter it is difficult to design and apply such a filter in practice[22] A Kalman filter is hence designed to observe the rattlespace and displacement of the unsprung mass

The discrete state space model for the quarter vehicle canbe written as

119909119896+1 = 119860119909119896 +119861119906119896 +119866119903119896 +119865119908119896

119910119896 = 119862119909119896 +119863119906119896 + V119896(23)

where 119906 is the control force 119903 is the road disturbance119908 is theroad velocity and V is the sensor noise

The system state vector is chosen as

997888119909 = [119909119887 119887 119909119908 119908]

119879 (24)

The system output vector is

997888119910 = [119887 119908]

119879 (25)

The system matrixes are

119860 = 119864+Δ119905 sdot

[[[[[[[[

[

0 1 0 0

minus119896119904

119898119887

0119896119904

119898119887

0

0 0 0 1119896119904

119898119908

0 minus119896119905 + 119896119904

119898119908

minus119888119905

119898119908

]]]]]]]]

]

119861 = Δ119905 sdot

[[[[[[[[

[

0

minus1119898119887

01119898119908

]]]]]]]]

]


3 5 6 70 1 2 4 8 9 10

0250201501005

0minus005minus01minus015minus02minus025 u

Adaptive gain calculation

Analyticalsolution

SuspensionMOOP

Roadlevel

Roadclassification

ANFISinversemodel

Road profile estimation

Controlforce

calculationSaturation

Feedback

Road input

Quartervehiclemodel

Statemeasurement

Stateestimator

Hybrid semiactivesuspension control


xw

xbxr

xr

Fd

[csky cgrd]

Foutputd

xb x xxb minus w w

xb minus xw xw

Figure 5 Structure of road estimation based hybrid control strategy

119866 = Δ119905 sdot

[[[[[[[

[

000119896119905

119898119908

]]]]]]]

]

119865 = Δ119905 sdot

[[[[[[[

[

000119888119905

119898119908

]]]]]]]

]

119862 =

[[[

[

minus119896119904

119898119887

0119896119904

119898119887

0119896119904

119898119908

0 minus119896119905

119898119908

minus119888119905

119898119908

]]]

]

119863 =

[[[

[

minus11198981198871119898119908

]]]

]

(26)

where 119864 is the identity matrix and the Δ119905 is the samplinginterval The procedure can be expressed as follows

Step 1 Time update is as follows

119909minus

119896= 119860119909119896minus1 +119861119906119896minus1

119875minus

119896= 119860119875119896minus1119860

119879+119876

(27)

Step 2 Measurement update is as follows

119870119896 = 119875minus

119896119862119879(119862119875minus

119896119862119879+119877)

minus1

119909119896 = 119909minus

119896+119870119896 [119910119896 minus (119862119909

minus

119896+119863119906119896)]

119875119896 = (119868 minus119870119896119862)119875minus

119896

(28)

where 119877 is the measurement noise covariance matrix 119876 isthe process noise covariance matrix 119875 is the estimate errorcovariance matrix 119870 is the Kalman gain and 119909

minus

119896and 119909119896 are

priori and posteriori state estimates respectively at step 119896Both 119875 and119870 will change iteratively and ultimately convergeto a constant value

7 Simulation Results

In this section the system structure of the proposed controlstrategy is introduced and a road profile with five differentlevels is utilised to validate the control strategy and roadestimation method An analysis of the simulation results isthen provided

The block diagram for the system structure is shown inFigure 5

As can be seen from Figure 5 the proposed strategyinvolves three elements calculation of adaptive control gainsroad profile estimation and hybrid suspension control Thefunctions and relationship between these three elements maybe described as follows

Adaptive gain calculation utilises the analytical expres-sions shown in Section 3 to calculate the damping coefficientscombination [119888sky 119888grd] for different road levels utilising theMOOP described in Section 4The results are then stored forcontrol force calculation

Road profile estimation corresponds to Section 5 Thisinvolves estimation of the road profile in the time domainby utilising the inverse ANFIS model with the results of awavelet transform for the estimated road unevenness119909119903 beingapplied for classification The obtained road level is then sentto the hybrid control stage


Table 2 Parameters of quarter vehicle

119898b Sprung mass 256 kg119898w Unsprung mass 30 kg119896t Tyre spring stiffness 186000Nm119896s Suspension spring stiffness 22000Nm119888p Passive damping coefficient 1100Nsm119888sky Skyhook damping coefficient range 500ndash5000Nsm119888grd Ground damping coefficient range 500ndash5000Nsm119888t Tyre damping coefficient 0Nsm119888min Hybrid minimum damping coefficient 200Nsm

The hybrid suspension control stage corresponds toSection 3 The ideal control force is calculated according tothe road level and control gain and this ideal control force 119865119889must then be compared with the limitation of the dampingforce that is the saturation The actual control force 119865output

119889

derived from this is next applied in the quarter vehiclemodelThe responses of the model [119887 119908] are used to observe theunknown variables and the observed variables are applied inthe inverse ANFISmodel and control force calculation blocksfor estimating the road profile and calculating the controlforce respectively

In order to evaluate the performance of the proposedcontrol strategy and road classification method a randomroad profile is generated and its performance is comparedwith a passive suspension system For the sake of comparisonand analysis unless otherwise stated the velocity is taken as40 kmh and the sample frequency is 1000Hz

The parameters of the passive quarter vehicle model aregiven in Table 2

A simple calculation reveals that the natural frequency ofthe sprung mass is 1198911 = 147Hz the natural frequency ofthe unsprung mass is 1198912 = 1325Hz and the damping ratiofor passive system is 120585 = 023 These parameters confirm thevalidity of the referenced passive quarter model

Since all the Pareto optimal solutions in Figure 3 areassumed to be equal (as stated in Section 4) the next stepis to choose control weights for the different road levelswith the choice of control weights directly determining thedamping coefficients of the hybrid control The choice ofcontrol weights is subjective however an effective generalprinciple upon which this choice may be based is as followsas stated in the introduction part the road handling canbe interpreted as the force between tyre and road surfaceSince higher road level means higher input energy whichwill lead to higher tyre force variation we need to assigngreater weighting to road handling aspect for worse roads toobtain better braking and steering ability as for good roadshowever a larger weighting of ride comfort is desirable inorder to enhance passenger experience Under this principlethe control weights and corresponding damping coefficientsare presented in Table 3 In order to save time and increaseefficiency the damping coefficients for different road level canbe precalculated and saved in the controller

The road excitation used for the simulation is shown inFigure 6(a)

Table 3 Control weights and damping coefficients for different roadlevels

Road level Weights [119908acc 119908tire] [119888sky 119888grd]

Very good (A B) [08 02] [3720 620]Good (C D) [06 04] [3265 950]Poor (E F) [04 06] [3030 1390]Very poor (G H) [02 08] [2750 1680]

minus04

minus03

minus02

minus01

0 20 40 60 80 100

00

01

02

03

04

level Clevel Flevel Elevel D

Am

plitu

de (m

)

Time (s)

ISO ISO ISO ISO ISO level B

(a)

0 20 40 60 80 100

Input roadEstimated road

minus04

minus03

minus02

minus01

00

01

02

03

04

Am

plitu

de (m

)

Time (s)

level Clevel Flevel Elevel DISO ISO ISO ISO ISO

level B

APE= 429

APE= 1043

APE= 632

APE= 514

APE= 357

(b)

Figure 6 Input road profile and its estimation (a) Road excitationin time domain (b) comparison for actual input and estimated roadprofile

It can be seen that the road profile is composed of fivedifferent road levels levels B D E F and C in successiveorder For the purpose of analysis two assumptions areapplied here

(1) During the driving process the velocity of the vehicleremains unchanged


0 20 40 60 80 100

000

002

004

006


level B

Am

plitu

de (m

)

Time (s)

minus006

minus004

minus002

Figure 7 Detail components for estimated road profile

(2) The road level remains unchanged within every 20seconds

With the proposed road profile estimation method andthe variables estimated with the Kalmanmethod as describedin Sections 5 and 6 the road profile can be estimated acrossthe time domainThe results of this are shown in Figure 6(b)In order to evaluate the performance of the proposedmethodthe index namedAPE (Average Percent Error) is utilised [44]

APE =1119875

119875

sum

119894=1

|119879 (119894) minus 119874 (119894)|

|119879 (119894)|

times 100 (29)

where 119875 is the amount of data and 119879(119894) and 119874(119894) are the 119894thactual output and calculated output values respectively

The results show that the proposed inversed ANFISmodel can estimate the road profile with a relatively highdegree of precision and that APE increases as road levelquality decreases Higher input amplitudes are associatedwith larger estimation errors and for the road input levelF the APE value reaches 1043 much higher than that forthe other levels This phenomenon can be interpreted as aresult of the excitation amplitude reaching or even exceeding025m which is the maximum amplitude of the trainingwhite noise signal which would lead to the appearanceof large local errors increasing the average APE of thewhole time period This is why the training signal mustbe comprehensive covering the entire time and frequencydomain

