Suppression of Switched Reluctance Motor Vibration of In ...downloads.hindawi.com/journals/jcse/2018/1689690.pdfSwitched reluctance motor (SRM) has achieved good per-formance due to

Research ArticleSuppression of Switched Reluctance Motor Vibration ofIn-Wheel Motor Electric Vehicle

Funing Yang and YanyangWang

The Key Laboratory of Automotive Engineering Xihua University Chengdu 610039 China

Correspondence should be addressed to Yanyang Wang yywangmailxhueducn

Received 18 May 2018 Revised 8 October 2018 Accepted 23 October 2018 Published 15 November 2018

Academic Editor Manuel Pineda-Sanchez

Copyright copy 2018 Funing Yang and Yanyang Wang This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Switched reluctance motor (SRM) has got great attention in in-wheel motor electric vehicle (IWM-EV) but SRM vertical forcethe vertical component of SRM unbalanced radial force yields SRM vertical vibration and does harm to dynamic performance ofIWM-EV In order to reduce the SRM vertical vibration electromagnetic active suspension and a linear quadratic Gaussian (LQG)controller were used to suppress the unbalanced radial force in this paper All the models and the controller were constructed inMatlabSimulink R2015b The controller considers five performance indexes vehicle body acceleration SRM airgap eccentricitySRM stator acceleration suspension dynamic deflections and tyre deformation Analytic Hierarchy Process (AHP) was used tocalculate the weighted coefficients of performance indexes Simulations indicate that this electromagnetic active suspension canreduce SRM vertical vibration obviously and improve dynamic performance of IWM-EV

1 Introduction

Switched reluctance motor (SRM) has achieved good per-formance due to its remarkable advantages high startingtorque wide operating speed range and high efficiencyTheseadvantages endow SRM with great potential on in-wheelmotor electric vehicles (IWM-EV) However asymmetricalmagnetic pull caused by airgap eccentricity yields unbalancedradial force this unbalanced radial force is recognized as oneof themain reasons for the SRMvibration [1ndash5] To reduce thevibration scholars have focused on exploring the structureand control strategies of SRM [6ndash8]

On SRM structure integrated design and the optimiza-tion of SRM components are main methods to reduce SRMvibration such asmultiobjective optimization designmethod[9] new stator tooth [10] new rotor tooth [11] and newpoles ratio [12] On SRM control strategies varieties ofmethods have been proposed such as torque distributioncontroller [13] multilevel systematic design method [14]and new motor torque controller [15] The above studiesdo reduce the SRM vibration however these studies focusonly on SRM itself the negative influence of SRM on vehicle

dynamic performance has not been fully considered As themain component that flexibly connects the wheel and thevehicle body suspension transmits the force acting betweenthe wheel and the vehicle body As a kind of suspensionsystem electromagnetic active suspension can produce con-trollable active force which enables the suspension systemto dynamically adjust the supporting force according to thevibration of wheel and vehicle body In the previous workwe analyzed the influence of the SRM unbalanced radialforce on comfort and stability of IWM-EV The conclusion[16 17] shows SRM vertical force is highly coupled with roadexcitation and SRM airgap eccentricity and this couplingyields SRM vertical vibration that does harm to comfort andstability This study used electromagnetic active suspensionand linear quadratic Gaussian (LQG) controller to reduce theSRM vertical vibration and the negative influence on vehicledynamic performance

In order to conduct this study a full IWM-EV modelSRM vertical force model and control diagram for the elec-tromagnetic active suspension are built in MatlabSimulinkR2015b Then the weighted coefficients are calculated andLQGcontroller is completed Finally the frequency responses

HindawiJournal of Control Science and EngineeringVolume 2018 Article ID 1689690 13 pageshttpsdoiorg10115520181689690

2 Journal of Control Science and Engineering

Table 1 The SRM parameter values

Definition Symbol Units ValueAirgap g m 000025Minimum inductance Lq H 00019Maximum inductance Ld H 00318Saturated inductance Ldsat H 00013Maximum flux linkage 120595m Wb 09

Figure 1 SRM vertical force

on stochastic roads and time responses on representativeroads are analyzed Conclusion shows that the electromag-netic active suspension can effectively reduce SRM vibrationand the negative influence on vehicle dynamic performance

