Research Article Energy Conservation Analysis and …downloads.hindawi.com/journals/sv/2016/6196542.pdf · Semiactive Suspension with Three Regulating ... e linear motor is considered

Research ArticleEnergy Conservation Analysis and Control of Hybrid ActiveSemiactive Suspension with Three Regulating Damping Levels

Long Chen1 Dehua Shi1 Ruochen Wang1 and Huawei Zhou2

1School of Automotive and Traffic Engineering Jiangsu University Zhenjiang 212013 China2School of Electrical and Information Jiangsu University Zhenjiang 212013 China

Correspondence should be addressed to Long Chen chenlongujseducn

Received 3 June 2015 Revised 13 September 2015 Accepted 4 October 2015

Academic Editor Edoardo Sabbioni

Copyright copy 2016 Long Chen 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

Active suspension has not been popularized for high energy consumption To address this issue this paper introduces the conceptof a new kind of suspension The linear motor is considered to be integrated into an adjustable shock absorber to form the hybridactive semiactive suspension (HASAS) To realize the superiority of HASAS its energy consumption and regenerationmechanismsare revealed And the system controller which is composed of linear quadratic regulator (LQR) controller mode decision and switchcontroller and the slidingmode control based thrust controller is developed LQR controller is designed tomaintain the suspensioncontrol objectives while mode decision and switch controller decides the optimal damping level to tune motor thrust The thrustcontroller ensures motor thrust tracking An adjustable shock absorber with three regulating levels to be used in HASAS is trialproduced and tested to obtain its working characteristics Finally simulation analysis is made with the experimental three dampingcharacteristicsThe impacts of adjustable damping on the motor force and energy consumption are investigated Simulation resultsdemonstrate the advantages of HASAS in energy conservation with various suspension control objectives Even self-powered activecontrol and energy regenerated to the power source can be realized

1 Introduction

Active suspension can coordinate the trade-off between ridecomfort and handling performance according to the controltargets and improve suspension dynamic performance sig-nificantly Compared with hydraulic and pneumatic actua-tors electromagnetic actuators have smaller response timeand wider effective bandwidth Therefore electromagneticactuators attract more attention in the recent years [1ndash3]However shortcomings of active suspension in high energyconsumption high cost and poor reliability in emergenciesprevent it from being widely used and commercialized [4]To address this urgent issue on one hand energy-harvestingtechniques are combined with active suspension to reducethe energy consumption on the other hand the concept ofhybrid active-passive suspension (HAPS) is proposed [5ndash7]

As for energy harvesting techniques both new energyregenerative structures and control theories have been dis-seminated in references Suda et al adopted two linear DC

motors to realize active control and energy regeneration Oneof the DC motors acts as an energy regenerative damper toharvest vibration energy while another one was used as anactuator to realize active control with the reclaimed energy[8] In 2003 Nakanoa et al further presented a method toevaluate the balance between suspension regenerated andconsumed energy The possibility to suppress the suspensionvibration with regenerated energy by using a single electricactuator was investigated And the practical system wasalso proposed [9] Zhang et al designed active and energyregenerative controllers to maintain ride comfort and energyregeneration respectivelyThe results indicated that althoughride comfort was not as good as that under active controlenergy regeneration into the battery was obtained [10] Zuoet al proposed different kinds of electromagnetic dampersmost of them acted as passive dampers to recuperatevibration energy Therefore these energy-harvesting shockabsorbers are weak in the improvement of the suspensiondynamic performance [11ndash13]

Hindawi Publishing CorporationShock and VibrationVolume 2016 Article ID 6196542 14 pageshttpdxdoiorg10115520166196542

2 Shock and Vibration

HAPS is a combination of active actuator and passivedamper (hydraulic or electromagnetic) Such new mecha-nism justifies less energy consumption and lower cost butthe same performance compared with the active suspensionMeanwhile the passive unit still provides passive dampingforce in case of emergencies In 2006 Hitachi exhibitedan electromagnetic suspension that consists of a hydraulicdamper and a tubular linear motor which acts as an actuatorTherefore it has advantages in response time and ridecomfort [14] Ebrahimi et al designed two configurations forthe hybrid damper mechanism One of the configurationsis designed based on the eddy current losses phenomenonwhile another one is integrated with a monotube shockabsorber and the oil damping provides the essential passivedamping The controllable force of both of these two config-urations is provided by electromagnetic unit [15 16] Martinset al proved superiority of such suspension in reducingenergy consumption and retaining the active suspensionperformance based on a two-DOF vehicle suspension model[17] And the impact of passive damping value on suspensionperformance and power consumption was analyzed throughsimulation [18]

However the damping of passive unit is certain Once therequired force of HAPS is decided the actuator active forceis also determined Therefore although HAPS allows themotor with lower rated capacity and maintains fail safety theactuator operating points are uniquely decided by the passivedamping with certain control target (certain suspensionforce) and reduction in energy consumption is limitedWhatis more ride comfort and road holding performance are hardto be balanced Better ride comfort often requires a relativelow damping If the passive damping is high the actuatorneeds to operate in motor mode to lower the damping Andif the passive damping is too low it is also hard to ensurefail safety and HAPS fails to reduce energy consumptiondistinctly Due to its various damping values it is viable foradjustable shock absorber to be used in active suspension toregulate the actuator force for the purpose of lower energyconsumption and higher energy regeneration

Although adjustable shock absorber varies in principlesand structures they can be classified into two main differentcategories One of the categories is that the viscosity ofthe medium can be adjusted while the other kind is thatwith adjustable orifices to change the oil throttling area[19 20] There is no doubt that a continuous adjustableshock absorber can tune the actuator force in a wide rangeHowever it will increase the demand for the system oncontroller development to harmonize shock absorber andactuator Limited several basing damping levels may be abetter choice For that the shock absorber with adjustableorifices has superiority in simple structure low cost andsafety the adjustable shock absorber with three dampingstates is introduced in HASAS [21] Besides considering thatthe linear electromagnetic actuator has now been priorityselection in the vehicle suspension system for fast responsecompact structure and linear motion without motion trans-formation mechanism this paper integrates linear motorinto the adjustable shock absorber paralleled with a coilspring and proposes the concept of HASAS with three

regulating damping levels Such suspension system is rarelyreported in the existing literatures A mode decision andswitch controller is further developed to decide optimaldamping level of adjustable shock absorber Considering thatforce tracking of the linear motor has a great influence onthe suspension vibration isolation and energy regenerationperformance while in many literatures the actuator dynamicsand influence of actuator servo-loop on the system controlperformance are often ignored the sliding mode controlbased thrust controller is designed tomaintain force trackingThe LQR controller as the outermost loop is employed toweigh ride comfort and handling performance

Specifically the rest of the paper is divided as followsIn Section 2 the concept and working principle of HASASis given Energy consumption principle of linear motor isalso presented Section 3 designs the system controller todecide the damping level and realize motor thrust trackingThe characteristic test of an adjustable shock absorber to befurther used is conducted in Section 4 to obtain the threedamping characteristics In Section 5 simulation analysis andsystematic comparisons aremade to highlight effectiveness ofHASAS At last Section 6 concludes the paper

2 Dynamic Model of HASAS

21 Overview of the Actuator The concept of the actuatorused in HASAS is depicted in Figure 1 The structure isobtained by integrating the linear motor into an adjustableshock absorber which is similar to the electromagnetic sys-tem in [14] except that the dual-tube oil damper is replacedby an adjustable shock absorber with three regulating levelsPermanent magnet is fixed to the tube of shock absorberwhilemotorwindings are linked to the piston rod In this waypermanent and shock absorber tube are fixed to unsprungmass while wingding and piston rod are connected tosprung mass The relative motion between sprung mass andunsprungmass can be damped by linearmotor and adjustableshock absorber

Both the piston rod and the valve of the adjustable shockabsorber are provided with orifices in the radial direction Aconnecting rod driven by step motor is placed inside the pis-ton rod to regulate the valversquos orificeTherefore the throttlingarea of the orifices between the piston rod and the valve isregulated by the stepmotorThere are three damping states ofthe adjustable shock absorber Different damping states (softmedium and stiff) correspond to different flowing areasWhen adjustable shock absorber operates in stiff state oiljust flows through holes in the piston which is the same asthe traditional oil shock absorber However when adjustableshock absorber operates in soft or medium state another oilflowing path through the orifices of the piston rod and thevalve is added besides the channel in the piston to decreaseoil damping And the throttling areas of orifices are differentwhen adjustable shock absorber operates in soft or mediumstate

22 Model of HASAS A quarter car model is applied toevaluate the dynamic performance and energy conservation

Shock and Vibration 3

Permanent magnet

Motor windingConnectingrod

Adjustable shock absorberPiston rod

Piston rod Valve

Figure 1 Schematic view of the proposed actuator in HASAS

zs

zt

zr

ms

mt

ks

kt

cs f

U

Figure 2 Quarter car model of the proposed active suspension

of HASAS as shown in Figure 2 The actuator force can beequivalent to the sum of adjustable damping forceand motorthrust 119891 Sprung mass and unsprung mass are denoted by119898119904and 119898

119905 respectively The symbols 119896

119904and 119896

119905represent the

suspension stiffness and tire stiffness respectively Adjustabledamping of the shock absorber is marked by 119888

119904 119911119904and 119911119905are

vertical displacements of sprung mass and unsprung massrespectively while 119911

119903stands for the road displacement

From the quarter car model of the proposed activesuspension the dynamic equations of the proposed systemare depicted as follows

119898119904119904= 119896119904(119911119905minus 119911119904) + 119880

119898119905119905= minus119896119904(119911119905minus 119911119904) minus 119896119905(119911119905minus 119911119903) minus 119880

(1)

where 119880 = 119888119904(119905minus 119904) + 119891

LQR controller is used to weigh suspension controltargets and find relevant optimal force119880ref [22]The criterionfunction is set as

119869

= lim119879rarrinfin

1

119879int119879

0

[11990212119904+ 1199022(119911119904minus 119911119905)2

+ 1199023(119911119905minus 119911119903)2

] 119889119905(2)

where 1199021 1199022 and 119902

3are weighting coefficients of sprungmass

acceleration suspension and tire deflection respectively

To design the LQR controller the system dynamic differ-ential equation is transformed into the state-space equation

X = AX + BU + F120596

Y = CX +DU(3)

The state vector and output vector are chosen as

X = [119911119904119911119905119904119905119911119903]119879

Y = [119904119911119904minus 119911119905119911119905minus 119911119903119896119905(119911119905minus 119911119903)]119879

(4)

Then the suspension optimal feedback control force is

U = minusKX = Rminus1B119879PX (5)

where P can be derived from Riccati equation by

A119879P + PA minus PBRminus1B119879P +Q = 0 (6)

where Q = C119879qC R = D119879qD N = C119879QD q = diag(119902119894)