Utilising the classification method proposed in Section 5the road classification results are presented below The resultof wavelet transform is shown in Figure 7 and the originaland estimated road classification results are compared inFigure 8

Figure 7 clearly shows the changes in amplitude acrossdifferent road levels Compared to the original road profilesshown in Figure 6(a) Figure 8 shows that the high frequencysection is in the dominant position facilitating the use of ahigh frequency based classification method

In Figure 8 we calculate and compare the RMS of boththe actual and the estimated road profiles and the calculation


level B

0 20 40 60 80 1000000

0001

0002

0003

0004

0005

RMS of input roadRMS of lower limit

Time (s)

RMS of estimated roadRMS of standard level

RMS

ofc 1

(t)

(m)

Figure 8 Classification of road profile with detail components

interval is chosen to be 500ms It should be noted thatthe choice of calculation interval is arbitrary in this paper500ms is sufficient to satisfy the real-time requirement sincewe assume that the road level will not frequently changewithin very short time interval which also correspond toour basic knowledge In this case there are 40 points foreach level and 200 points in total for the whole time periodThe solid triangles represent the RMS of the estimated roadand the circles represent the RMS of the actual input roadwhile the long dashes and short dashes represent the standardand lower bounds respectively for each road level Althoughsome errors are apparent during the estimation process asshown in Figure 6(b) the RMS of the estimated roads isstill located within the same range as the correct road levelmeaning that accuracy requirements are satisfied It can alsobe seen that the estimated RMS converges quite rapidly to fitnew road levels meaning that the delays in the classificationprocedure are negligible with an interval of 500ms Thisdemonstrates that the proposed method meets real-timerequirements It should be noted that the average RMS valuesand lower limits for the different road levels are just points ofreference used for classification purposes In order to derivethe reference points each road level is generated 100 secondsin advance and the RMS values are calculated utilising thedetail part of signal for every 500msThe standard and lowerlimit values (reference points) are the mean values of these200 points

After road level classification the damping coefficientscan be altered adaptively according to the road level andthe control weights combinations shown in Table 3 In orderto evaluate the performance of the proposed hybrid controlalgorithm both ride comfort and road handling (the acceler-ation of sprungmass and the tyre force resp) are compared intime and frequency domain with the results shown in Table 4and Figures 9 and 10

Table 4 shows that both sprung mass acceleration andtyre force increase as the road level increases in both the


Table 4 Comparison of ride comfort and road handling

Roadlevel

RMS of sprung massacceleration (ms2) RMS of tyre force (N)

Passive Semiactive Passive SemiactiveB 0561 0479 2612 2778D 2245 2186 10445 10468E 4491 5049 20889 19891F 8982 10131 41779 39733C 1123 1093 5222 5233

1 1020

30

40

50

60

Gai

n of

spru

ng m

ass a

cc (

dB)

Passive[08 02][06 04]

[04 06][02 08]

Frequency (Hz)

wacc increase

Figure 9 Comparison of frequency responses of 119887119909119903for different

control weights

passive and the semiactive system From road levels from Bto F the passive systemrsquos RMS of sprung mass accelerationincreases from 0561ms2 to 8982ms2 while the value ofthe semiactive systemchanges from0479ms2 to 10131ms2This shows that the semiactive suspension system with theproposed algorithm can better isolate the vibration for thesprung mass on good road conditions however for poorroad excitation the ride comfort performance degrades Interms of road handling the tyre force RMS for the passivesystem increases from 2612N to 41779N while that of thesemiactive system varies from 2778N to 39733N whichmay be interpreted as demonstrating better road handlingperformance for poor roads and worse performance for goodroads

Figure 9 shows that as the road quality becomes worsethe acceleration response of sprung mass for both sprungmass natural frequency (147Hz) and human sensitive fre-quency range (4sim8Hz) keeps increasing It should be notedthat all four control weights combinations can better isolatevibration at about 15Hz than passive system and onlycontrol weights combinations for road levels A and B canimprove the ride comfort for 4sim8Hz which result in thedegradation of RMS for road levels E and F as shown inTable 4 Figure 10 demonstrates that with the increasing of

1 1070

80

90

100

110

120

Frequency (Hz)

Gai

n of

tire

forc

e (dB

)

wtire increase wtire increase

Passive[08 02][06 04]

[04 06][02 08]

Figure 10 Comparison of frequency responses of 119891119863119909119903for differ-

ent control weights

119908tire the hybrid semiactive suspension system can effectuallydepress the response around unsprung mass natural fre-quency for ldquopoorrdquo and ldquovery poorrdquo road conditions howeverthe response of these two control weights combinations for4sim8Hz is worse than that of passive system leading to thesmaller improvement of road handling for ldquoErdquo and ldquoFrdquo levels

From the above discussion we can see that with thedegradation of road quality the semiactive suspension systemwith the hybrid control algorithm changes from being ridecomfort oriented to being road handling oriented Accordingto the results shown in Table 3 it can be seen that as theweighting given to road handling increases the dampingcoefficient of 119888sky will decrease while that of 119888grd will increaseThis corresponds to the basic operation of vibration controlby increasing the damping coefficient the vibration of theconnected mass can be reduced

It should also be noted that with changes of the roadlevel the improvement in road handling is relatively smallerthan that of ride comfort This may be interpreted as followsalthough the groundhook control strategy involves setting animaginary inertial reference and installing the correspond-ing damping between the unsprung mass and the inertialreference as shown in Figure 1(a) the simulation resultsreveal that the velocity of the road profile is much largerthan the velocity of the unsprung mass which means thatthe unsprung mass is affected by both road input and thesuspension system In this case the influence of the roadprofile velocity cannot be ignored It should similarly benoted that for the skyhook control the sprung mass is onlyaffected by the suspension system In this case in order tobetter eliminate the influence of the road input one possiblesolution is to alter the groundhook force expression from119865grd = 119888grd119908 to 119865grd = 119888grd(119908 minus 119903) The simulation resultshowever show that although this method can considerablyimprove road handling the changes in damping force will


also influence the sprung mass significantly increasing theacceleration of the sprung mass In this case the proposedmethod may prove more suitable

8 Conclusion

In this paper an adaptive semiactive suspension systemcontrol strategy based on road profile estimation is proposedAnalytical expressions for ride comfort road handling andrattle space with respect to road conditions are derivedin order to depict the systemrsquos response to random roadexcitation The choice of control gains [119888sky 119888grd] for differentroad levels is then transformed into a MOOP and NSGA-II is applied to solve this problem A new road profileestimation method is moreover proposed to accompany thehybrid control strategy which estimates the road profilein the time domain utilising an inverse ANFIS model andfurther applies wavelet transforms to calculate the input roadlevel A specially designed road profile with five differentlevels is utilised to verify the proposed control and roadestimationmethods and a Kalman filter is applied to observethe unknown system statesThe simulation results reveal thatthe proposed road estimation method can accurately andrapidly identify the road level and based on the estimatedroad level the hybrid control strategy can adaptively alterthe control gains to suit different road levels Due to theinteractions of the damping force for the sprungmass and theunsprung mass ride comfort and road handling cannot bothbe improved simultaneously

Themain contributions of this paper are as follows firstlyto solve the problem of choice of damping coefficients forhybrid control the analytical expressions for ride comfortroad handling and rattle space are presented and corre-sponding damping coefficients are calculated by NSGA-IISecondly a new road level classificationmethod is developedwhich can be widely used for randomly profiled roadsFinally suggestions are made regarding how to effectivelyselect control gains for the semiactive suspension system andtheir interaction with road estimation

Further research may proceed in the following aspects(1) As the control strategy presented here is derived

based on a quarter vehicle model when applied toa full vehicle model the influence of the proposedcontrol strategy on pitch and roll angle for this controlstrategy requires further study

(2) As can be seen from Section 3 the suspension systemis modelled linearly It is generally accepted howeverthat actual vehicle suspension systems are typicallynonlinear displaying variance over time To accountfor this theKalmanfilter could bemodified to anEKF(Extended Kalman Filter) in future work It shouldbe noted that the proposed method of road profileestimation can however be used for nonlinear systemsonly if the training signal is comprehensive

(3) Since the proposed method is based only on theoret-ical analysis and validation via simulation an actualbench test for the quarter vehicle model is needed inthe future to validate the proposed control strategy

(4) The control frequency is 1000Hz in this paper andsince the delay of realistic controllable damper mightbe larger than this control interval that is 1ms torealize hybrid control in real suspension system wewill conduct some experiments to investigate theinfluence of control frequency and control delay in thenear future

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] S M Savaresi C P Vassal C Spelta et al Semi-ActiveSuspension Control Design for Vehicles Elsevier Oxford UK2010

[2] E Guglielmino T Sireteanu C W Stammers G Ghita andMGiuclea Semi-Active Suspension Control Improved Vehicle Rideand Road Friendliness Springer London UK 2008