2 IWM-EV Modeling

Two models were constructed for studying the effects ofelectromagnetic active suspension One is SRM vertical forcemodel that reflects the SRM vertical force exerting on thewheel another is full IWM-EV model that reflects theinfluence of electromagnetic active suspension force andunbalanced vertical force on vehicle

21 SRM Vertical Force Model Because of the geometricallybalanced motor structure the SRM radial force is alwaysconsidered zero But the vehicle load and road excitation [17]will yield SRM airgap eccentricity due to which the radialforce is always not zero In this study The primary objectiveis to reduce the vertical vibration of SRM and the negativeinfluence on vehicle dynamic performance the well-known64 outside-rotor SRM like [18 19] is shown in Figure 1TheSRMparameter values are listed in Table 1 According to [20]the difference magnetic pull between each pair of poles yields

the unbalanced radial force and the radial force of oppositestator poles can be described as follows

F1= minus sin (120579

0)

gm minus ΔgT = minus r sin (1205790)gm minus Δg Ft (1)


0)

gm + ΔgT = minus r sin (1205790)gm + Δg Ft (2)

The unbalanced radial force is follows

Fr = F1minus F2 (3)

The vertical force that is the vertical component of theunbalanced radial force can be described as

Fv = Fr sin (1205791015840) (4)

where 1205790is the overlap angle of stator and rotor Ft is

tyre tangential force gm is airgap length of SRM Δg isthe airgap eccentricity and 1205791015840 is the angle between statorand wheel longitudinal axis Each pair of opposite statorwith eccentricity will yield unbalanced radial force for theconvenience of presentation only stators 1 and 4 are pickedout to investigate the influence of SRM vertical force on SRMvibration and vehicle dynamic performance When the 1205791015840 is90∘ SRM unbalanced radial force is equal to SRM verticalforce

22 Vehicle Model To simulate the effects of electromagneticactive suspension force on IWM-EV the required vehicledynamics model needs to reflect contributions of both elec-tromagnetic active suspension force and SRM vertical forceA vehicle model which has been proved reasonably well inprevious work [16 17] is developed as shown in Figure 2and the governing equations of the vehicle motions can bedescribed as

Mtx = minus (Fxfl + Fxfr) cos 120575 minus (Fyfl + Fyfr) sin 120575 minus Fxrl

minus Fxrr(5)

Journal of Control Science and Engineering 3

θv

2cf

Fc Fc

2cr

h dRoll CenterSzfl Szfr

Fyfl

Fyfl

Fvrl Fvfl

Fxflksrl ksfl

kmsrl kmsfl

zmsrl zmsflMmsrl

Murl Mufl

Mmsfl

zurl zufl

qrl qflktrl ktfl

csrl csfl

FyfrFyrr

Fyfr

FyrlFxrl

FxrrFxfr

Mbay

Mbg

a b

v

CG

Z

α δ

Figure 2 Schematic diagram of the vehicle model

Mty = minus (Fxfl + Fxfr) sin 120575 + (Fyfl + Fyfr) cos 120575 + Fyrl

+ Fyrr(6)

Mb z = Szfl + Szfr + Szrl + Szrr minus Fcfl minus Fcf r minus Fcrl

minus Fcrr(7)

Ixp = cf (Szfl minus Szfr) + cr (Szrl minus Szrr)+ hc [minus (Fxfl + Fxfr) sin 120575 + (Fyfl + Fyfr) cos 120575+ Fyrl + Fyrr] +Mbg (hcg minus hc) sin 120588

(8)

Iy 120579 = minusa (Szfl + Szfr) + b (Szrl + Szrr)+ hp [(Fxfl + Fxfr) cos 120575 + (Fyfl + Fyfr) sin 120575 + Fxrl

+ Fxrr] +Mbg (hcg minus hp) sin 120579(9)

Iz = a [minus (Fxfl + Fxfr) sin 120575 + (Fyfl + Fyfr) cos 120575]minus b (Fyrl + Fyrr) + cf [(Fxfl minus Fxfr) cos 120575+ (Fyfl minus Fyfr) sin 120575] + cr (Fxrl minus Fxrr)