(119894 = 1 2 3)The input model of the road surface is simulated by

filtered white noise as

119903= minus2120587119891

0119911119903+ 2120587119899

0radic119866119902(1198990) 119906120596 (7)

where120596 is thewhiteGaussian noise of random road inputs1198910

denotes the lower cut-off frequency which equals 00628Hz1198990is the reference spatial frequency and is recorded as

01mminus1 119906 represents the vehicle velocity and 119866119902(1198990) is road

roughness coefficient

23 Energy Consumption of Linear Motor The equivalentcircuit of motor is modeled as in Figure 3 In the figure 119864

119886

is the induced voltage of linear motor119872 and 119871 and 119877 are themotor inductance and resistance respectively The motor isconnected to the power source with the variable voltage 119864The circuit equation is

119864 = 119871119889119894

119889119905+ 119894119877 + 119864

119886 (8)

Under random road excitation the induced voltage 119864119886is

given by

119864119886= 119870119864V (9)


M

R

L

E

i

Ea

Figure 3 Equivalent circuit model of linear motor

where 119870119864is the back electromotive voltage (EMF) constant

and V is the motor working velocity Usually the motorinductance 119871 can be neglected and the motor windingcurrent 119894 and thrust 119891 are defined by

119894 =119864 minus 119864

119886

119877

119891 = 119870119868119894

(10)

where119870119868is thrust constant

Assuming that the desired actuator force is 119880ref thenrequired thrust 119891ref of the linear motor is given by

119891ref = 119880ref minus 119888119904 (119905 minus 119904) (11)

Hence to obtain the desired motor force 119891ref requiredvoltage 119864ref of the power source is obtained by

119864ref =119891ref119877

119870119868

+ 119870119864V (12)

And electrical power 119875ele supplied by the power source isderived as

119875ele = (119891ref119870119868

)2

119877 +119870119864V

119870119868

119891ref (13)

Besides the mechanical power of the linear motor is

119875mec = 119891refV (14)

When 119875ele lt 0 part of vibration mechanical energyis converted into electrical energy and delivered to thepower source It is defined that linear motor operates inldquoregeneration moderdquo While 119875ele gt 0 if 119875mec gt 0 thelinear motor works as a motor and it consumes electricalenergy from the power source to acquire the desired thrust If119875mec lt 0 and 119875ele gt 0 the energy that is both regenerated bythe motor and accepted from the power source is dissipatedas heat in the motor resistance And the linear motor stillconsumes electrical energy from the power source although itoperates as a generator in this case Therefore when 119875ele gt 0the linearmotor can be defined by operating in ldquoconsumptionmoderdquo

If there is no power source to power the motor thelinear motor just operates as a generator to provide theelectromagnetic damping force When the motor windings

Table 1 Comparison between motor thrust and damping force

Velocity 119891ref Relations between 119891ref and 119891ed 119875ele Mode

V gt 0119891ref gt 0 mdash 119875ele gt 0 Con

119891ref lt 0119891ref lt 119891ed 119875ele gt 0 Con119891ref gt 119891ed 119875ele lt 0 Reg

V lt 0119891ref lt 0 mdash 119875ele gt 0 Con

119891ref gt 0119891ref gt 119891ed 119875ele gt 0 Con119891ref lt 119891ed 119875ele lt 0 Reg

are directly short circuited the motor is equivalent to apassive electromagnetic damper depicted by

119891ed = minus119870119868119870119864V

119877 (15)

where 119891ed is the electromagnetic damping force when themotor windings are directly short circuited that is thecircuit resistance is 119877 Furthermore the following equationis obtained

119875ele =119891ref119877

1198702119868

(119891ref minus 119891ed) (16)

From (16) it is convenient to analyze the energy con-sumption situation 119875ele and the motor operation mode bycomparing 119891ref and 119891ed as shown in Table 1 It can beconcluded that 119875ele gt 0 when |119891ref | gt |119891ed| or 119891ref sdot119891ed lt 0 Under this circumstance the linear motor needsto consume energy from the power source However while|119891ref | lt |119891ed| and 119891ref sdot 119891ed gt 0 119875ele lt 0 and thelinear motor just operates as a generator could produceenough damping force to isolate the suspension vibrationinstead of consuming electrical energy which is beneficial forreducing the system consumption Therefore by regulatingthe damping of adjustable shock absorber the linear motoroperation thrust is better to be tuned to satisfy |119891ref | lt |119891ed|and 119891ref sdot 119891ed gt 0 for the purpose of avoiding high energyconsumption and even realize energy recovery

3 System Controller Scheme

The adjustable shock absorber can be regulated among threedamping levels soft medium and stiff while the linearmotor can operate as a motor or generator to realize thetransformation between electrical energy and mechanicalenergy The block scheme of HASAS system is depicted inFigure 4 In the figure road displacement 119911

119903 motor actual

thrust 119891119898act and damping value 119888

119904119898(where 119898 = 119886 119887 or

119888 represent soft medium and stiff damping resp) are thequarter car model control inputsThe controller is composedof the damping mode decision and switch controller theinnermost loop thrust controller and the outermost loopLQR controller which calculate the ideal control force 119880refwith the system measurable full state Based on the dampingswitch rules of the mode decision and switch controller thereference linear motor force 119891ref and the desired dampinglevel 119888

119904119898are decided The innermost thrust controller which

is based on sliding mode control contributes to the reference


Mode decision

and switch

controllerThrust

controller

LQR controller

Quarter car model

Road input

Controller

csm

fmref

Uref

fmact

[zs zt zs zt zr]T

zr

Figure 4 Block scheme of HASAS system

Table 2 Description of the active suspension operation states

Operation state ofactive suspension Damping level Mode of linear motor

i Soft Regii Soft Coniii Medium Regiv Medium Conv Stiff Regvi Stiff Con

force tracking (current tracking of linear motor) of the linearmotor

31 Mode Decision and Switch In each damping state of theadjustable shock absorber the linear motor can operate inldquoregeneration moderdquo or ldquoconsumption moderdquo if ignoring thesituation 119875ele119898 = 0 Hence the active suspension with threeregulating damping levels totally owes 6 kinds of operationstates as listed in Table 2 At anymoment only one operationstate is activated

311 Mode Decision Rules As mentioned previously theelectrical power 119875ele supplied by the power source is usedto evaluate the system energy consumption Therefore theinstantaneous electrical power 119875ele under different dampinglevels is selected as the distinguishing basis for the modedecision and switch controller And the following basic switchrules are designed

(1) Preferably the linear motor should be controlled tooperate in ldquoregeneration moderdquo that is the damping

Table 3 Relations between119873 and the motor mode under differentdamping levels

Damping level Operation mode of linear motorSoft Reg Reg Reg Reg Con Con Con ConMedium Reg Reg Con Con Con Reg Reg ConStiff Reg Con Con Reg Reg Reg Con Con119873 0 4 6 2 3 1 5 7

coefficient 119888119904119898

that ensures the linear motor to meet119875ele119898 lt 0 is preferred

(2) If the motor instantaneous power consumption119875ele119898 gt 0 under all of the three damping levels it indi-cates that the motor always operates in ldquoconsumptionmoderdquo with all the damping levels In this case thedamping coefficient 119888

119904119898which meets min(119875ele1198982) is

preferred to ensure least energy consumption(3) If the motor instantaneous power consumption

119875ele119898 lt 0 under all of the three damping levelsthe motor always operates in ldquoregeneration moderdquoto transform part of mechanical energy into elec-trical energy Therefore to recycle more vibrationenergy the damping coefficient 119888

119904119898which meets

max(119875ele1198982) is preferred

312 Mode Selection Algorithm According to the optimalcontrol force 119880ref the adjustable shock absorber and thelinear motor harmonized to produce the required forceThe motor operation mode varies with the adjustable shockabsorber damping level And it is detailed in Table 3 Once thedamping of the adjustable shock absorber is confirmed thecertainmotor thrust is also determined so is the correspond-ing energy consumption of the motor When the adjustable


Sliding mode control

Equivalent circuit model

fmref

imref

fmact

KE

KI

minus

minus+ +e

1KI

Figure 5 Control scheme of linear motor

Table 4 Relations between 119873 and the motor optimal powerconsumption

119873 Motor power consumption Damping level0 max(119875ele1198982) (119898 = 119886 119887 119888) Soft or stiff1 max(119875ele1198982) (119898 = 119887 119888) Medium or stiff2 max(119875ele1198982) (119898 = 119886 119888) Soft or stiff3 119875

119888Stiff

4 max(119875ele1198982) (119898 = 119886 119887) Soft or medium5 119875

119887Medium

6 119875119886

Soft7 min(119875ele1198982) (119898 = 119886 119887 119888) Soft or stiff

shock absorber operates in soft medium and stiff state thelinear motor operation mode is recorded as119872

119886119872119887 and119872

119888

respectively119872119886119872119887 and119872

119888are defined as

119872119898=

0 Regeneration (Reg)

1 Comsumption (Con) (119898 = 119886 119887 119888) (17)

The state selection function of the proposed active sus-pension is expressed as

119873 = 119872119886+ 2119872119887+ 4119872119888 (18)

In combination with the mode decision rules the rela-tions between the state selection value 119873 and the motoroptimal power consumption are summarized in Table 4Based on this table the damping level that ensures best motoroperation state can be derived

32 Thrust Controller Since the damping of the adjustableshock absorber with regulating orifices can be easily realizedby controlling the pulse signals of the stepmotor the dampingcharacteristics of different damping levels are directly used inthe simulation assuming that they can be accurately achieved[23] And the tracking to the reference thrust is obtainedby controlling the motor current through the motor currentloopThe thrust controller is designed based on sliding modecontrol of the current loop and circuit model of linear motoras shown in Figure 5 Proportional-integral (PI) controller isusually used to tune the controllable power source voltage119864 to realize the current tracking [24 25] However thereis a wide variation of motor circuit parameters when themotor operates in different states Both changing of systemparameters and external disturbance will have a negativeinfluence on the system control Certain PI control gains can-not ensure good dynamic performance of the force trackingThe nonlinear sliding mode control has an advantage over PI

control for its strong robustness with parameter perturbationand external disturbance And slidingmode control is appliedto obtain the required power supply 119864 [26 27]

When the motor suffers parameters perturbation theequivalent circuit model is described as

119864 = (119871 + Δ119871)119889119894

119889119905+ 119894 (119877 + Δ119877) + 119870

119864(V + ΔV) (19)

where Δ119871 and Δ119877 denote the parameters perturbation ofmotor characteristic parameters andΔV denotes the variationof motor velocity (ie suspension relative velocity state)caused by the perturbation The general perturbation 119864

119903is

further defined as

119864119903= Δ119871

119889119894

119889119905+ 119894Δ119877 + 119870

119864ΔV (20)

Assuming that the current error 119890 between 119894ref and 119894 is thesystem state variable and the control input is 119864 then the errorequation of the current loop is given by