[3] E M Elbeheiry and D C Karnopp ldquoOptimal control of vehiclerandom vibration with constrained suspension deflectionrdquoJournal of Sound andVibration vol 189 no 5 pp 547ndash564 1996

[4] M Gobbi and G Mastinu ldquoAnalytical description and opti-mization of the dynamic behaviour of passively suspended roadvehiclesrdquo Journal of Sound andVibration vol 245 no 3 pp 457ndash481 2001

[5] A Turnip and K S Hong ldquoRoad-frequency based optimisationof damping coefficients for semi-active suspension systemsrdquoInternational Journal of Vehicle Design vol 63 no 1 pp 84ndash1012013

[6] International Organization for Standardization MechanicalVibration and Shock-Evaluation of Human Exposure to Whole-BodyVibration International Organization for StandardizationLondon UK 1997

[7] D Karnopp M J Crosby and R A Harwood ldquoVibration con-trol using semi-active force generatorsrdquo Journal of Engineeringfor Industry vol 96 no 2 pp 619ndash626 1974

[8] P W Nugroho W Li H Du G Alici and J Yang ldquoAn adaptiveneuro fuzzy hybrid control strategy for a semiactive suspensionwith magneto rheological damperrdquo Advances in MechanicalEngineering vol 6 Article ID 487312 2014

[9] D Hrovat ldquoSurvey of advanced suspension developments andrelated optimal control applicationsrdquoAutomatica vol 33 no 10pp 1781ndash1817 1997

[10] L H Nguyen K-S Hong and S Park ldquoRoad-frequency adap-tive control for semi-active suspension systemsrdquo InternationalJournal of Control Automation and Systems vol 8 no 5 pp1029ndash1038 2010

[11] J D Robson and C J Dodds ldquoThe description of road surfaceroughnessrdquo Journal of Sound and Vibration vol 31 no 2 pp175ndash183 1973

[12] R S Sharp and D A Crolla ldquoRoad vehicle suspension systemdesignmdasha reviewrdquo Vehicle System Dynamics vol 16 no 3 pp167ndash192 1987

[13] K-S Hong H-C Sohn and J K Hedrick ldquoModified skyhookcontrol of semi-active suspensions a new model gain schedul-ing and hardware-in-the-loop tuningrdquo Journal of DynamicSystems Measurement and Control vol 124 no 1 pp 158ndash1672002


[14] A A Aly and F A Salem ldquoVehicle suspension systems controla reviewrdquo International Journal of Control Automation andSystems vol 2 no 2 pp 46ndash54 2013

[15] L Balamurugan and J Jancirani ldquoAn investigation on semi-active suspension damper and control strategies for vehicle ridecomfort and road holdingrdquo Proceedings of the Institution ofMechanical Engineers Part I Journal of Systems and ControlEngineering vol 226 no 8 pp 1119ndash1129 2012

[16] M Valasek M Novak Z Sika and O Vaculın ldquoExtendedground-hookmdashnew concept of semi-active control of truckrsquossuspensionrdquo Vehicle System Dynamics vol 27 no 5-6 pp 289ndash303 1997

[17] Y Hurmuzlu andOD NwokahTheMechanical SystemsDesignHandbook Modeling Measurement and Control CRC PressDanvers Mass USA 2001

[18] H Du K Yim Sze and J Lam ldquoSemi-active 119867infin

control ofvehicle suspensionwithmagneto-rheological dampersrdquo Journalof Sound and Vibration vol 283 no 3ndash5 pp 981ndash996 2005

[19] N Giorgetti A Bemporad H E Tseng andD Hrovat ldquoHybridmodel predictive control application towards optimal semi-active suspensionrdquo International Journal of Control vol 79 no5 pp 521ndash533 2006

[20] M Canale M Milanese and C Novara ldquoSemi-active suspen-sion control using lsquofastrsquo model-predictive techniquesrdquo IEEETransactions on Control Systems Technology vol 14 no 6 pp1034ndash1046 2006

[21] M Ahmadian and N Vahdati ldquoTransient dynamics of semi-active suspensions with hybrid controlrdquo Journal of IntelligentMaterial Systems and Structures vol 17 no 2 pp 145ndash153 2006

[22] V Sankaranarayanan E M Emekli L Guvenc et al ldquoSemi-active suspension control of a light commercial vehiclerdquoIEEEASME Transactions on Mechatronics vol 13 no 5 pp598ndash604 2008

[23] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fastand elitist multiobjective genetic algorithm NSGA-IIrdquo IEEETransactions on Evolutionary Computation vol 6 no 2 pp 182ndash197 2002

[24] K Deb Multi-Objective Optimization Using Evolutionary Algo-rithms John Wiley amp Sons Chichester UK 2001

[25] Y Qin R Langari and L Gu ldquoThe use of vehicle dynamicresponse to estimate road profile input in time domainrdquo in Pro-ceedings of the ASME Dynamic Systems and Control Conference(DSCC rsquo14) p 8 San Antonio Tex USA October 2014

[26] International Organization for Standardization MechanicalVibration-Road Surface Profiles-Reporting of Measured DataInternational Organization for Standardization London UK1995

[27] MMitschke andHWallentowitzDynamik der KraftfahrzeugeSpringer Berlin Germany 1972

[28] P Michelberger L Palkovics and J Bokor ldquoRobust designof active suspension systemrdquo International Journal of VehicleDesign vol 14 no 2-3 pp 145ndash165 1993

[29] Z C Wu S Z Chen L Yang and B Zhang ldquoModel ofroad roughness in time domain based on rational functionrdquoTransaction of Beijing Institute of Technology vol 29 no 9 pp795ndash798 2009

[30] M Ahmadian and C A Pare ldquoA quarter-car experimentalanalysis of alternative semiactive control methodsrdquo Journal ofIntelligent Material Systems and Structures vol 11 no 8 pp604ndash612 2001

[31] J-H Koo M Ahmadian M Setareh and T M MurrayldquoIn search of suitable control methods for semi-active tunedvibration absorbersrdquo Journal of Vibration and Control vol 10no 2 pp 163ndash174 2004

[32] T ButsuenThe design of semi-active suspensions for automotivevehicles [PhD thesis] Massachusetts Institute of TechnologyCambridge Mass USA 1989

[33] R RajamaniVehicleDynamics andControl SpringerNewYorkNY USA 2011

[34] CDMcgillem andGR CooperProbabilisticMethods of Signaland SystemAnalysis OxfordUniversity PressOxfordUK 1986

[35] R G Brown and P Y Hwang Introduction to Random Signalsand Applied Kalman Filtering With MATLAB Exercises andSolutions John Wiley amp Sons New York NY USA 1997

[36] K Deb Optimization for Engineering Design Algorithms andExamples PHI Learning Pvt Ltd New Delhi India 2012

[37] C C Coello G B Lamont and V D A Van EvolutionaryAlgorithms for Solving Multi-Objective Problems Springer NewYork NY USA 2007

[38] M Doumiati A Victorino A Charara and D LechnerldquoEstimation of road profile for vehicle dynamics motionexperimental validationrdquo inProceedings of the AmericanControlConference (ACC rsquo11) pp 5237ndash5242 San Francisco Calif USAJuly 2011

[39] H Imine Y Delanne and N K MrsquoSirdi ldquoRoad profile inputestimation in vehicle dynamics simulationrdquo Vehicle SystemDynamics vol 44 no 4 pp 285ndash303 2006

[40] A Gonzalez E J OrsquoBrien Y-Y Li and K Cashell ldquoThe use ofvehicle accelerationmeasurements to estimate road roughnessrdquoVehicle System Dynamics vol 46 no 6 pp 483ndash499 2008

[41] A Rabhi N K Mrsquosirdi L Fridman and Y Delanne ldquoSecondorder sliding mode observer for estimation of road profilerdquo inProceedings of the International Workshop on Variable StructureSystems (VSS rsquo06) pp 161ndash165 Alghero Italy June 2006

[42] G Koch T Kloiber and B Lohmann ldquoNonlinear and filterbased estimation for vehicle suspension controlrdquo in Proceedingsof the 49th IEEE Conference on Decision and Control (CDC rsquo10)pp 5592ndash5597 IEEE Atlanta Ga USA December 2010

[43] R McCann and S Nguyen ldquoSystem identification for a model-based observer of a road roughness profilerrdquo in Proceedings ofthe IEEE Region 5 Technical Conference (TPS rsquo07) pp 336ndash343April 2007

[44] J-S R Jang ldquoANFIS adaptive-network-based fuzzy inferencesystemrdquo IEEE Transactions on Systems Man and Cyberneticsvol 23 no 3 pp 665ndash685 1993

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Chemical EngineeringInternational Journal of Antennas and

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Navigation and Observation



DistributedSensor Networks



the acceleration of the sprung mass is typically usedas the metric upon which comparison is based [1 47 15ndash17 19]