(10)

where Szij the suspension vertical forces at each corner is asfollows

Szfl = minusksfl (z + cf120588 minus a120579 minus zmsfl)minus csfl ( z + cf 120588 minus a 120579 minus zmsfl)

Szfr = minusksf r (z minus cf120588 minus a120579 minus zmsfr)minus csf r ( z minus cf 120588 minus a 120579 minus zmsfr)

Szrl = minusksrl (z + cr120588 + b120579 minus zmsrl)minus csrl ( z + cr 120588 + b 120579 minus zmsrl)

Szrr = minusksrr (z minus cr120588 + b120579 minus zmsrr)minus csrr ( z minus cr 120588 + b 120579 minus zmsrr)

(11)

Equations of the vertical motion of the aggregate mass ofthe tyres the rims and the SRM rotors at each corner are asfollows

Mufl zufl = kmsfl (zmsfl minus zufl) minus ktfl (zufl minus qfl) minus Fvfl

Mufr zufr = kmsfr (zmsfr minus zufr) minus ktf r (zufr minus qf r) minus Fvfr

Murl zurl = kmsrl (zmsrl minus zurl) minus ktrl (zurl minus qrl) minus Fvrl

Murr zurr = kmsrr (zmsrr minus zurr) minus ktrr (zurr minus qrr) minus Fvrr

(12)

Equations of the vertical motion of the aggregate mass of theSRM stator and housing are

Mmsfl zmsfl = ksfl (z + cf120588 minus a120579 minus zmsfl)+ csfl (z + cf120588 minus a120579 minus zmsfl)


Table 2 The vehicle parameter values

Definition Symbol Units ValueVehicle total mass Mt kg 1770Sprung mass Mb kg 1350Mass of tyre rim and SRM rotor of front wheel Mufj kg 70Mass of tyre rim and SRM rotor of rear wheel Murj kg 65Mass of SRM stator and housing Mmsij kg 37 5Roll moment of inertia Ix Kg m2 480Pitch moment of inertia Iy Kg m2 1895Yaw moment of inertia Iz Kg m2 1875Height of CG hcg m 0 504Height of pitch center hp m 0 4Height of roll center hc m 0 25Distance from CG to front axle a m 1 08Distance from CG to rear axle b m 1 62Track width of front axle cf m 1 4Track width of rear axle cr m 1 385Wheel inertia Iwi Kg m2 1 8Effective radius of wheel R m 0 269Stiffness of front suspension ksf j Nm 22500Stiffness of rear suspension ksrj Nm 19600Damping of frontrear suspension csij Nsm 1695Sum of SRM and hub bearing stiffness kmsij Nm 6500000Stiffness of tyre ktij Nm 150000

minus kmsfl (zmsfl minus zufl) + Fvfl + Fcfl

Mmsfr zmsfr = ksf r (z minus cf120588 minus a120579 minus zmsfr)+ csf r (z minus cf120588 minus a120579 minus zmsfr)minus kmsfr (zmsfr minus zufr) + Fvf r + Fcf r

Mmsrl zmsrl = ksrl (z + cr120588 + b120579 minus zmsrl)+ csrl (z + cr120588 + b120579 minus zmsrl)minus kmsrl (zmsrl minus zurl) + Fvrl + Fcrl

Mmsrr zmsrr = ksrr (z minus cr120588 + b120579 minus zmsrr)+ csrr (z minus cr120588 + b120579 minus zmsrr)minus kmsrr (zmsrr minus zurr) + Fvrr + Fcrr

(13)

where x y and z are the longitudinal displacement the lateraldisplacement and the vertical displacement respectively ofthe sprung mass of the vehicle 120588 120579 and 120595 are the verticalpitch and roll motion of the sprung mass of the vehicle 120575 isthe steering angle Fc is the electromagnetic active suspensionforce Fxij and Fyij are the longitudinal tyre force and thelateral tyre force at each wheel qij is road displacementexcitation at each wheel Fvij is the unbalanced vertical forceof each SRM Mmsij is the aggregate mass of tyre hub andSRM rotor Muij is the aggregate mass of SRM stator andhousing and kmsij is the bearing stiffness The subscripts i

in the equations refer to the front (f) or rear (r) and thesubscripts j in the equations refers to the left (l) side or theright (r) sideThe vehicle parameter values used for this studyare listed in Table 2