119890 = minus119886119903119890 minus 119887119903119906 + 119888119903 (21)

where 119886119903= 119877119871 119887

119903= 1119871 119888

119903= (119870119864V+119877119894ref +119864119903)119871 and 119906 = 119864

is the control inputTo ensure the sliding modality during the control process

and eliminate the system steady-state error the sliding modecontrol with integral forms is designed and the sliding line is

119904 = 119890 + 119888119894119898int119905

0

119890 (120591) 119889120591 (22)

119888119894119898

is the integral coefficient To ensure that the slidingmotion moves towards zero 119888

119894119898is greater than 0 For the

sliding mode control both the improvement of reachingmotion to the sliding modality region and the reduction ofsystembuffeting should be realized Exponential reaching lawof sliding mode control is a good choice to address this issueAnd the reaching law is written as

119904 = minus120576 sgn (119904) minus 120578119904 (23)

where 120576 is the switching gain and 120578 is the exponentialcoefficient

According to (21)sim(22) 119906eq is derived as (in this case 119864119903

is assumed to be 0)

119906 = (119871119888119894119898minus 119877) 119890 + 119877119894ref + 119870119864V + 120576 sgn (119904) + 120578119904 (24)

To guarantee the existence and accessibility condition ofslidingmode control the chosen Lyapunov function based onLyapunov stability theory should meet

= 119904 119904 lt 0 (25)

According to (19)sim(24) (25) is derived as

= 119904 119904 = 119904 [minus120576 sgn (119904) minus 120578119904 + 119864119903]

le minus |119904| (120576 minus10038161003816100381610038161198641199031003816100381610038161003816) minus 120578119904

2(26)

Therefore when 120576 gt |119864119903| and 120578 gt 0 the existence and

accessibility condition can be realized and the control systemis stable


Figure 6 Components of the adjustable shock absorber andexperimental setup

minus08 minus06 minus04 -02 0 02 04 06 08minus1

minus05

0

05

1

15

Velocity (ms)

SoftMediumStiff

Dam

ping

forc

e (kN

)

Figure 7 Characteristics of adjustable shock absorber on differentdamping state

4 Characteristic Experiments of theAdjustable Shock Absorber

Theprototype of adjustable shock absorber to be used is firstlytrial produced and tested to obtain its characteristic param-eters The characteristics of the adjustable shock absorberare tested in a hydraulic servo vibration testing machine asshown in Figure 6 The initial position of the shock absorberis set as equilibrium position Inputs of the excitation are50mm sinusoidal signals with five different frequencies 0510 15 20 and 25Hz

Figure 7 describes the force-velocity relationships indifferent states Apparently three different kinds of force-velocity relationships are obtained by regulating the throttlingarea For further simulation analysis the model of adjustableshock absorber is built based on the bench test data of thethree force-velocity relationships By looking up the 2D tableand establishing the interpolation algorithm the damping

Table 5 Parameter of model

Description Symbol ValueSprung mass 119898

119904320 kg

Unsprung mass 119898119905

37 kgSuspension stiffness coefficient 119896

11990416 kNm

Tire stiffness coefficient 119896119905

159 kNmThrust constant 119870

119868657NA

Back EMF constant 119870119864

535 V(ms)Internal resistance 119877 42ΩPole pitch 120591 712mmInductance 119871 52mH

Table 6 Weightings for different control targets

Targets 1199021

1199022

1199023

Handling 092 65080 9 times 105

Trade-off 1 4800 38 times 104

Ride comfort 487 4842 30150

force of adjustable shock absorber with different velocities iscalculated

5 Simulation Analysis

In order to validate the effect of the controller and superiorityof HASAS in energy conservationMATLABSimulink basedsimulation model with the designed controller is built Bothrandom road and bump road are adopted to reveal theresponses of the proposed system Simulation results of thesuspensionrsquos three evaluation indexes are compared with apassive counterpart whose passive damping coefficient is13 kNsdotsm Simulation parameters are listed in Table 5

51 Random Road Input

511 Suspension Dynamic Performance Ride comfort androad holding performance (handling performance) are twocritical evaluation indexes of the suspension that are hardto be compromised Usually improvement of one criterionleads to the deterioration of the other As a consequence threecontrol targets are chosen to judge the HASAS performancehandling ride comfort and trade-off respectively Handlingand ride comfort are intended for the reduction of tiredynamic load and sprung mass acceleration respectivelywhile trade-off objective is a compromise between comfortand handling The principle of trade-off is to improve ridecomfort with an acceptable handling performance The threecontrol targets are realized by adjusting 119902

1 1199022 and 119902

3of LQR

controller as listed in Table 6The actual responses of HASAS are compared to the

reference responses under LQR control to validate the effec-tiveness of the designed thrust controller The random roadinput is acquired by assuming that the vehicle is driven onC-class road (roughness coefficient is 256 times 10minus6m3) at thespeed of 20ms The three damping characteristics obtainedfrom bench test are used in the simulation analysis Figure 8


0 05 1 15 2minus4

minus2

0

2

4

Time (s)

ReferenceActual

Acce

lera

tion

(ms2)

(a) Sprung mass acceleration

0 05 1 15 2minus3000

minus2000

minus1000

0

1000

2000

3000

Time (s)

ReferenceActual

Tire

dyn

amic

load

(N)

(b) Tire dynamic load

Figure 8 Actual responses comparing to the reference responses

Table 7 RMS values of hybrid suspension for the three objectives

Suspension Objective Attribute 119886rms(ms2) SWSrmsm DTLrmsNPassive mdash 1660 00174 9037

Hybrid active semiactive

HandlingReference 2300 00108 6902Actual 2295 00108 6993mdash 3825 minus3793 minus2262

Trade-offReference 1309 00140 9575Actual 1317 00140 9587mdash minus2114 minus1954 609

Ride comfortReference 0883 00178 13384Actual 0899 00177 13227mdash minus4584 172 4636

gives the sprung mass acceleration and tire dynamic loadtracking to the reference responses while Figure 9 showstime responses of sprung mass acceleration and tire dynamicload between HASAS and passive suspension for the threedifferent control targets Table 7 describes RMS values ofthe suspensionrsquos three evaluation indexes including RMScomparisons between actual responses and reference oneswhere 119886rms SWSrms and DTLrms represent sprung massacceleration suspension deflection and tire dynamic loadrespectively It can be seen from Figure 8 and Table 7 that theproposed HASAS with designed thrust control can track thereference responses well As a result the slidingmode controlbased thrust controller is effective in HASAS to guaranteemotor thrust tracking Combining Figure 9 and Table 7 itindicates that when handling is emphasized obvious 3793and 2262 reductions of suspension deflection and tiredynamic load are achieved When ride comfort is as controltarget the visible 4584 reduction of sprung mass accelera-tion is obtained at the sacrifice of tire dynamic load which isincreased by 4636 For trade-off objective the attenuationdegree of sprungmass acceleration and suspension deflectionin HASAS are as much as 2114 and 1954 respectivelyAlthough tire dynamic load is inferior to that of the passiveone the 609 deterioration of handling is much smaller

than the improvement in ride comfort It is within acceptablerange

512 Energy Conservation Performance To highlight thesuperiority of HASAS in energy conservation and less depen-dence on motor rated capacity the results are analyzed bycomparing the linear motor thrust and energy consumptionfor five cases ulteriorly In Case A the active suspension isadopted and suspension force 119880 is provided by the linearmotor alone Cases B C and D denote the situation when theadjustable shock absorber is in stiff medium and soft staterespectively (also considered as HAPS with different passivedamping) And Case E indicates the situation that HASAS isused with mode and switch controller

In Figure 10 motor force of Cases A and E for trade-offobjective is shownThe required peak force in Cases A and Eis 1447N and 618N while the required RMS motor force is4252N and 1576N respectively Furthermore motor thrustRMS values of the five cases for different control targets areshown in Figure 11With ride comfort as control target a largepassive damping (stiff state) corresponds to a large motorforce because for ride comfort the large damping needs tobe lowered by motor Conversely large passive damping is


5 52 54 56 58 6minus6

minus4

minus2

0

2

4

6

Times (s)

HandlingPassive

Trade-offComfort

Acce

lera

tion

(ms2)


HandlingPassive

Trade-offComfort

5 52 54 56 58 6minus3000

minus2000

minus1000

0

1000

2000

3000

Times (s)

Tire

dyn

amic

load

(N)


Figure 9 Actual responses of the proposed suspension comparing to passive suspension

0 05 1 15 2 25 3minus1500

minus1000

minus500

0

500

1000

1500

Time (s)

Case ACase E

Mot

or th

rust

(N)

Figure 10 Thrust of the linear motor

Handling Tradeoff Ride comfort0

200

400

600

800

Case ACase BCase C

Case DCase E

RMS

valu

e of m

otor

forc

e (N

)

Figure 11 RMS value of motor thrust

necessary tomitigate themotor force for handling Comparedwith the active suspension the hybrid suspension with largedamping is superior in reducing the motor force for handingwhile small damping is superior in the motor force reductionfor ride comfort objective It is obvious that a relative highperformance of linear motor in terms of rated thrust isrequired to meet the various control targets with a certainpassive damping when HAPS is employed However thereis no exception that HASAS system requires minimum RMSmotor force for all of the three control targets Thereforedemand for motor rated thrust in HASAS system is reducedapparently for different control targets which means thatlower cost and smaller lighter motors are allowed

Suppose that the total electrical energy consumption ofthe simulation time history (119905sim) is 119882tot which is obtainedby

119882tot = int119905sim

0

119875ele119889119905 (27)

Let the simulation time be 30 s then energy consumptionof linear motor for the three different control targets is shownin Figure 12 It can be seen that active suspension shows lessenergy consumption for ride comfort (only 7481 J) and trade-off (1537 J) while a great amount of energy consumptionfor handling (as much as 107 times 104 J) As for Cases BsimDsmall damping (Case D) causes less energy consumptionfor ride comfort and trade-off (4982 J for comfort and only1284 J for trade-off) while large damping (Case B) leadsto much more energy consumption (286 times 104 J for ridecomfort and 5641 J for trade-off) because linear motor needsto consume more electrical energy to lower the suspensiondamping For handling large damping corresponds to 6154 Jenergy consumption while that of small damping is 6972 JAlthough energy consumption of HASAS for ride comfortis more than that of active suspension the advantages ofHASAS in energy conservation for trade-off and handling areobvious especially for trade-off and the energy consumptionis minus1491 J which means that self-powered active control is


Handling Tradeoff Ride comfortminus5000

0

5000

10000

15000

20000

25000

30000

Case ACase BCase C

Case DCase E

Wele

(J)

Figure 12 Energy consumption of linear motor

realized Therefore HASAS is a good choice in terms ofenergy conservation and motor thrust reduction throughcomprehensive comparisons To further improve the energyconservation performance the adjustable range of dampingvalves can be expanded It can be inferred that smaller damp-ing value allows better energy conservation performance ofHASAS for ride comfort