(2) Road handling This criterion measures the abilityof a suspension system to maintain contact with theroad surface [6] Generally speaking tyre force or tyredeflection is normally chosen for use as a comparisonmetric [1 15] In order to obtain better accelerationbraking and steering ability when driving in worseroad conditions the tyre force or deflection shouldbe small

(3) Rattle space (working space) The rattle space repre-sents the distance between the sprung and unsprungmass This is a constraint for the suspension systemand under the assumption that the road input isa Gaussian distribution process [20] and the wholesystem is linear the variance of rattle space should bedesigned not to exceed plusmn13 of the constraint valueThis will ensure that the rattle space remains withinthe constraint range 997 of the time [3 4]

To combine the merits of both skyhook and groundhooksuspension systems for ride comfort and road handlingrespectively the hybrid control is proposed [19 21 22] Thehybrid control is a typical semiactive suspension controlstrategy since it can rapidly adjust damping coefficientaccording to system states feedback By adjusting the weight-ing of hybrid control rule operators can change the sus-pensionrsquos operating characteristics from being ride comfortoriented to being road handling oriented to suit whateversuspension performance they most desire at that time

For the suspension hybrid control that have beenexplored in the literatures little focus has been given to thechoice of damping coefficients for hybrid control systems andhow to cooperate this strategy with varying road conditionTo address this a road estimation based semiactive suspen-sion hybrid control strategy is proposed in this paper Themain contributions and innovations of this paper are as fol-lows Firstly the analytical expressions for three performancecriterions with respect to road excitation are derived and thechoice of damping coefficients is transformed into a MOOP(Multiobjective Optimization Problem) which is solved byNSGA-II (Nondominated Sorting Genetic Algorithm-II) [2324] Secondly the cooperation between hybrid control androad estimation is built A new road classification methodbased on ANFIS (Adaptive Neurofuzzy Inference System)and wavelet transform is presented for estimating the roadprofile level [25] so that the damping coefficients can adap-tively vary according to road condition and the accordingsolution of MOOP

This paper proceeds as follows Section 2 briefly intro-duces the road model and its generation in the time domainSection 3 presents the quarter vehicle model and the controlstrategy Section 4 illustrates the calculation of dampingcoefficients with NSGA-II Section 5 discusses road profileestimation and classification Section 6 describes the designof observer Section 7 contains numerical simulations fordifferent road levels and a conclusion is drawn at last

2 Road Model

The distance between the road surface and the base plateis typically defined as a function of road irregularitiesOften the road profile is assumed to be a homogeneousand isotropic Gaussian random process and its statisticalcharacteristics can be described by Power Spectral Density(PSD) [20] According to ISO 8601 [26] the PSD of roadroughness can be defined as

119866119902 (119899) = 119866119902 (1198990) (119899

1198990)

minus119882

(1)

where 119899 is spatial frequency in mminus1 and 1198990 is reference spatialfrequency with value of 01mminus1 119866119902(1198990) is the PSD value inthe reference spatial frequency in m3 and increasing valuesof 119866119902(1198990) are assigned for different road levels ranging fromA (very good) to H (very poor) 119882 is termed wavinessand reflects the approximate frequency structure of the roadprofile commonly taken as 119882 = 2 During the applicationprocess some researchers have however noted two problemswith (1)

(1) When the spatial frequency approximates zero thePSD of the road profile will approach infinity [20 27]

(2) According to actual roadmeasurements the PSD cal-culated by (1) will always overestimate the amplitudeof the road in the low frequency sections [4 20]

Because of this another formulation for calculating roadprofile PSD has been suggested by [17 28] and is used hereas shown in the following

119866119902 (119899) =120572120588

2

120587 (1205722+ 119899

2)

(2)

where 120572 is the road characteristic parameter in mminus1 and120588 is the road variance in m The values of both 120572 and 120588

are presented in Table 1 [29] It should be noted that thevalues in Table 1 have been carefully validated according tothe standard road level defined by the ISO The road profilein the time domain can be modelled as a first order linearprocess by [2 16 28]

119902 (119905) = minus 120572V119902 (119905) +119908 (119905) (3)

where 119902(119905) is road unevenness inm V is the vehicle velocity inkmh and119908(119905) is a white noise series with covariance shownas follows

cov [119908 (119905)] = 119864 [119908 (119905) 119908 (119905 + 120591)] = 21205882119886V120575 (120591) (4)

where 120575(sdot) is the Dirac delta function

3 Quarter Vehicle Model

In this section the hybrid control strategy and correspondingquarter vehicle model are created and analytical expressionsfor sprung mass acceleration tyre force and rattle space withrespect to road excitation are derived




31 Hybrid Control


119865sky =




119865grd =












119865output119889

=

119865max119889

if 119865119889 gt 119865max119889

119865119889 if 119865max119889

gt 119865119889 gt 119865min119889

119865min119889

if 119865min119889

gt 119865119889

(9)


119898119887119887 + 119896119904 (119909119887 minus119909119908) + 119865119889 = 0


minus 119865119889 = 0

(10)


119867(119904) 119909119887sim119909119903=119883119887 (119904)

119883119903 (119904)

=

119888grd1198881199051199044+ (119888grd119896119905 + 119888119905119896119904) 119904

3+ 119896119904119896119905119904

2

119860

119867 (119904)119909119908sim119909119903

=119883119908 (119904)

119883119903 (119904)

=

1198881199051198981198871199043+ (119898119887119896119905 + 119888sky119888119905) 119904

2+ (119888sky119896119905 + 119888119905119896119904) 119904 + 119896119904119896119905

119860

119867 (119904)119891119863sim119909119903= 119896119905 (

119883119908 (119904)

119883119903 (119904)

minus 1) = 119896119905

119863

119860

119867 (119904)(119909119887minus119909119908)sim119909119903

=119883119908 (119904)

119883119903 (119904)

=


2+ (119888grd119896119905 minus 119888sky119896119905) 119904

119860

(11)


csky

cgrd ct

ks

kt

mb

mw

xb

xw

xr

(a)

ct

ks

kt

mb

mw

xb

xw

xr

xb minus xwFd

Tyre

Unsprung mass

Suspension

Sprung mass

Rattle space

(b)


where

119860 = 1198981199081198981198871199044+ (119888grd119898119887 + 119888sky119898119908 + 119888119905119898119887) 119904

3

+ (119898119908119896119904 +119898119887119896119904 +119898119887119896119905 + 119888sky119888119905) 1199042

+ (119888sky119896119905 + 119888119905119896119904) 119904 + 119896119905119896119904


3

minus (119898119887119896119904 +119898119908119896119904) 1199042

(12)


1205902119901=

12120587

int

infin

minusinfin

119878119901 (120596) 119889120596 (13)


119878119901 (120596) =10038161003816100381610038161003816119867 (119895120596)

119901sim119909119903

10038161003816100381610038161003816

2119878119909119903

(119895120596) (14)



119901exists [35]

119878119901 (120596) =


119863119896 (119895120596)119863119896 (minus119895120596)

(15)


119863119896 (119895120596) = 119889119896 (119895120596)119896+119889119896minus1 (119895120596)



+ 119899119896minus2 (119895120596)119896minus2


(16)


119866119902 (119891) =119886V1205882

120587 [(119886V)2 + 1198912]

997888rarr 119878119909119903(119895120596) =

119886V1205882

120587

1(119886V + 119895120596)

1(119886V minus 119895120596)

(17)


10038161003816100381610038161003816119867 (119895120596)

119901sim119909119903

10038161003816100381610038161003816

2= 119867 (119895120596)

119901sim119909119903119867(minus119895120596)

119901sim119909119903 (18)



[16]1205902

=

(119899241198881198980 + (119899

23 minus 211989921198994) 1198881198981 + 11989911989801198881198982 + (119899

21 minus 211989901198992) 1198881198983 + 119899

201198881198984)

21198890 (11988911198881198984 minus 11988931198881198983 + 11988951198881198982)

(19)


1198991198980 = 11989922 minus 211989911198993 + 211989901198994

1198881198980 =11988931198881198981 minus 11988911198881198982

1198895

1198881198981 = minus11988901198893 +11988911198892

1198881198982 = minus11988901198895 +11988911198894

1198881198983 =11988921198881198982 minus 11988941198881198981

1198890

1198881198984 =11988921198881198983 minus 11988941198881198982

1198890

(20)
















Generatesolutions

Non-dominated

sorting


Tournamentselection


Combine

offspringparent and

Yes

No

OutputPareto

solution

Gen + 1








min 1198911 (119888sky 119888grd) = 1205902119909119887

1198912 (119888sky 119888grd) = 1205902119891119863


500 (Nsm) le 119888sky le 5000 (Nsm)

500 (Nsm) le 119888grd le 5000 (Nsm)

(21)


2 3 4 5 6 7 8 9 10 11 1208

085

09

095

10

11

11


f2(c s

kyc

grd)

(N)

f1(csky cgrd) (ms2)

times106


where 1205902119909119887and 120590

2119891119863


5 Road Estimation













Nonlinear


Inverse

model

quarternonlinear

vehicle model

Inverse

quarter

ANFIS

xr

xr

xb minus xwFdxw

+

minus xr

e

sum

xw



119909119903 = 119891 (119908 119909119908 (119909119908 minus119909119887) 119865119889) (22)










119909119896+1 = 119860119909119896 +119861119906119896 +119866119903119896 +119865119908119896

119910119896 = 119862119909119896 +119863119906119896 + V119896(23)



997888119909 = [119909119887 119887 119909119908 119908]

119879 (24)


997888119910 = [119887 119908]

119879 (25)


119860 = 119864+Δ119905 sdot

[[[[[[[[

[

0 1 0 0

minus119896119904

119898119887

0119896119904

119898119887

0

0 0 0 1119896119904

119898119908

0 minus119896119905 + 119896119904

119898119908

minus119888119905

119898119908

]]]]]]]]

]

119861 = Δ119905 sdot

[[[[[[[[

[

0

minus1119898119887

01119898119908

]]]]]]]]

]


3 5 6 70 1 2 4 8 9 10

0250201501005



Analyticalsolution

SuspensionMOOP

Roadlevel

Roadclassification

ANFISinversemodel


Controlforce


Feedback

Road input

Quartervehiclemodel

Statemeasurement

Stateestimator



xw

xbxr

xr

Fd

[csky cgrd]

Foutputd

xb x xxb minus w w

xb minus xw xw


119866 = Δ119905 sdot

[[[[[[[

[

000119896119905

119898119908

]]]]]]]

]

119865 = Δ119905 sdot

[[[[[[[

[

000119888119905

119898119908

]]]]]]]

]

119862 =

[[[

[

minus119896119904

119898119887

0119896119904

119898119887

0119896119904

119898119908

0 minus119896119905

119898119908

minus119888119905

119898119908

]]]

]

119863 =

[[[

[

minus11198981198871119898119908

]]]

]

(26)



119909minus

119896= 119860119909119896minus1 +119861119906119896minus1

119875minus

119896= 119860119875119896minus1119860

119879+119876

(27)


119870119896 = 119875minus

119896119862119879(119862119875minus

119896119862119879+119877)

minus1

119909119896 = 119909minus

119896+119870119896 [119910119896 minus (119862119909

minus

119896+119863119906119896)]

119875119896 = (119868 minus119870119896119862)119875minus

119896

(28)


minus

119896and 119909119896 are












119889










minus04

minus03

minus02

minus01

0 20 40 60 80 100

00

01

02

03

04


Am

plitu

de (m

)

Time (s)


(a)

0 20 40 60 80 100


minus04

minus03

minus02

minus01

00

01

02

03

04

Am

plitu

de (m

)

Time (s)


level B

APE= 429

APE= 1043

APE= 632

APE= 514

APE= 357

(b)





0 20 40 60 80 100

000

002

004

006


level B

Am

plitu

de (m

)

Time (s)

minus006

minus004

minus002




APE =1119875

119875

sum

119894=1

|119879 (119894) minus 119874 (119894)|

|119879 (119894)|

times 100 (29)







level B

0 20 40 60 80 1000000

0001

0002

0003

0004

0005


Time (s)


RMS

ofc 1

(t)

(m)







Roadlevel



1 1020

30

40

50

60

Gai

n of

spru

ng m

ass a

cc (

dB)

Passive[08 02][06 04]

[04 06][02 08]

Frequency (Hz)

wacc increase


control weights



1 1070

80

90

100

110

120

Frequency (Hz)

Gai

n of

tire

forc

e (dB

)


Passive[08 02][06 04]

[04 06][02 08]


ent control weights






8 Conclusion










References

















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












31 Hybrid Control


119865sky =




119865grd =












119865output119889

=

119865max119889

if 119865119889 gt 119865max119889

119865119889 if 119865max119889

gt 119865119889 gt 119865min119889

119865min119889

if 119865min119889

gt 119865119889

(9)


119898119887119887 + 119896119904 (119909119887 minus119909119908) + 119865119889 = 0


minus 119865119889 = 0

(10)


119867(119904) 119909119887sim119909119903=119883119887 (119904)

119883119903 (119904)

=

119888grd1198881199051199044+ (119888grd119896119905 + 119888119905119896119904) 119904

3+ 119896119904119896119905119904

2

119860

119867 (119904)119909119908sim119909119903

=119883119908 (119904)

119883119903 (119904)

=

1198881199051198981198871199043+ (119898119887119896119905 + 119888sky119888119905) 119904

2+ (119888sky119896119905 + 119888119905119896119904) 119904 + 119896119904119896119905

119860

119867 (119904)119891119863sim119909119903= 119896119905 (

119883119908 (119904)

119883119903 (119904)

minus 1) = 119896119905

119863

119860

119867 (119904)(119909119887minus119909119908)sim119909119903

=119883119908 (119904)

119883119903 (119904)

=


2+ (119888grd119896119905 minus 119888sky119896119905) 119904

119860

(11)


csky

cgrd ct

ks

kt

mb

mw

xb

xw

xr

(a)

ct

ks

kt

mb

mw

xb

xw

xr

xb minus xwFd

Tyre

Unsprung mass

Suspension

Sprung mass

Rattle space

(b)


where

119860 = 1198981199081198981198871199044+ (119888grd119898119887 + 119888sky119898119908 + 119888119905119898119887) 119904

3

+ (119898119908119896119904 +119898119887119896119904 +119898119887119896119905 + 119888sky119888119905) 1199042

+ (119888sky119896119905 + 119888119905119896119904) 119904 + 119896119905119896119904


3

minus (119898119887119896119904 +119898119908119896119904) 1199042

(12)


1205902119901=

12120587

int

infin

minusinfin

119878119901 (120596) 119889120596 (13)


119878119901 (120596) =10038161003816100381610038161003816119867 (119895120596)

119901sim119909119903

10038161003816100381610038161003816

2119878119909119903

(119895120596) (14)



119901exists [35]

119878119901 (120596) =


119863119896 (119895120596)119863119896 (minus119895120596)

(15)


119863119896 (119895120596) = 119889119896 (119895120596)119896+119889119896minus1 (119895120596)



+ 119899119896minus2 (119895120596)119896minus2


(16)


119866119902 (119891) =119886V1205882

120587 [(119886V)2 + 1198912]

997888rarr 119878119909119903(119895120596) =

119886V1205882

120587

1(119886V + 119895120596)

1(119886V minus 119895120596)

(17)


10038161003816100381610038161003816119867 (119895120596)

119901sim119909119903

10038161003816100381610038161003816

2= 119867 (119895120596)

119901sim119909119903119867(minus119895120596)

119901sim119909119903 (18)



[16]1205902

=

(119899241198881198980 + (119899

23 minus 211989921198994) 1198881198981 + 11989911989801198881198982 + (119899

21 minus 211989901198992) 1198881198983 + 119899

201198881198984)

21198890 (11988911198881198984 minus 11988931198881198983 + 11988951198881198982)

(19)


1198991198980 = 11989922 minus 211989911198993 + 211989901198994

1198881198980 =11988931198881198981 minus 11988911198881198982

1198895

1198881198981 = minus11988901198893 +11988911198892

1198881198982 = minus11988901198895 +11988911198894

1198881198983 =11988921198881198982 minus 11988941198881198981

1198890

1198881198984 =11988921198881198983 minus 11988941198881198982

1198890

(20)
















Generatesolutions

Non-dominated

sorting


Tournamentselection


Combine

offspringparent and

Yes

No

OutputPareto

solution

Gen + 1








min 1198911 (119888sky 119888grd) = 1205902119909119887

1198912 (119888sky 119888grd) = 1205902119891119863


500 (Nsm) le 119888sky le 5000 (Nsm)

500 (Nsm) le 119888grd le 5000 (Nsm)

(21)


2 3 4 5 6 7 8 9 10 11 1208

085

09

095

10

11

11


f2(c s

kyc

grd)

(N)

f1(csky cgrd) (ms2)

times106


where 1205902119909119887and 120590

2119891119863


5 Road Estimation













Nonlinear


Inverse

model

quarternonlinear

vehicle model

Inverse

quarter

ANFIS

xr

xr

xb minus xwFdxw

+

minus xr

e

sum

xw



119909119903 = 119891 (119908 119909119908 (119909119908 minus119909119887) 119865119889) (22)










119909119896+1 = 119860119909119896 +119861119906119896 +119866119903119896 +119865119908119896

119910119896 = 119862119909119896 +119863119906119896 + V119896(23)



997888119909 = [119909119887 119887 119909119908 119908]

119879 (24)


997888119910 = [119887 119908]

119879 (25)


119860 = 119864+Δ119905 sdot

[[[[[[[[

[

0 1 0 0

minus119896119904

119898119887

0119896119904

119898119887

0

0 0 0 1119896119904

119898119908

0 minus119896119905 + 119896119904

119898119908

minus119888119905

119898119908

]]]]]]]]