To better understand energy consumption of linearmotor comparisons between the electrical power consump-tion119875ele and themotormechanical power119875mec are conductedin Cases A B and E for trade-off objective for their typicalfeatures as shown in Figure 13 In Case B it is apparentthat the motor chiefly acts as a motor (119875mec gt 0) toconsume electrical energy However in Case A although themotor mainly acts as a generator (119875mec lt 0) in the wholetime history it still consumes a large amount of electricalenergy (119875ele gt 0) The reason is that in Case A largemotor thrust leads to high wingding current thus both theregenerated energy from suspension vibration and energyacquired from the power source are dissipated by the motorinternal resistance as copper losses InCase EHASAS realizesenergy regeneration (119875ele lt 0) in many regions whichleads to the 1491 J energy regeneration Therefore althoughvibration isolation performance remains the same for thesecases part of the vibration energy is converted into electricalenergy by HASAS

Figure 14 shows the probability distribution of 119873 for thethree different objectives It is shown that the situation119873 = 0and 119873 = 2 cannot be achieved for all of the three differentcontrol objectives By combining the results in Table 1 thereasons for such phenomenon are visible For that 119873 = 2cannot be realized the main contradiction is between thesoft damping state and stiff one If the motor operates inregenerationmode under softdamping itmeans that |119891ref119886| lt|119891ed| and 119891ref119886 sdot 119891ed gt 0 (119891ref119886 denotes the reference motorthrust under soft damping) in soft damping state Then iflinear motor operates in energy consumption mode undermedium state it means that the oil damping force is too largeand linearmotor acts as amotor to provide an opposite thrust

to offset part of oil damping force that is 119891ref119887 sdot 119891ed lt 0occurs (119891ref119887 denotes the reference motor thrust in mediumstate) Therefore when adjustable shock absorber is in stiffstate linear motor should still operate in consumption modeto offset part of oil damping force instead of regeneratingenergy Vice versa if linear motor operates in regenerationmode under stiff damping and consumption mode undermediumdamping then it should still operate in consumptionmode in soft state With regard to 119873 = 0 which means thatthe linear motor operates in regeneration mode under all thethree damping levels this problemmay be solved by choosingthemotorwith larger back EMF coefficient thrust coefficientand lower internal resistance In this way the motor justoperates as a generator that can produce the required activeforce without consuming electrical energy from the powersource

52 Bump Road Input To evaluate the transient responsecharacteristics of HASAS with respect to discrete irregular-ities the road excitation is assumed as bump profile [28] andis described by

119911119903=

119860119898

2(1 minus cos(2120587119906

119871119905)) 0 le 119905 le

119871

119906

0 119905 le119871

119906

(28)

where 119860119898

is the height of the bump profile and 119871 is thebump width Here 119860

119898and 119871 are set to be 008m and 4m

respectively And the vehicle velocity 119906 is set to be 10msFigure 15 describes time responses of passive suspension

and HASAS for the three control targets with bump roadinput It can be seen that minimum sprung mass accelerationand tire dynamic load happen when ride comfort is stressedfollowed by the values with trade-off control target Forhandling sprung mass acceleration and tire dynamic loadare even larger than those of passive suspension The timeresponses of HASAS for different control targets on bumproad are different from those results on random road Thereason is that the frequency range of the bump input ismainly 0sim5Hz The response characteristics of HASAS inrelative low frequency regions under LQR control lead to theresults For sprung mass acceleration minimum value forride comfort (compared with trade-off handling and passivesuspension) and maximum value for handling happen nearall the frequency regions As for tire dynamic load ridecomfort control target maintains minimum value from 0Hzto 5Hz and maximum value from 8Hz to 12Hz whilehandling control targetmaintains opposite results (minimumvalue from 8Hz to 15Hz and maximum value from 2Hz to5Hz)

The results of motor thrust of the 5 cases for three dif-ferent control objectives are represented by Figure 16 Activesuspension (Case A) demands high motor force for all of thethree targets especially for handling Minimum peak valuesof motor thrust in HAPS (Cases BsimD) happen in Cases D Cand B for ride comfort trade-off and handling respectivelyIt is worth noting that the motor peak thrust of Case B forride comfort is even larger than that of active suspension


5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(a) Case A

5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(b) Case B

5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(c) Case E

Figure 13 Comparisons between 119875ele and 119875mec

76

224

1

15

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(a) Ride comfort

38

35

5

4

4

14

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(b) Trade-off

687

7

3

6

9

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(c) Handling

Figure 14 Probability of119873 for trade-off

which means that large passive damping has a bad effecton reducing the motor action force when ride comfort isstressed However large passive damping shows a muchsmaller peak thrust when handling is emphasized FromFigure 16 it is also apparent that motor thrust of HASAS

(Case E) follows along the thrust trajectories of Cases B Cand D in different time regions Such phenomenon denotesthat HASAS switches among different damping values toensure the superior performance in reducingmotor thrust fordifferent control targets


0 05 1 15 2minus6

minus4

minus2

0

2

4

6

Times (s)

HandlingPassive

TradeoffComfort

Acce

lera

tion

(ms2)


HandlingPassive

TradeoffComfort

0 05 1 15 2minus3000

minus2000

minus1000

0

1000

2000

3000

Times (s)

Tire

dyn

amic

load

(N)



0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Case ACase BCase C

Case DCase E

Mot

or th

rust

(N)

(a) Ride comfort

Case ACase BCase C

Case DCase E

0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Mot

or th

rust

(N)

(b) Trade-off

Case ACase BCase C

Case DCase E

0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Mot

or th

rust

(N)

(c) Handling

Figure 16 Motor thrust with different control targets



100

200

300

400

Case ACase BCase C

Case DCase E

Wele

(J)

Figure 17 Energy consumption of linear motor with bump road

With respect to the discrete bump input energy con-sumption of linear motor from Cases AsimE for the threecontrol targets is shown in Figure 17 It shows that less energyconsumption with small damping (Case D) and more energyconsumption with large damping (Case B) for ride comforthappen For handling large damping is a better choice toreduce energy consumption while small damping corre-sponds to large energy consumption Meanwhile energyconsumption of HASAS is least for all of the three controlobjectives with bump input The superiority of HASAS inenergy conservation is validated

6 Conclusions

This paper proposes the concept of HASAS by integrating theadjustable shock absorber with a linear motor By providingthree kinds of base damping force the adjustable shockabsorber can not only reduce demands on the linear motorrated capacity but also tune the motor operating points torealize energy conservation for various control targets andeven ensure energy regeneration Based on the energy flowprinciple between linear motor and the power source themode decision and switch controller is developed And thesystem controller is further designed to exert the superiorityof HASAS

Simulation results validate the effectiveness of the pro-posed suspension system under random road and bump roadinputs Compared to active suspension and HAPS the motorpeak and RMS thrust are reduced apparently while the samevibration isolation performance can be achieved Althoughenergy conservation of HASAS for ride comfort objectivecannot be achieved compared to the active suspension withrandom road excitation HASAS is superior for handingand trade-off objectives Energy conservation of HASAS issuitable for various control objectives Study on the impactof adjustable damping on motor power consumption ishelpful for the optimization of motor operation points toimprove energy regeneration performance By harmonizing

the adjustable shock absorber and linear motor self-poweredactive control is realized and even extra regenerative energystored into the power source can also be obtained More-over the energy conservation performance can be furtherimproved by expanding the range of adjustable damping

In our further study the real linear motor will beintegrated into the trial produced adjustable shock absorberThe real controller especially the thrust controller will bedeveloped to realize the motor active control on practicalbench test to testify HASAS and analyze energy consumptionof linear motor In fact since EV and HEV have their ownelectrical power source the usage of energy regenerativesuspension in new energy vehicles to coordinate the sus-pension dynamic performance (ride comfort handling) andenergy consumption performance of power source (energyconsumption and regeneration) is of great significance

Conflict of Interests

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

Acknowledgments

The authors would like to express their great gratitude for thesupport from the project funded by the Priority AcademicProgram Development of Jiangsu Higher Education Institu-tions (PAPD) the National Natural Science Foundation ofChina (Grant no 51407086) the Natural Science Foundationof Jiangsu Province (BK 2012714) Project funded by ChinaPostdoctoral Science Foundation (2014M551518) and theScientific Research Innovation Projects of Jiangsu Province(KYLX 1022)The authorswould also like to thank the editorsfor improving the readability of the paper

References

[1] B L J Gysen J L G Janssen J J H Paulides and E ALomonova ldquoDesign aspects of an active electromagnetic sus-pension system for automotive applicationsrdquo IEEE Transactionson Industry Applications vol 45 no 5 pp 1589ndash1597 2009

[2] S Lee and W-J Kim ldquoActive suspension control with direct-drive tubular linear brushless permanent-magnet motorrdquo IEEETransactions on Control Systems Technology vol 18 no 4 pp859ndash870 2010

[3] B L J Gysen J J H Paulides J L G Janssen and E ALomonova ldquoActive electromagnetic suspension system forimproved vehicle dynamicsrdquo IEEE Transactions on VehicularTechnology vol 59 no 3 pp 1156ndash1163 2010

[4] I Martins J Esteves G D Marques and F P da SilvaldquoPermanent-magnets linear actuators applicability in auto-mobile active suspensionsrdquo IEEE Transactions on VehicularTechnology vol 55 no 1 pp 86ndash94 2006

[5] Y Suda and T Shiiba ldquoA new hybrid suspension system withactive control and energy regenerationrdquoVehicle SystemDynam-ics vol 25 supplement 1 pp 641ndash654 1996

[6] K Nakano ldquoCombined type self-powered active vibration con-trol of truck cabinsrdquo Vehicle System Dynamics vol 41 no 6 pp449ndash473 2004


[7] W Hu and N M Wereley ldquoHybrid magnetorheological fluid-elastomeric lag dampers for helicopter stability augmentationrdquoSmart Materials and Structures vol 17 no 4 Article ID 0450212008

[8] Y Suda S Nakadai and K Nakano ldquoHybrid suspension systemwith skyhook control and energy regeneration (development ofself-powered active suspension)rdquoVehicle System Dynamics vol29 supplement 1 pp 619ndash634 1998

[9] K Nakanoa Y Suda and S Nakadai ldquoSelf-powered activevibration control using a single electric actuatorrdquo Journal ofSound and Vibration vol 260 no 2 pp 213ndash235 2003

[10] G Zhang J Cao and F Yu ldquoDesign of active and energy-regenerative controllers for DC-motor-based suspensionrdquoMechatronics vol 22 no 8 pp 1124ndash1134 2012

[11] L Zuo B Scully J Shestani and Y Zhou ldquoDesign and char-acterization of an electromagnetic energy harvester for vehiclesuspensionsrdquo Smart Materials and Structures vol 19 no 4Article ID 045003 2010