]

119861 = Δ119905 sdot

[[[[[[[[

[

0

minus1119898119887

01119898119908

]]]]]]]]

]


3 5 6 70 1 2 4 8 9 10

0250201501005



Analyticalsolution

SuspensionMOOP

Roadlevel

Roadclassification

ANFISinversemodel


Controlforce


Feedback

Road input

Quartervehiclemodel

Statemeasurement

Stateestimator



xw

xbxr

xr

Fd

[csky cgrd]

Foutputd

xb x xxb minus w w

xb minus xw xw


119866 = Δ119905 sdot

[[[[[[[

[

000119896119905

119898119908

]]]]]]]

]

119865 = Δ119905 sdot

[[[[[[[

[

000119888119905

119898119908

]]]]]]]

]

119862 =

[[[

[

minus119896119904

119898119887

0119896119904

119898119887

0119896119904

119898119908

0 minus119896119905

119898119908

minus119888119905

119898119908

]]]

]

119863 =

[[[

[

minus11198981198871119898119908

]]]

]

(26)



119909minus

119896= 119860119909119896minus1 +119861119906119896minus1

119875minus

119896= 119860119875119896minus1119860

119879+119876

(27)


119870119896 = 119875minus

119896119862119879(119862119875minus

119896119862119879+119877)

minus1

119909119896 = 119909minus

119896+119870119896 [119910119896 minus (119862119909

minus

119896+119863119906119896)]

119875119896 = (119868 minus119870119896119862)119875minus

119896

(28)


minus

119896and 119909119896 are












119889










minus04

minus03

minus02

minus01

0 20 40 60 80 100

00

01

02

03

04


Am

plitu

de (m

)

Time (s)


(a)

0 20 40 60 80 100


minus04

minus03

minus02

minus01

00

01

02

03

04

Am

plitu

de (m

)

Time (s)


level B

APE= 429

APE= 1043

APE= 632

APE= 514

APE= 357

(b)





0 20 40 60 80 100

000

002

004

006


level B

Am

plitu

de (m

)

Time (s)

minus006

minus004

minus002




APE =1119875

119875

sum

119894=1

|119879 (119894) minus 119874 (119894)|

|119879 (119894)|

times 100 (29)







level B

0 20 40 60 80 1000000

0001

0002

0003

0004

0005


Time (s)


RMS

ofc 1

(t)

(m)







Roadlevel



1 1020

30

40

50

60

Gai

n of

spru

ng m

ass a

cc (

dB)

Passive[08 02][06 04]

[04 06][02 08]

Frequency (Hz)

wacc increase


control weights



1 1070

80

90

100

110

120

Frequency (Hz)

Gai

n of

tire

forc

e (dB

)


Passive[08 02][06 04]

[04 06][02 08]


ent control weights






8 Conclusion










References

















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










csky

cgrd ct

ks

kt

mb

mw

xb

xw

xr

(a)

ct

ks

kt

mb

mw

xb

xw

xr

xb minus xwFd

Tyre

Unsprung mass

Suspension

Sprung mass

Rattle space

(b)


where

119860 = 1198981199081198981198871199044+ (119888grd119898119887 + 119888sky119898119908 + 119888119905119898119887) 119904

3

+ (119898119908119896119904 +119898119887119896119904 +119898119887119896119905 + 119888sky119888119905) 1199042

+ (119888sky119896119905 + 119888119905119896119904) 119904 + 119896119905119896119904


3

minus (119898119887119896119904 +119898119908119896119904) 1199042

(12)


1205902119901=

12120587

int

infin

minusinfin

119878119901 (120596) 119889120596 (13)


119878119901 (120596) =10038161003816100381610038161003816119867 (119895120596)

119901sim119909119903

10038161003816100381610038161003816

2119878119909119903

(119895120596) (14)



119901exists [35]

119878119901 (120596) =


119863119896 (119895120596)119863119896 (minus119895120596)

(15)


119863119896 (119895120596) = 119889119896 (119895120596)119896+119889119896minus1 (119895120596)



+ 119899119896minus2 (119895120596)119896minus2


(16)


119866119902 (119891) =119886V1205882

120587 [(119886V)2 + 1198912]

997888rarr 119878119909119903(119895120596) =

119886V1205882

120587

1(119886V + 119895120596)

1(119886V minus 119895120596)

(17)


10038161003816100381610038161003816119867 (119895120596)

119901sim119909119903

10038161003816100381610038161003816

2= 119867 (119895120596)

119901sim119909119903119867(minus119895120596)

119901sim119909119903 (18)



[16]1205902

=

(119899241198881198980 + (119899

23 minus 211989921198994) 1198881198981 + 11989911989801198881198982 + (119899

21 minus 211989901198992) 1198881198983 + 119899

201198881198984)

21198890 (11988911198881198984 minus 11988931198881198983 + 11988951198881198982)

(19)


1198991198980 = 11989922 minus 211989911198993 + 211989901198994

1198881198980 =11988931198881198981 minus 11988911198881198982

1198895

1198881198981 = minus11988901198893 +11988911198892

1198881198982 = minus11988901198895 +11988911198894

1198881198983 =11988921198881198982 minus 11988941198881198981

1198890

1198881198984 =11988921198881198983 minus 11988941198881198982

1198890

(20)
















Generatesolutions

Non-dominated

sorting


Tournamentselection


Combine

offspringparent and

Yes

No

OutputPareto

solution

Gen + 1








min 1198911 (119888sky 119888grd) = 1205902119909119887

1198912 (119888sky 119888grd) = 1205902119891119863


500 (Nsm) le 119888sky le 5000 (Nsm)

500 (Nsm) le 119888grd le 5000 (Nsm)

(21)


2 3 4 5 6 7 8 9 10 11 1208

085

09

095

10

11

11


f2(c s

kyc

grd)

(N)

f1(csky cgrd) (ms2)

times106


where 1205902119909119887and 120590

2119891119863


5 Road Estimation













Nonlinear


Inverse

model

quarternonlinear

vehicle model

Inverse

quarter

ANFIS

xr

xr

xb minus xwFdxw

+

minus xr

e

sum

xw



119909119903 = 119891 (119908 119909119908 (119909119908 minus119909119887) 119865119889) (22)










119909119896+1 = 119860119909119896 +119861119906119896 +119866119903119896 +119865119908119896

119910119896 = 119862119909119896 +119863119906119896 + V119896(23)



997888119909 = [119909119887 119887 119909119908 119908]

119879 (24)


997888119910 = [119887 119908]

119879 (25)


119860 = 119864+Δ119905 sdot

[[[[[[[[

[

0 1 0 0

minus119896119904

119898119887

0119896119904

119898119887

0

0 0 0 1119896119904

119898119908

0 minus119896119905 + 119896119904

119898119908

minus119888119905

119898119908

]]]]]]]]

]

119861 = Δ119905 sdot

[[[[[[[[

[

0

minus1119898119887

01119898119908

]]]]]]]]

]


3 5 6 70 1 2 4 8 9 10

0250201501005



Analyticalsolution

SuspensionMOOP

Roadlevel

Roadclassification

ANFISinversemodel


Controlforce


Feedback

Road input

Quartervehiclemodel

Statemeasurement

Stateestimator



xw

xbxr

xr

Fd

[csky cgrd]

Foutputd

xb x xxb minus w w

xb minus xw xw


119866 = Δ119905 sdot

[[[[[[[

[

000119896119905

119898119908

]]]]]]]

]

119865 = Δ119905 sdot

[[[[[[[

[

000119888119905

119898119908

]]]]]]]

]

119862 =

[[[

[

minus119896119904

119898119887

0119896119904

119898119887

0119896119904

119898119908

0 minus119896119905

119898119908

minus119888119905

119898119908

]]]

]

119863 =

[[[

[

minus11198981198871119898119908

]]]

]

(26)



119909minus

119896= 119860119909119896minus1 +119861119906119896minus1

119875minus

119896= 119860119875119896minus1119860

119879+119876

(27)


119870119896 = 119875minus

119896119862119879(119862119875minus

119896119862119879+119877)

minus1

119909119896 = 119909minus

119896+119870119896 [119910119896 minus (119862119909

minus

119896+119863119906119896)]

119875119896 = (119868 minus119870119896119862)119875minus

119896

(28)


minus

119896and 119909119896 are












119889










minus04

minus03

minus02

minus01

0 20 40 60 80 100

00

01

02

03

04


Am

plitu

de (m

)

Time (s)


(a)

0 20 40 60 80 100


minus04

minus03

minus02

minus01

00

01

02

03

04

Am

plitu

de (m

)

Time (s)


level B

APE= 429

APE= 1043

APE= 632

APE= 514

APE= 357

(b)





0 20 40 60 80 100

000

002

004

006


level B

Am

plitu

de (m

)

Time (s)

minus006

minus004

minus002




APE =1119875

119875

sum

119894=1

|119879 (119894) minus 119874 (119894)|

|119879 (119894)|

times 100 (29)







level B

0 20 40 60 80 1000000

0001

0002

0003

0004

0005


Time (s)


RMS

ofc 1

(t)

(m)







Roadlevel



1 1020

30

40

50

60

Gai

n of

spru

ng m

ass a

cc (

dB)

Passive[08 02][06 04]

[04 06][02 08]

Frequency (Hz)

wacc increase


control weights



1 1070

80

90

100

110

120

Frequency (Hz)

Gai

n of

tire

forc

e (dB

)


Passive[08 02][06 04]

[04 06][02 08]


ent control weights






8 Conclusion










References

















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
























Generatesolutions

Non-dominated

sorting


Tournamentselection


Combine

offspringparent and

Yes

No

OutputPareto

solution

Gen + 1








min 1198911 (119888sky 119888grd) = 1205902119909119887

1198912 (119888sky 119888grd) = 1205902119891119863


500 (Nsm) le 119888sky le 5000 (Nsm)

500 (Nsm) le 119888grd le 5000 (Nsm)

(21)


2 3 4 5 6 7 8 9 10 11 1208

085

09

095

10

11

11


f2(c s

kyc

grd)

(N)

f1(csky cgrd) (ms2)

times106


where 1205902119909119887and 120590

2119891119863


5 Road Estimation













Nonlinear


Inverse

model

quarternonlinear

vehicle model

Inverse

quarter

ANFIS

xr

xr

xb minus xwFdxw

+

minus xr

e

sum

xw



119909119903 = 119891 (119908 119909119908 (119909119908 minus119909119887) 119865119889) (22)










119909119896+1 = 119860119909119896 +119861119906119896 +119866119903119896 +119865119908119896

119910119896 = 119862119909119896 +119863119906119896 + V119896(23)



997888119909 = [119909119887 119887 119909119908 119908]

119879 (24)


997888119910 = [119887 119908]

119879 (25)


119860 = 119864+Δ119905 sdot

[[[[[[[[

[

0 1 0 0

minus119896119904

119898119887

0119896119904

119898119887

0

0 0 0 1119896119904

119898119908

0 minus119896119905 + 119896119904

119898119908

minus119888119905

119898119908

]]]]]]]]

]

119861 = Δ119905 sdot

[[[[[[[[

[

0

minus1119898119887

01119898119908

]]]]]]]]

]


3 5 6 70 1 2 4 8 9 10

0250201501005



Analyticalsolution

SuspensionMOOP

Roadlevel

Roadclassification

ANFISinversemodel


Controlforce


Feedback

Road input

Quartervehiclemodel

Statemeasurement

Stateestimator



xw

xbxr

xr

Fd

[csky cgrd]

Foutputd

xb x xxb minus w w

xb minus xw xw


119866 = Δ119905 sdot

[[[[[[[

[

000119896119905

119898119908

]]]]]]]

]

119865 = Δ119905 sdot

[[[[[[[

[

000119888119905

119898119908

]]]]]]]

]

119862 =

[[[

[

minus119896119904

119898119887

0119896119904

119898119887

0119896119904

119898119908

0 minus119896119905

119898119908

minus119888119905

119898119908

]]]

]

119863 =

[[[

[

minus11198981198871119898119908

]]]

]

(26)



119909minus

119896= 119860119909119896minus1 +119861119906119896minus1

119875minus

119896= 119860119875119896minus1119860

119879+119876

(27)


119870119896 = 119875minus

119896119862119879(119862119875minus

119896119862119879+119877)

minus1

119909119896 = 119909minus

119896+119870119896 [119910119896 minus (119862119909

minus

119896+119863119906119896)]

119875119896 = (119868 minus119870119896119862)119875minus

119896

(28)


minus

119896and 119909119896 are












119889










minus04

minus03

minus02

minus01

0 20 40 60 80 100

00

01

02

03

04


Am

plitu

de (m

)

Time (s)


(a)

0 20 40 60 80 100


minus04

minus03

minus02

minus01

00

01

02

03

04

Am

plitu

de (m

)

Time (s)


level B

APE= 429

APE= 1043

APE= 632

APE= 514

APE= 357

(b)





0 20 40 60 80 100

000

002

004

006


level B

Am

plitu

de (m

)

Time (s)

minus006

minus004

minus002




APE =1119875

119875

sum

119894=1

|119879 (119894) minus 119874 (119894)|

|119879 (119894)|

times 100 (29)







level B

0 20 40 60 80 1000000

0001

0002

0003

0004

0005


Time (s)


RMS

ofc 1

(t)

(m)







Roadlevel



1 1020

30

40

50

60

Gai

n of

spru

ng m

ass a

cc (

dB)

Passive[08 02][06 04]

[04 06][02 08]

Frequency (Hz)

wacc increase


control weights



1 1070

80

90

100

110

120

Frequency (Hz)

Gai

n of

tire

forc

e (dB

)


Passive[08 02][06 04]

[04 06][02 08]


ent control weights






8 Conclusion










References

















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










2 3 4 5 6 7 8 9 10 11 1208

085

09

095

10

11

11


f2(c s

kyc

grd)

(N)

f1(csky cgrd) (ms2)

times106


where 1205902119909119887and 120590

2119891119863


5 Road Estimation













Nonlinear


Inverse

model

quarternonlinear

vehicle model

Inverse

quarter

ANFIS

xr

xr

xb minus xwFdxw

+

minus xr

e

sum

xw



119909119903 = 119891 (119908 119909119908 (119909119908 minus119909119887) 119865119889) (22)










119909119896+1 = 119860119909119896 +119861119906119896 +119866119903119896 +119865119908119896

119910119896 = 119862119909119896 +119863119906119896 + V119896(23)



997888119909 = [119909119887 119887 119909119908 119908]

119879 (24)


997888119910 = [119887 119908]

119879 (25)


119860 = 119864+Δ119905 sdot

[[[[[[[[

[

0 1 0 0

minus119896119904

119898119887

0119896119904

119898119887

0

0 0 0 1119896119904

119898119908

0 minus119896119905 + 119896119904

119898119908

minus119888119905

119898119908

]]]]]]]]

]

119861 = Δ119905 sdot

[[[[[[[[

[

0

minus1119898119887

01119898119908

]]]]]]]]

]


3 5 6 70 1 2 4 8 9 10

0250201501005



Analyticalsolution

SuspensionMOOP

Roadlevel

Roadclassification

ANFISinversemodel


Controlforce


Feedback

Road input

Quartervehiclemodel

Statemeasurement

Stateestimator



xw

xbxr

xr

Fd

[csky cgrd]

Foutputd

xb x xxb minus w w

xb minus xw xw


119866 = Δ119905 sdot

[[[[[[[

[

000119896119905

119898119908

]]]]]]]

]

119865 = Δ119905 sdot

[[[[[[[

[

000119888119905

119898119908

]]]]]]]

]

119862 =

[[[

[

minus119896119904

119898119887

0119896119904

119898119887

0119896119904

119898119908

0 minus119896119905

119898119908

minus119888119905

119898119908

]]]

]

119863 =

[[[

[

minus11198981198871119898119908

]]]

]

(26)



119909minus

119896= 119860119909119896minus1 +119861119906119896minus1

119875minus

119896= 119860119875119896minus1119860

119879+119876

(27)


119870119896 = 119875minus

119896119862119879(119862119875minus

119896119862119879+119877)

minus1

119909119896 = 119909minus

119896+119870119896 [119910119896 minus (119862119909

minus

119896+119863119906119896)]

119875119896 = (119868 minus119870119896119862)119875minus

119896

(28)


minus

119896and 119909119896 are












119889










minus04

minus03

minus02

minus01

0 20 40 60 80 100

00

01

02

03

04


Am

plitu

de (m

)

Time (s)


(a)

0 20 40 60 80 100


minus04

minus03

minus02

minus01

00

01

02

03

04

Am

plitu

de (m

)

Time (s)


level B

APE= 429

APE= 1043

APE= 632

APE= 514

APE= 357

(b)





0 20 40 60 80 100

000

002

004

006


level B

Am

plitu

de (m

)

Time (s)

minus006

minus004

minus002




APE =1119875

119875

sum

119894=1

|119879 (119894) minus 119874 (119894)|

|119879 (119894)|

times 100 (29)







level B

0 20 40 60 80 1000000

0001

0002

0003

0004

0005


Time (s)


RMS

ofc 1

(t)

(m)







Roadlevel



1 1020

30

40

50

60

Gai

n of

spru

ng m

ass a

cc (

dB)

Passive[08 02][06 04]

[04 06][02 08]

Frequency (Hz)

wacc increase


control weights



1 1070

80

90

100

110

120

Frequency (Hz)

Gai

n of

tire

forc

e (dB

)


Passive[08 02][06 04]