[12] Z Li L Zuo G Luhrs L Lin and Y-X Qin ldquoElectromagneticenergy-harvesting shock absorbers design modeling and roadtestsrdquo IEEE Transactions on Vehicular Technology vol 62 no 3pp 1065ndash1074 2013

[13] Z Li L Zuo J Kuang and G Luhrs ldquoEnergy-harvesting shockabsorber with a mechanical motion rectifierrdquo Smart Materialsand Structures vol 22 no 2 Article ID 025008 2013

[14] Y Akami H Chikuma S Ohsawa et al ldquoElectromagneticsuspension systemrdquo US Patent 7219781 2007

[15] B Ebrahimi M B Khamesee and F Golnaraghi ldquoDesignof a hybrid electromagnetichydraulic damper for automotivesuspension systemsrdquo in Proceedings of the IEEE InternationalConference on Mechatronics and Automation (ICMA rsquo09) pp3196ndash3200 Changchun China August 2009

[16] B Ebrahimi H Bolandhemmat M B Khamesee and F Gol-naraghi ldquoA hybrid electromagnetic shock absorber for activevehicle suspension systemsrdquo Vehicle System Dynamics vol 49no 1-2 pp 311ndash332 2011

[17] I Martins J Esteves F Pina da Silva and P Verdelho ldquoElectro-magnetic hybrid active-passive vehicle suspension systemrdquo inProceedings of the IEEE 49th Vehicular Technology Conferencevol 3 pp 2273ndash2277 Houston Tex USA July 1999

[18] B L J Gysen T P J van der Sande J J H Paulides and EA Lomonova ldquoEfficiency of a regenerative direct-drive elec-tromagnetic active suspensionrdquo IEEE Transactions on VehicularTechnology vol 60 no 4 pp 1384ndash1393 2011

[19] Q-H Nguyen and S-B Choi ldquoOptimal design of MR shockabsorber and application to vehicle suspensionrdquo Smart Mate-rials and Structures vol 18 no 3 Article ID 035012 2009

[20] H Chen C Long C-C Yuan and H-B Jiang ldquoNon-linearmodelling and control of semi-active suspensions with variabledampingrdquo Vehicle System Dynamics vol 51 no 10 pp 1568ndash1587 2013

[21] H-B Jiang Y-J Du and S-C Ye ldquoStroke-dependent stiffnesscharacteristics of a new type of integrated suspension strutrdquoJournal of Vibration and Shock vol 31 no 22 pp 66ndash70 2012

[22] X-M Dong M Yu C-R Liao and W-M Chen ldquoCompar-ative research on semi-active control strategies for magneto-rheological suspensionrdquo Nonlinear Dynamics vol 59 no 3 pp433ndash453 2010

[23] R CWangH B Jiang L Chen et al ldquoModelling and control ofsemi-active susppensionwith nonlinear dampingrdquoTransactionsof the Chinese Society for Agricultural Machinery vol 39 no 12pp 14ndash17 2008

[24] Y Kawamoto Y Suda H Inoue and T Kondo ldquoModeling ofelectromagnetic damper for automobile suspensionrdquo Journal ofSystem Design and Dynamics vol 1 no 3 pp 524ndash535 2007

[25] K Huang Y-C Zhang F Yu and Y-H Gu ldquoCoordinateoptimization for synthetical performance of electrical energy-regenerative active suspensionrdquo Journal of Shanghai JiaotongUniversity vol 43 no 2 pp 226ndash230 2009

[26] H Kim J Son and J Lee ldquoA high-speed sliding-mode observerfor the sensorless speed control of a PMSMrdquo IEEE Transactionson Industrial Electronics vol 58 no 9 pp 4069ndash4077 2011

[27] Y He and F L Luo ldquoSliding-mode control for dc-dc converterswith constant switching frequencyrdquo IEE Proceedings ControlTheory and Applications vol 153 no 1 pp 37ndash45 2006

[28] H Li J Yu C Hilton and H Liu ldquoAdaptive sliding-modecontrol for nonlinear active suspension vehicle systems using T-S fuzzy approachrdquo IEEE Transactions on Industrial Electronicsvol 60 no 8 pp 3328ndash3338 2013

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



HAPS is a combination of active actuator and passivedamper (hydraulic or electromagnetic) Such new mecha-nism justifies less energy consumption and lower cost butthe same performance compared with the active suspensionMeanwhile the passive unit still provides passive dampingforce in case of emergencies In 2006 Hitachi exhibitedan electromagnetic suspension that consists of a hydraulicdamper and a tubular linear motor which acts as an actuatorTherefore it has advantages in response time and ridecomfort [14] Ebrahimi et al designed two configurations forthe hybrid damper mechanism One of the configurationsis designed based on the eddy current losses phenomenonwhile another one is integrated with a monotube shockabsorber and the oil damping provides the essential passivedamping The controllable force of both of these two config-urations is provided by electromagnetic unit [15 16] Martinset al proved superiority of such suspension in reducingenergy consumption and retaining the active suspensionperformance based on a two-DOF vehicle suspension model[17] And the impact of passive damping value on suspensionperformance and power consumption was analyzed throughsimulation [18]

However the damping of passive unit is certain Once therequired force of HAPS is decided the actuator active forceis also determined Therefore although HAPS allows themotor with lower rated capacity and maintains fail safety theactuator operating points are uniquely decided by the passivedamping with certain control target (certain suspensionforce) and reduction in energy consumption is limitedWhatis more ride comfort and road holding performance are hardto be balanced Better ride comfort often requires a relativelow damping If the passive damping is high the actuatorneeds to operate in motor mode to lower the damping Andif the passive damping is too low it is also hard to ensurefail safety and HAPS fails to reduce energy consumptiondistinctly Due to its various damping values it is viable foradjustable shock absorber to be used in active suspension toregulate the actuator force for the purpose of lower energyconsumption and higher energy regeneration

Although adjustable shock absorber varies in principlesand structures they can be classified into two main differentcategories One of the categories is that the viscosity ofthe medium can be adjusted while the other kind is thatwith adjustable orifices to change the oil throttling area[19 20] There is no doubt that a continuous adjustableshock absorber can tune the actuator force in a wide rangeHowever it will increase the demand for the system oncontroller development to harmonize shock absorber andactuator Limited several basing damping levels may be abetter choice For that the shock absorber with adjustableorifices has superiority in simple structure low cost andsafety the adjustable shock absorber with three dampingstates is introduced in HASAS [21] Besides considering thatthe linear electromagnetic actuator has now been priorityselection in the vehicle suspension system for fast responsecompact structure and linear motion without motion trans-formation mechanism this paper integrates linear motorinto the adjustable shock absorber paralleled with a coilspring and proposes the concept of HASAS with three

regulating damping levels Such suspension system is rarelyreported in the existing literatures A mode decision andswitch controller is further developed to decide optimaldamping level of adjustable shock absorber Considering thatforce tracking of the linear motor has a great influence onthe suspension vibration isolation and energy regenerationperformance while in many literatures the actuator dynamicsand influence of actuator servo-loop on the system controlperformance are often ignored the sliding mode controlbased thrust controller is designed tomaintain force trackingThe LQR controller as the outermost loop is employed toweigh ride comfort and handling performance

Specifically the rest of the paper is divided as followsIn Section 2 the concept and working principle of HASASis given Energy consumption principle of linear motor isalso presented Section 3 designs the system controller todecide the damping level and realize motor thrust trackingThe characteristic test of an adjustable shock absorber to befurther used is conducted in Section 4 to obtain the threedamping characteristics In Section 5 simulation analysis andsystematic comparisons aremade to highlight effectiveness ofHASAS At last Section 6 concludes the paper

2 Dynamic Model of HASAS

21 Overview of the Actuator The concept of the actuatorused in HASAS is depicted in Figure 1 The structure isobtained by integrating the linear motor into an adjustableshock absorber which is similar to the electromagnetic sys-tem in [14] except that the dual-tube oil damper is replacedby an adjustable shock absorber with three regulating levelsPermanent magnet is fixed to the tube of shock absorberwhilemotorwindings are linked to the piston rod In this waypermanent and shock absorber tube are fixed to unsprungmass while wingding and piston rod are connected tosprung mass The relative motion between sprung mass andunsprungmass can be damped by linearmotor and adjustableshock absorber

Both the piston rod and the valve of the adjustable shockabsorber are provided with orifices in the radial direction Aconnecting rod driven by step motor is placed inside the pis-ton rod to regulate the valversquos orificeTherefore the throttlingarea of the orifices between the piston rod and the valve isregulated by the stepmotorThere are three damping states ofthe adjustable shock absorber Different damping states (softmedium and stiff) correspond to different flowing areasWhen adjustable shock absorber operates in stiff state oiljust flows through holes in the piston which is the same asthe traditional oil shock absorber However when adjustableshock absorber operates in soft or medium state another oilflowing path through the orifices of the piston rod and thevalve is added besides the channel in the piston to decreaseoil damping And the throttling areas of orifices are differentwhen adjustable shock absorber operates in soft or mediumstate

22 Model of HASAS A quarter car model is applied toevaluate the dynamic performance and energy conservation


Permanent magnet



Piston rod Valve


zs

zt

zr

ms

mt

ks

kt

cs f

U




119904and 119896

119905represent the


119904 119911119904and 119911119905are




119898119904119904= 119896119904(119911119905minus 119911119904) + 119880


(1)

where 119880 = 119888119904(119905minus 119904) + 119891


119869


1

119879int119879

0

[11990212119904+ 1199022(119911119904minus 119911119905)2

+ 1199023(119911119905minus 119911119903)2

] 119889119905(2)

where 1199021 1199022 and 119902




X = AX + BU + F120596

Y = CX +DU(3)


X = [119911119904119911119905119904119905119911119903]119879


(4)








119903= minus2120587119891

0119911119903+ 2120587119899

0radic119866119902(1198990) 119906120596 (7)






119886


119864 = 119871119889119894

119889119905+ 119894119877 + 119864

119886 (8)


given by

119864119886= 119870119864V (9)


M

R

L

E

i

Ea




119894 =119864 minus 119864

119886

119877

119891 = 119870119868119894

(10)





119864ref =119891ref119877

119870119868

+ 119870119864V (12)


119875ele = (119891ref119870119868

)2

119877 +119870119864V

119870119868

119891ref (13)


119875mec = 119891refV (14)










119891ed = minus119870119868119870119864V

119877 (15)


119875ele =119891ref119877

1198702119868

(119891ref minus 119891ed) (16)




119903 motor actual


119904119898(where 119898 = 119886 119887 or





Mode decision

and switch

controllerThrust

controller

LQR controller

Quarter car model

Road input

Controller

csm

fmref

Uref

fmact

[zs zt zs zt zr]T

zr











coefficient 119888119904119898












fmref

imref

fmact

KE

KI

minus

minus+ +e

1KI




119888Stiff


119887Medium

6 119875119886



119886119872119887 and119872

119888



119872119898=


1 Comsumption (Con) (119898 = 119886 119887 119888) (17)


119873 = 119872119886+ 2119872119887+ 4119872119888 (18)





119864 = (119871 + Δ119871)119889119894

119889119905+ 119894 (119877 + Δ119877) + 119870

119864(V + ΔV) (19)


119903is

further defined as

119864119903= Δ119871

119889119894

119889119905+ 119894Δ119877 + 119870

119864ΔV (20)


119890 = minus119886119903119890 minus 119887119903119906 + 119888119903 (21)

where 119886119903= 119877119871 119887

119903= 1119871 119888

119903= (119870119864V+119877119894ref +119864119903)119871 and 119906 = 119864



119904 = 119890 + 119888119894119898int119905

0

119890 (120591) 119889120591 (22)

119888119894119898




119904 = minus120576 sgn (119904) minus 120578119904 (23)



is assumed to be 0)

119906 = (119871119888119894119898minus 119877) 119890 + 119877119894ref + 119870119864V + 120576 sgn (119904) + 120578119904 (24)


= 119904 119904 lt 0 (25)


= 119904 119904 = 119904 [minus120576 sgn (119904) minus 120578119904 + 119864119903]


2(26)






minus05

0

05

1

15

Velocity (ms)

SoftMediumStiff

Dam

ping

forc

e (kN

)







119904320 kg



11990416 kNm



119868657NA




Targets 1199021

1199022

1199023









1 1199022 and 119902

3of LQR




0 05 1 15 2minus4

minus2

0

2

4

Time (s)

ReferenceActual

Acce

lera

tion

(ms2)


0 05 1 15 2minus3000

minus2000

minus1000

0

1000

2000

3000

Time (s)

ReferenceActual

Tire

dyn

amic

load

(N)














5 52 54 56 58 6minus6

minus4

minus2

0

2

4

6

Times (s)

HandlingPassive

Trade-offComfort

Acce

lera

tion

(ms2)


HandlingPassive

Trade-offComfort

5 52 54 56 58 6minus3000

minus2000

minus1000

0

1000

2000

3000

Times (s)

Tire

dyn

amic

load

(N)



0 05 1 15 2 25 3minus1500

minus1000

minus500

0

500

1000

1500

Time (s)

Case ACase E

Mot

or th

rust

(N)



200

400

600

800

Case ACase BCase C

Case DCase E

RMS

valu

e of m

otor

forc

e (N

)




119882tot = int119905sim

0

119875ele119889119905 (27)




0

5000

10000

15000

20000

25000

30000

Case ACase BCase C

Case DCase E

Wele

(J)







119911119903=

119860119898

2(1 minus cos(2120587119906

119871119905)) 0 le 119905 le

119871

119906

0 119905 le119871

119906

(28)

where 119860119898







5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(a) Case A

5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(b) Case B

5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(c) Case E


76

224

1

15

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(a) Ride comfort

38

35

5

4

4

14

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(b) Trade-off

687

7

3

6

9

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(c) Handling





0 05 1 15 2minus6

minus4

minus2

0

2

4

6

Times (s)

HandlingPassive

TradeoffComfort

Acce

lera

tion

(ms2)


HandlingPassive

TradeoffComfort

0 05 1 15 2minus3000

minus2000

minus1000

0

1000

2000

3000

Times (s)

Tire

dyn

amic

load

(N)



0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Case ACase BCase C

Case DCase E

Mot

or th

rust

(N)

(a) Ride comfort

Case ACase BCase C

Case DCase E

0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Mot

or th

rust

(N)

(b) Trade-off

Case ACase BCase C

Case DCase E

0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Mot

or th

rust

(N)

(c) Handling




100

200

300

400

Case ACase BCase C

Case DCase E

Wele

(J)



6 Conclusions







Acknowledgments


References
































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Permanent magnet



Piston rod Valve


zs

zt

zr

ms

mt

ks

kt

cs f

U




119904and 119896

119905represent the


119904 119911119904and 119911119905are




119898119904119904= 119896119904(119911119905minus 119911119904) + 119880


(1)

where 119880 = 119888119904(119905minus 119904) + 119891


119869


1

119879int119879

0

[11990212119904+ 1199022(119911119904minus 119911119905)2

+ 1199023(119911119905minus 119911119903)2

] 119889119905(2)

where 1199021 1199022 and 119902




X = AX + BU + F120596

Y = CX +DU(3)


X = [119911119904119911119905119904119905119911119903]119879


(4)








119903= minus2120587119891

0119911119903+ 2120587119899

0radic119866119902(1198990) 119906120596 (7)






119886


119864 = 119871119889119894

119889119905+ 119894119877 + 119864

119886 (8)


given by

119864119886= 119870119864V (9)


M

R

L

E

i

Ea




119894 =119864 minus 119864

119886

119877

119891 = 119870119868119894

(10)





119864ref =119891ref119877

119870119868

+ 119870119864V (12)


119875ele = (119891ref119870119868

)2

119877 +119870119864V

119870119868

119891ref (13)


119875mec = 119891refV (14)










119891ed = minus119870119868119870119864V

119877 (15)


119875ele =119891ref119877

1198702119868

(119891ref minus 119891ed) (16)




119903 motor actual


119904119898(where 119898 = 119886 119887 or





Mode decision

and switch

controllerThrust

controller

LQR controller

Quarter car model

Road input

Controller

csm

fmref

Uref

fmact

[zs zt zs zt zr]T

zr











coefficient 119888119904119898












fmref

imref

fmact

KE

KI

minus

minus+ +e

1KI




119888Stiff


119887Medium

6 119875119886



119886119872119887 and119872

119888



119872119898=


1 Comsumption (Con) (119898 = 119886 119887 119888) (17)


119873 = 119872119886+ 2119872119887+ 4119872119888 (18)





119864 = (119871 + Δ119871)119889119894

119889119905+ 119894 (119877 + Δ119877) + 119870

119864(V + ΔV) (19)


119903is

further defined as

119864119903= Δ119871

119889119894

119889119905+ 119894Δ119877 + 119870

119864ΔV (20)


119890 = minus119886119903119890 minus 119887119903119906 + 119888119903 (21)

where 119886119903= 119877119871 119887

119903= 1119871 119888

119903= (119870119864V+119877119894ref +119864119903)119871 and 119906 = 119864



119904 = 119890 + 119888119894119898int119905

0

119890 (120591) 119889120591 (22)

119888119894119898




119904 = minus120576 sgn (119904) minus 120578119904 (23)



is assumed to be 0)

119906 = (119871119888119894119898minus 119877) 119890 + 119877119894ref + 119870119864V + 120576 sgn (119904) + 120578119904 (24)


= 119904 119904 lt 0 (25)


= 119904 119904 = 119904 [minus120576 sgn (119904) minus 120578119904 + 119864119903]


2(26)






minus05

0

05

1

15

Velocity (ms)

SoftMediumStiff

Dam

ping

forc

e (kN

)







119904320 kg



11990416 kNm



119868657NA




Targets 1199021

1199022

1199023









1 1199022 and 119902

3of LQR




0 05 1 15 2minus4

minus2

0

2

4

Time (s)

ReferenceActual

Acce

lera

tion

(ms2)


0 05 1 15 2minus3000

minus2000

minus1000

0

1000

2000

3000

Time (s)

ReferenceActual

Tire

dyn

amic

load

(N)














5 52 54 56 58 6minus6

minus4

minus2

0

2

4

6

Times (s)

HandlingPassive

Trade-offComfort

Acce

lera

tion

(ms2)


HandlingPassive

Trade-offComfort

5 52 54 56 58 6minus3000

minus2000

minus1000

0

1000

2000

3000

Times (s)

Tire

dyn

amic

load

(N)



0 05 1 15 2 25 3minus1500

minus1000

minus500

0

500

1000

1500

Time (s)

Case ACase E

Mot

or th

rust

(N)



200

400

600

800

Case ACase BCase C

Case DCase E

RMS

valu

e of m

otor

forc

e (N

)




119882tot = int119905sim

0

119875ele119889119905 (27)




0

5000

10000

15000

20000

25000

30000

Case ACase BCase C

Case DCase E

Wele

(J)







119911119903=

119860119898

2(1 minus cos(2120587119906

119871119905)) 0 le 119905 le

119871

119906

0 119905 le119871

119906

(28)

where 119860119898







5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(a) Case A

5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(b) Case B

5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(c) Case E


76

224

1

15

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(a) Ride comfort

38

35

5

4

4

14

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(b) Trade-off

687

7

3

6

9

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(c) Handling





0 05 1 15 2minus6

minus4

minus2

0

2

4

6

Times (s)

HandlingPassive

TradeoffComfort

Acce

lera

tion

(ms2)


HandlingPassive

TradeoffComfort

0 05 1 15 2minus3000

minus2000

minus1000

0

1000

2000

3000

Times (s)

Tire

dyn

amic

load

(N)



0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Case ACase BCase C

Case DCase E

Mot

or th

rust

(N)

(a) Ride comfort

Case ACase BCase C

Case DCase E

0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Mot

or th

rust

(N)

(b) Trade-off

Case ACase BCase C

Case DCase E

0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Mot

or th

rust

(N)

(c) Handling




100

200

300

400

Case ACase BCase C

Case DCase E

Wele

(J)



6 Conclusions







Acknowledgments


References
































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










M

R

L

E

i

Ea




119894 =119864 minus 119864

119886

119877

119891 = 119870119868119894

(10)





119864ref =119891ref119877

119870119868

+ 119870119864V (12)


119875ele = (119891ref119870119868

)2

119877 +119870119864V

119870119868

119891ref (13)


119875mec = 119891refV (14)










119891ed = minus119870119868119870119864V

119877 (15)


119875ele =119891ref119877

1198702119868

(119891ref minus 119891ed) (16)




119903 motor actual


119904119898(where 119898 = 119886 119887 or





Mode decision

and switch

controllerThrust

controller

LQR controller

Quarter car model

Road input

Controller

csm

fmref

Uref

fmact

[zs zt zs zt zr]T

zr











coefficient 119888119904119898












fmref

imref

fmact

KE

KI

minus

minus+ +e

1KI




119888Stiff


119887Medium

6 119875119886



119886119872119887 and119872

119888



119872119898=


1 Comsumption (Con) (119898 = 119886 119887 119888) (17)


119873 = 119872119886+ 2119872119887+ 4119872119888 (18)





119864 = (119871 + Δ119871)119889119894

119889119905+ 119894 (119877 + Δ119877) + 119870

119864(V + ΔV) (19)


119903is

further defined as

119864119903= Δ119871

119889119894

119889119905+ 119894Δ119877 + 119870

119864ΔV (20)