[04 06][02 08]


ent control weights






8 Conclusion










References

















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Nonlinear


Inverse

model

quarternonlinear

vehicle model

Inverse

quarter

ANFIS

xr

xr

xb minus xwFdxw

+

minus xr

e

sum

xw



119909119903 = 119891 (119908 119909119908 (119909119908 minus119909119887) 119865119889) (22)










119909119896+1 = 119860119909119896 +119861119906119896 +119866119903119896 +119865119908119896

119910119896 = 119862119909119896 +119863119906119896 + V119896(23)



997888119909 = [119909119887 119887 119909119908 119908]

119879 (24)


997888119910 = [119887 119908]

119879 (25)


119860 = 119864+Δ119905 sdot

[[[[[[[[

[

0 1 0 0

minus119896119904

119898119887

0119896119904

119898119887

0

0 0 0 1119896119904

119898119908

0 minus119896119905 + 119896119904

119898119908

minus119888119905

119898119908

]]]]]]]]

]

119861 = Δ119905 sdot

[[[[[[[[

[

0

minus1119898119887

01119898119908

]]]]]]]]

]


3 5 6 70 1 2 4 8 9 10

0250201501005



Analyticalsolution

SuspensionMOOP

Roadlevel

Roadclassification

ANFISinversemodel


Controlforce


Feedback

Road input

Quartervehiclemodel

Statemeasurement

Stateestimator



xw

xbxr

xr

Fd

[csky cgrd]

Foutputd

xb x xxb minus w w

xb minus xw xw


119866 = Δ119905 sdot

[[[[[[[

[

000119896119905

119898119908

]]]]]]]

]

119865 = Δ119905 sdot

[[[[[[[

[

000119888119905

119898119908

]]]]]]]

]

119862 =

[[[

[

minus119896119904

119898119887

0119896119904

119898119887

0119896119904

119898119908

0 minus119896119905

119898119908

minus119888119905

119898119908

]]]

]

119863 =

[[[

[

minus11198981198871119898119908

]]]

]

(26)



119909minus

119896= 119860119909119896minus1 +119861119906119896minus1

119875minus

119896= 119860119875119896minus1119860

119879+119876

(27)


119870119896 = 119875minus

119896119862119879(119862119875minus

119896119862119879+119877)

minus1

119909119896 = 119909minus

119896+119870119896 [119910119896 minus (119862119909

minus

119896+119863119906119896)]

119875119896 = (119868 minus119870119896119862)119875minus

119896

(28)


minus

119896and 119909119896 are












119889










minus04

minus03

minus02

minus01

0 20 40 60 80 100

00

01

02

03

04


Am

plitu

de (m

)

Time (s)


(a)

0 20 40 60 80 100


minus04

minus03

minus02

minus01

00

01

02

03

04

Am

plitu

de (m

)

Time (s)


level B

APE= 429

APE= 1043

APE= 632

APE= 514

APE= 357

(b)





0 20 40 60 80 100

000

002

004

006


level B

Am

plitu

de (m

)

Time (s)

minus006

minus004

minus002




APE =1119875

119875

sum

119894=1

|119879 (119894) minus 119874 (119894)|

|119879 (119894)|

times 100 (29)







level B

0 20 40 60 80 1000000

0001

0002

0003

0004

0005


Time (s)


RMS

ofc 1

(t)

(m)







Roadlevel



1 1020

30

40

50

60

Gai

n of

spru

ng m

ass a

cc (

dB)

Passive[08 02][06 04]

[04 06][02 08]

Frequency (Hz)

wacc increase


control weights



1 1070

80

90

100

110

120

Frequency (Hz)

Gai

n of

tire

forc

e (dB

)


Passive[08 02][06 04]

[04 06][02 08]


ent control weights






8 Conclusion










References

















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










3 5 6 70 1 2 4 8 9 10

0250201501005



Analyticalsolution

SuspensionMOOP

Roadlevel

Roadclassification

ANFISinversemodel


Controlforce


Feedback

Road input

Quartervehiclemodel

Statemeasurement

Stateestimator



xw

xbxr

xr

Fd

[csky cgrd]

Foutputd

xb x xxb minus w w

xb minus xw xw


119866 = Δ119905 sdot

[[[[[[[

[

000119896119905

119898119908

]]]]]]]

]

119865 = Δ119905 sdot

[[[[[[[

[

000119888119905

119898119908

]]]]]]]

]

119862 =

[[[

[

minus119896119904

119898119887

0119896119904

119898119887

0119896119904

119898119908

0 minus119896119905

119898119908

minus119888119905

119898119908

]]]

]

119863 =

[[[

[

minus11198981198871119898119908

]]]

]

(26)



119909minus

119896= 119860119909119896minus1 +119861119906119896minus1

119875minus

119896= 119860119875119896minus1119860

119879+119876

(27)


119870119896 = 119875minus

119896119862119879(119862119875minus

119896119862119879+119877)

minus1

119909119896 = 119909minus

119896+119870119896 [119910119896 minus (119862119909

minus

119896+119863119906119896)]

119875119896 = (119868 minus119870119896119862)119875minus

119896

(28)


minus

119896and 119909119896 are












119889










minus04

minus03

minus02

minus01

0 20 40 60 80 100

00

01

02

03

04


Am

plitu

de (m

)

Time (s)


(a)

0 20 40 60 80 100


minus04

minus03

minus02

minus01

00

01

02

03

04

Am

plitu

de (m

)

Time (s)


level B

APE= 429

APE= 1043

APE= 632

APE= 514

APE= 357

(b)





0 20 40 60 80 100

000

002

004

006


level B

Am

plitu

de (m

)

Time (s)

minus006

minus004

minus002




APE =1119875

119875

sum

119894=1

|119879 (119894) minus 119874 (119894)|

|119879 (119894)|

times 100 (29)







level B

0 20 40 60 80 1000000

0001

0002

0003

0004

0005


Time (s)


RMS

ofc 1

(t)

(m)







Roadlevel



1 1020

30

40

50

60

Gai

n of

spru

ng m

ass a

cc (

dB)

Passive[08 02][06 04]

[04 06][02 08]

Frequency (Hz)

wacc increase


control weights



1 1070

80

90

100

110

120

Frequency (Hz)

Gai

n of

tire

forc

e (dB

)


Passive[08 02][06 04]

[04 06][02 08]


ent control weights






8 Conclusion










References

















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













119889










minus04

minus03

minus02

minus01

0 20 40 60 80 100

00

01

02

03

04


Am

plitu

de (m

)

Time (s)


(a)

0 20 40 60 80 100


minus04

minus03

minus02

minus01

00

01

02

03

04

Am

plitu

de (m

)

Time (s)


level B

APE= 429

APE= 1043

APE= 632

APE= 514

APE= 357

(b)





0 20 40 60 80 100

000

002

004

006


level B

Am

plitu

de (m

)

Time (s)

minus006

minus004

minus002




APE =1119875

119875

sum

119894=1

|119879 (119894) minus 119874 (119894)|

|119879 (119894)|

times 100 (29)







level B

0 20 40 60 80 1000000

0001

0002

0003

0004

0005


Time (s)


RMS

ofc 1

(t)

(m)







Roadlevel



1 1020

30

40

50

60

Gai

n of

spru

ng m

ass a

cc (

dB)

Passive[08 02][06 04]

[04 06][02 08]

Frequency (Hz)

wacc increase


control weights



1 1070

80

90

100

110

120

Frequency (Hz)

Gai

n of

tire

forc

e (dB

)


Passive[08 02][06 04]

[04 06][02 08]


ent control weights






8 Conclusion










References

















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 20 40 60 80 100

000

002

004

006


level B

Am

plitu

de (m

)

Time (s)

minus006

minus004

minus002




APE =1119875

119875

sum

119894=1

|119879 (119894) minus 119874 (119894)|

|119879 (119894)|

times 100 (29)







level B

0 20 40 60 80 1000000

0001

0002

0003

0004

0005


Time (s)


RMS

ofc 1

(t)

(m)







Roadlevel



1 1020

30

40

50

60

Gai

n of

spru

ng m

ass a

cc (

dB)

Passive[08 02][06 04]

[04 06][02 08]

Frequency (Hz)

wacc increase


control weights



1 1070

80

90

100

110

120

Frequency (Hz)

Gai

n of

tire

forc

e (dB

)


Passive[08 02][06 04]

[04 06][02 08]


ent control weights






8 Conclusion










References

















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Roadlevel



1 1020

30

40

50

60

Gai

n of

spru

ng m

ass a

cc (

dB)

Passive[08 02][06 04]

[04 06][02 08]

Frequency (Hz)

wacc increase


control weights



1 1070

80

90

100

110

120

Frequency (Hz)

Gai

n of

tire

forc

e (dB

)


Passive[08 02][06 04]

[04 06][02 08]


ent control weights






8 Conclusion










References

















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











8 Conclusion










References

















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Research Article Adaptive Hybrid Control of Vehicle