119890 = minus119886119903119890 minus 119887119903119906 + 119888119903 (21)

where 119886119903= 119877119871 119887

119903= 1119871 119888

119903= (119870119864V+119877119894ref +119864119903)119871 and 119906 = 119864



119904 = 119890 + 119888119894119898int119905

0

119890 (120591) 119889120591 (22)

119888119894119898




119904 = minus120576 sgn (119904) minus 120578119904 (23)



is assumed to be 0)

119906 = (119871119888119894119898minus 119877) 119890 + 119877119894ref + 119870119864V + 120576 sgn (119904) + 120578119904 (24)


= 119904 119904 lt 0 (25)


= 119904 119904 = 119904 [minus120576 sgn (119904) minus 120578119904 + 119864119903]


2(26)






minus05

0

05

1

15

Velocity (ms)

SoftMediumStiff

Dam

ping

forc

e (kN

)







119904320 kg



11990416 kNm



119868657NA




Targets 1199021

1199022

1199023









1 1199022 and 119902

3of LQR




0 05 1 15 2minus4

minus2

0

2

4

Time (s)

ReferenceActual

Acce

lera

tion

(ms2)


0 05 1 15 2minus3000

minus2000

minus1000

0

1000

2000

3000

Time (s)

ReferenceActual

Tire

dyn

amic

load

(N)














5 52 54 56 58 6minus6

minus4

minus2

0

2

4

6

Times (s)

HandlingPassive

Trade-offComfort

Acce

lera

tion

(ms2)


HandlingPassive

Trade-offComfort

5 52 54 56 58 6minus3000

minus2000

minus1000

0

1000

2000

3000

Times (s)

Tire

dyn

amic

load

(N)



0 05 1 15 2 25 3minus1500

minus1000

minus500

0

500

1000

1500

Time (s)

Case ACase E

Mot

or th

rust

(N)



200

400

600

800

Case ACase BCase C

Case DCase E

RMS

valu

e of m

otor

forc

e (N

)




119882tot = int119905sim

0

119875ele119889119905 (27)




0

5000

10000

15000

20000

25000

30000

Case ACase BCase C

Case DCase E

Wele

(J)







119911119903=

119860119898

2(1 minus cos(2120587119906

119871119905)) 0 le 119905 le

119871

119906

0 119905 le119871

119906

(28)

where 119860119898







5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(a) Case A

5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(b) Case B

5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(c) Case E


76

224

1

15

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(a) Ride comfort

38

35

5

4

4

14

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(b) Trade-off

687

7

3

6

9

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(c) Handling





0 05 1 15 2minus6

minus4

minus2

0

2

4

6

Times (s)

HandlingPassive

TradeoffComfort

Acce

lera

tion

(ms2)


HandlingPassive

TradeoffComfort

0 05 1 15 2minus3000

minus2000

minus1000

0

1000

2000

3000

Times (s)

Tire

dyn

amic

load

(N)



0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Case ACase BCase C

Case DCase E

Mot

or th

rust

(N)

(a) Ride comfort

Case ACase BCase C

Case DCase E

0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Mot

or th

rust

(N)

(b) Trade-off

Case ACase BCase C

Case DCase E

0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Mot

or th

rust

(N)

(c) Handling




100

200

300

400

Case ACase BCase C

Case DCase E

Wele

(J)



6 Conclusions







Acknowledgments


References
































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Mode decision

and switch

controllerThrust

controller

LQR controller

Quarter car model

Road input

Controller

csm

fmref

Uref

fmact

[zs zt zs zt zr]T

zr











coefficient 119888119904119898












fmref

imref

fmact

KE

KI

minus

minus+ +e

1KI




119888Stiff


119887Medium

6 119875119886



119886119872119887 and119872

119888



119872119898=


1 Comsumption (Con) (119898 = 119886 119887 119888) (17)


119873 = 119872119886+ 2119872119887+ 4119872119888 (18)





119864 = (119871 + Δ119871)119889119894

119889119905+ 119894 (119877 + Δ119877) + 119870

119864(V + ΔV) (19)


119903is

further defined as

119864119903= Δ119871

119889119894

119889119905+ 119894Δ119877 + 119870

119864ΔV (20)


119890 = minus119886119903119890 minus 119887119903119906 + 119888119903 (21)

where 119886119903= 119877119871 119887

119903= 1119871 119888

119903= (119870119864V+119877119894ref +119864119903)119871 and 119906 = 119864



119904 = 119890 + 119888119894119898int119905

0

119890 (120591) 119889120591 (22)

119888119894119898




119904 = minus120576 sgn (119904) minus 120578119904 (23)



is assumed to be 0)

119906 = (119871119888119894119898minus 119877) 119890 + 119877119894ref + 119870119864V + 120576 sgn (119904) + 120578119904 (24)


= 119904 119904 lt 0 (25)


= 119904 119904 = 119904 [minus120576 sgn (119904) minus 120578119904 + 119864119903]


2(26)






minus05

0

05

1

15

Velocity (ms)

SoftMediumStiff

Dam

ping

forc

e (kN

)







119904320 kg



11990416 kNm



119868657NA




Targets 1199021

1199022

1199023









1 1199022 and 119902

3of LQR




0 05 1 15 2minus4

minus2

0

2

4

Time (s)

ReferenceActual

Acce

lera

tion

(ms2)


0 05 1 15 2minus3000

minus2000

minus1000

0

1000

2000

3000

Time (s)

ReferenceActual

Tire

dyn

amic

load

(N)














5 52 54 56 58 6minus6

minus4

minus2

0

2

4

6

Times (s)

HandlingPassive

Trade-offComfort

Acce

lera

tion

(ms2)


HandlingPassive

Trade-offComfort

5 52 54 56 58 6minus3000

minus2000

minus1000

0

1000

2000

3000

Times (s)

Tire

dyn

amic

load

(N)



0 05 1 15 2 25 3minus1500

minus1000

minus500

0

500

1000

1500

Time (s)

Case ACase E

Mot

or th

rust

(N)



200

400

600

800

Case ACase BCase C

Case DCase E

RMS

valu

e of m

otor

forc

e (N

)




119882tot = int119905sim

0

119875ele119889119905 (27)




0

5000

10000

15000

20000

25000

30000

Case ACase BCase C

Case DCase E

Wele

(J)







119911119903=

119860119898

2(1 minus cos(2120587119906

119871119905)) 0 le 119905 le

119871

119906

0 119905 le119871

119906

(28)

where 119860119898







5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(a) Case A

5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(b) Case B

5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(c) Case E


76

224

1

15

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(a) Ride comfort

38

35

5

4

4

14

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(b) Trade-off

687

7

3

6

9

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(c) Handling





0 05 1 15 2minus6

minus4

minus2

0

2

4

6

Times (s)

HandlingPassive

TradeoffComfort

Acce

lera

tion

(ms2)


HandlingPassive

TradeoffComfort

0 05 1 15 2minus3000

minus2000

minus1000

0

1000

2000

3000

Times (s)

Tire

dyn

amic

load

(N)



0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Case ACase BCase C

Case DCase E

Mot

or th

rust

(N)

(a) Ride comfort

Case ACase BCase C

Case DCase E

0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Mot

or th

rust

(N)

(b) Trade-off

Case ACase BCase C

Case DCase E

0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Mot

or th

rust

(N)

(c) Handling




100

200

300

400

Case ACase BCase C

Case DCase E

Wele

(J)



6 Conclusions







Acknowledgments


References
































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












fmref

imref

fmact

KE

KI

minus

minus+ +e

1KI




119888Stiff


119887Medium

6 119875119886



119886119872119887 and119872

119888



119872119898=


1 Comsumption (Con) (119898 = 119886 119887 119888) (17)


119873 = 119872119886+ 2119872119887+ 4119872119888 (18)





119864 = (119871 + Δ119871)119889119894

119889119905+ 119894 (119877 + Δ119877) + 119870

119864(V + ΔV) (19)


119903is

further defined as

119864119903= Δ119871

119889119894

119889119905+ 119894Δ119877 + 119870

119864ΔV (20)


119890 = minus119886119903119890 minus 119887119903119906 + 119888119903 (21)

where 119886119903= 119877119871 119887

119903= 1119871 119888

119903= (119870119864V+119877119894ref +119864119903)119871 and 119906 = 119864



119904 = 119890 + 119888119894119898int119905

0

119890 (120591) 119889120591 (22)

119888119894119898




119904 = minus120576 sgn (119904) minus 120578119904 (23)



is assumed to be 0)

119906 = (119871119888119894119898minus 119877) 119890 + 119877119894ref + 119870119864V + 120576 sgn (119904) + 120578119904 (24)


= 119904 119904 lt 0 (25)


= 119904 119904 = 119904 [minus120576 sgn (119904) minus 120578119904 + 119864119903]


2(26)






minus05

0

05

1

15

Velocity (ms)

SoftMediumStiff

Dam

ping

forc

e (kN

)







119904320 kg



11990416 kNm



119868657NA




Targets 1199021

1199022

1199023









1 1199022 and 119902

3of LQR




0 05 1 15 2minus4

minus2

0

2

4

Time (s)

ReferenceActual

Acce

lera

tion

(ms2)


0 05 1 15 2minus3000

minus2000

minus1000

0

1000

2000

3000

Time (s)

ReferenceActual

Tire

dyn

amic

load

(N)














5 52 54 56 58 6minus6

minus4

minus2

0

2

4

6

Times (s)

HandlingPassive

Trade-offComfort

Acce

lera

tion

(ms2)


HandlingPassive

Trade-offComfort

5 52 54 56 58 6minus3000

minus2000

minus1000

0

1000

2000

3000

Times (s)

Tire

dyn

amic

load

(N)



0 05 1 15 2 25 3minus1500

minus1000

minus500

0

500

1000

1500

Time (s)

Case ACase E

Mot

or th

rust

(N)



200

400

600

800

Case ACase BCase C

Case DCase E

RMS

valu

e of m

otor

forc

e (N

)




119882tot = int119905sim

0

119875ele119889119905 (27)




0

5000

10000

15000

20000

25000

30000

Case ACase BCase C

Case DCase E

Wele

(J)







119911119903=

119860119898

2(1 minus cos(2120587119906

119871119905)) 0 le 119905 le

119871

119906

0 119905 le119871

119906

(28)

where 119860119898







5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(a) Case A

5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(b) Case B

5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(c) Case E


76

224

1

15

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(a) Ride comfort

38

35

5

4

4

14

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(b) Trade-off

687

7

3

6

9

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(c) Handling





0 05 1 15 2minus6

minus4

minus2

0

2

4

6

Times (s)

HandlingPassive

TradeoffComfort

Acce

lera

tion

(ms2)


HandlingPassive

TradeoffComfort

0 05 1 15 2minus3000

minus2000

minus1000

0

1000

2000

3000

Times (s)

Tire

dyn

amic

load

(N)



0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Case ACase BCase C

Case DCase E

Mot

or th

rust

(N)

(a) Ride comfort

Case ACase BCase C

Case DCase E

0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Mot

or th

rust

(N)

(b) Trade-off

Case ACase BCase C

Case DCase E

0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Mot

or th

rust

(N)

(c) Handling




100

200

300

400

Case ACase BCase C

Case DCase E

Wele

(J)



6 Conclusions







Acknowledgments


References
































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












minus05

0

05

1

15

Velocity (ms)

SoftMediumStiff

Dam

ping

forc

e (kN

)







119904320 kg



11990416 kNm



119868657NA




Targets 1199021

1199022

1199023









1 1199022 and 119902

3of LQR




0 05 1 15 2minus4

minus2

0

2

4

Time (s)

ReferenceActual

Acce

lera

tion

(ms2)


0 05 1 15 2minus3000

minus2000

minus1000

0

1000

2000

3000

Time (s)

ReferenceActual

Tire

dyn

amic

load

(N)














5 52 54 56 58 6minus6

minus4

minus2

0

2

4

6

Times (s)

HandlingPassive

Trade-offComfort

Acce

lera

tion

(ms2)


HandlingPassive

Trade-offComfort

5 52 54 56 58 6minus3000

minus2000

minus1000

0

1000

2000

3000

Times (s)

Tire

dyn

amic

load

(N)



0 05 1 15 2 25 3minus1500

minus1000

minus500

0

500

1000

1500

Time (s)

Case ACase E

Mot

or th

rust

(N)



200

400

600

800

Case ACase BCase C

Case DCase E

RMS

valu

e of m

otor

forc

e (N

)




119882tot = int119905sim

0

119875ele119889119905 (27)




0

5000

10000

15000

20000

25000

30000

Case ACase BCase C

Case DCase E

Wele

(J)







119911119903=

119860119898

2(1 minus cos(2120587119906

119871119905)) 0 le 119905 le

119871

119906

0 119905 le119871

119906

(28)

where 119860119898







5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(a) Case A

5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(b) Case B

5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(c) Case E


76

224

1

15

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(a) Ride comfort

38

35

5

4

4

14

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(b) Trade-off

687

7

3

6

9

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(c) Handling





0 05 1 15 2minus6

minus4

minus2

0

2

4

6

Times (s)

HandlingPassive

TradeoffComfort

Acce

lera

tion

(ms2)


HandlingPassive

TradeoffComfort

0 05 1 15 2minus3000

minus2000

minus1000

0

1000

2000

3000

Times (s)

Tire

dyn

amic

load

(N)



0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Case ACase BCase C

Case DCase E

Mot

or th

rust

(N)

(a) Ride comfort

Case ACase BCase C

Case DCase E

0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Mot

or th

rust

(N)

(b) Trade-off

Case ACase BCase C

Case DCase E

0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Mot

or th

rust

(N)

(c) Handling




100

200

300

400

Case ACase BCase C

Case DCase E

Wele

(J)



6 Conclusions







Acknowledgments


References
































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 05 1 15 2minus4

minus2

0

2

4

Time (s)

ReferenceActual

Acce

lera

tion

(ms2)


0 05 1 15 2minus3000

minus2000

minus1000

0

1000

2000

3000

Time (s)

ReferenceActual

Tire

dyn

amic

load

(N)














5 52 54 56 58 6minus6

minus4

minus2

0

2

4

6

Times (s)

HandlingPassive

Trade-offComfort

Acce

lera

tion

(ms2)


HandlingPassive

Trade-offComfort

5 52 54 56 58 6minus3000

minus2000

minus1000

0

1000

2000

3000

Times (s)

Tire

dyn

amic

load

(N)



0 05 1 15 2 25 3minus1500

minus1000

minus500

0

500

1000

1500

Time (s)

Case ACase E

Mot

or th

rust

(N)



200

400

600

800

Case ACase BCase C

Case DCase E

RMS

valu

e of m

otor

forc

e (N

)




119882tot = int119905sim

0

119875ele119889119905 (27)




0

5000

10000

15000

20000

25000

30000

Case ACase BCase C

Case DCase E

Wele

(J)







119911119903=

119860119898

2(1 minus cos(2120587119906

119871119905)) 0 le 119905 le

119871

119906

0 119905 le119871

119906

(28)

where 119860119898







5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(a) Case A

5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(b) Case B

5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(c) Case E


76

224

1

15

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(a) Ride comfort

38

35

5

4

4

14

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(b) Trade-off

687

7

3

6

9

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(c) Handling





0 05 1 15 2minus6

minus4

minus2

0

2

4

6

Times (s)

HandlingPassive

TradeoffComfort

Acce

lera

tion

(ms2)


HandlingPassive

TradeoffComfort

0 05 1 15 2minus3000

minus2000

minus1000

0

1000

2000

3000

Times (s)

Tire

dyn

amic

load

(N)



0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Case ACase BCase C

Case DCase E

Mot

or th

rust

(N)

(a) Ride comfort

Case ACase BCase C

Case DCase E

0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Mot

or th

rust

(N)

(b) Trade-off

Case ACase BCase C

Case DCase E

0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Mot

or th

rust

(N)

(c) Handling




100

200

300

400

Case ACase BCase C

Case DCase E

Wele

(J)



6 Conclusions







Acknowledgments


References
































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










5 52 54 56 58 6minus6

minus4

minus2

0

2

4

6

Times (s)

HandlingPassive

Trade-offComfort

Acce

lera

tion

(ms2)


HandlingPassive

Trade-offComfort

5 52 54 56 58 6minus3000

minus2000

minus1000

0

1000

2000

3000

Times (s)

Tire

dyn

amic

load

(N)



0 05 1 15 2 25 3minus1500

minus1000

minus500

0

500

1000

1500

Time (s)

Case ACase E

Mot

or th

rust

(N)



200

400

600

800

Case ACase BCase C

Case DCase E

RMS

valu

e of m

otor

forc

e (N

)




119882tot = int119905sim

0

119875ele119889119905 (27)




0

5000

10000

15000

20000

25000

30000

Case ACase BCase C

Case DCase E

Wele

(J)







119911119903=

119860119898

2(1 minus cos(2120587119906

119871119905)) 0 le 119905 le

119871

119906

0 119905 le119871

119906

(28)

where 119860119898







5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(a) Case A

5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(b) Case B

5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(c) Case E


76

224

1

15

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(a) Ride comfort

38

35

5

4

4

14

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(b) Trade-off

687

7

3

6

9

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(c) Handling





0 05 1 15 2minus6

minus4

minus2

0

2

4

6

Times (s)

HandlingPassive

TradeoffComfort

Acce

lera

tion

(ms2)


HandlingPassive

TradeoffComfort

0 05 1 15 2minus3000

minus2000

minus1000

0

1000

2000

3000

Times (s)

Tire

dyn

amic

load

(N)



0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Case ACase BCase C

Case DCase E

Mot

or th

rust

(N)

(a) Ride comfort

Case ACase BCase C

Case DCase E

0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Mot

or th

rust

(N)

(b) Trade-off

Case ACase BCase C

Case DCase E

0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Mot

or th

rust

(N)

(c) Handling




100

200

300

400

Case ACase BCase C

Case DCase E

Wele

(J)



6 Conclusions







Acknowledgments


References
































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











0

5000

10000

15000

20000

25000

30000

Case ACase BCase C

Case DCase E

Wele

(J)







119911119903=

119860119898

2(1 minus cos(2120587119906

119871119905)) 0 le 119905 le

119871

119906

0 119905 le119871

119906

(28)

where 119860119898







5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(a) Case A

5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(b) Case B

5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(c) Case E


76

224

1

15

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(a) Ride comfort

38

35

5

4

4

14

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(b) Trade-off

687

7

3

6

9

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(c) Handling





0 05 1 15 2minus6

minus4

minus2

0

2

4

6

Times (s)

HandlingPassive

TradeoffComfort

Acce

lera

tion

(ms2)


HandlingPassive

TradeoffComfort

0 05 1 15 2minus3000

minus2000

minus1000

0

1000

2000

3000

Times (s)

Tire

dyn

amic

load

(N)



0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Case ACase BCase C

Case DCase E

Mot

or th

rust

(N)

(a) Ride comfort

Case ACase BCase C

Case DCase E

0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Mot

or th

rust

(N)

(b) Trade-off

Case ACase BCase C

Case DCase E

0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Mot

or th

rust

(N)

(c) Handling




100

200

300

400

Case ACase BCase C

Case DCase E

Wele

(J)



6 Conclusions







Acknowledgments


References
































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(a) Case A

5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(b) Case B

5 52 54 56 58 6minus800

minus400

0

400

800

1200

Time (s)

Pow

er (W

)

PmecPele

(c) Case E


76

224

1

15

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(a) Ride comfort

38

35

5

4

4

14

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(b) Trade-off

687

7

3

6

9

N = 1

N = 3

N = 4

N = 5

N = 6

N = 7

(c) Handling





0 05 1 15 2minus6

minus4

minus2

0

2

4

6

Times (s)

HandlingPassive

TradeoffComfort

Acce

lera

tion

(ms2)


HandlingPassive

TradeoffComfort

0 05 1 15 2minus3000

minus2000

minus1000

0

1000

2000

3000

Times (s)

Tire

dyn

amic

load

(N)



0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Case ACase BCase C

Case DCase E

Mot

or th

rust

(N)

(a) Ride comfort

Case ACase BCase C

Case DCase E

0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Mot

or th

rust

(N)

(b) Trade-off

Case ACase BCase C

Case DCase E

0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Mot

or th

rust

(N)

(c) Handling




100

200

300

400

Case ACase BCase C

Case DCase E

Wele

(J)



6 Conclusions







Acknowledgments


References
































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 05 1 15 2minus6

minus4

minus2

0

2

4

6

Times (s)

HandlingPassive

TradeoffComfort

Acce

lera

tion

(ms2)


HandlingPassive

TradeoffComfort

0 05 1 15 2minus3000

minus2000

minus1000

0

1000

2000

3000

Times (s)

Tire

dyn

amic

load

(N)



0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Case ACase BCase C

Case DCase E

Mot

or th

rust

(N)

(a) Ride comfort

Case ACase BCase C

Case DCase E

0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Mot

or th

rust

(N)

(b) Trade-off

Case ACase BCase C

Case DCase E

0 02 04 06 08 1minus2000

minus1500

minus1000

minus500

0

500

1000

1500

Times (s)

Mot

or th

rust

(N)

(c) Handling




100

200

300

400

Case ACase BCase C

Case DCase E

Wele

(J)



6 Conclusions







Acknowledgments


References
































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











100

200

300

400

Case ACase BCase C

Case DCase E

Wele

(J)



6 Conclusions







Acknowledgments


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 Energy Conservation Analysis and …downloads.hindawi.com/journals/sv/2016/6196542.pdf · Semiactive Suspension with Three Regulating ... e linear motor is considered