The Pacejka nonlinear tyre model [21] is adopted in thispaper to simulate the nonlinearity tyre force The equationsof the Pacejka nonlinear tyre mode are

Fxij (120582) = Dx

sdot sin (Cx arctan By120582 minus Ex [Bx120582 minus arctan (Bx120582)])(14)

Fyij (120572) = Dy

sdot sin (Cy arctan By120572 minus Ey [Bx120572 minus arctan (Bx120572)])(15)

Bx = a3sin [2 arctan (Fza4)]

CxDx

Cx = b0

Dx = a1F2z + a

2Fz

1000Ex = a

5Fz + a

6

By = b3sin [2 arctan (Fzb4)]

CyDy

Cy = b0


Dy = b1F2z + b

2Fz

1000Ey = b

5Fz + b

6

(16)

where 120582 is the slip ratio and Bx Cx Dx Ex By Cy Dy and Eyare empirical parameters Fxij Fyij are the longitudinal forceand lateral force

3 LQG Controller of ElectromagneticActive Suspension

In this paper several performance indexes of IWM-EV areconsidered by linear quadratic Gaussian (LQG) controllersuch us vehicle body acceleration airgap eccentricity SRMstator acceleration suspension dynamic deflections and tyre

deformation It is easy to use the methodology of AnalyticHierarchy Process (AHP) to select the weighted coefficientsof performance indexes [22]This LQG controller is based onoptimal control theory and the controller can propose dif-ferent objective functions according to design requirementsand improve the vehicle performance by comprehensivelyconsidering various performance indexes

31 State Equation 24 state variables and 14 output variablesare chosen to constitute the vehicle system for controller andthe state equation can be described as

X = AX + Bu + GQ (17)

Y = CX +Du (18)

where

X = [ z 120579 z 120579 zmsfl zmsfr zmsrl zmsrr zmsfl zmsfr zmsrl zmsrr zufl zufr zurl zurr zufl zufr zurl zurr qfl qf r qrl qrr]T (19)

Y = [z 120579 Zmsfl Zmsfr Zmsrl Zmsrr Zufl Zufr Zurl Zurr qfl qf r qrl qrr]T (20)

u = Fc (21)

where X is the state variables Y is the output variables u isthe control vector and A is the system matrix B is controlmatrix G is disturbance matrix C is the output matrix D istransfer matrix

32 Selection of Performance Indexesrsquo Weighted Coefficientsfor LQG Controller AHP is a decision-making method Itdecomposes elements that are always related to decision-making into objectives criteria and programs and thenmakes qualitative and quantitative analysis on this basisIt was used to select weighted coefficients of performanceindexes for LQG controller [23]

321 Quantitating Scale Factor Theroot mean square (RMS)of dynamic characteristics of the passive suspension vehiclecan be produced by simulating the passive suspension vehiclemodel under the corresponding conditions According tothe literature [22 23] scale factors of vehicle dynamiccharacteristics can be described by the following equations

1205902BA times 1 = 1205902PA times 120573PA = 1205902AEij times 120573AEij = 1205902TDij times 120573TDij= 1205902SDDij times 120573SDDij

(22)

where 120590BA 120590PA 120590AEij 120590TDij 120590SDDij are RMS of vehicle bodyvertical acceleration (BVA) pitch angle (PA) airgap eccen-tricity (AE) tyre deformation (TD) and suspension dynamicdeflections (SDD) 120573PA 120573AEij 120573TDij 120573SDDij are pitch anglescale factor airgap eccentricity scale factor tyre deformationscale factor and suspension dynamic deflections scale factorvehicle body vertical acceleration (BVA) scale factor is 1

322 Subjective Weighted Coefficient

(1) Making Judgment Matrix 119867 hij (no unit) is the relativeimportance ratio of the index i and j Table 3 is a comparisontable of the relative importance of each index According toTable 3 judgmentmatrixH shown in (23) can be constructed

H = (hij)nxn =

1 h12

h13

sdot sdot sdot sdot sdot sdot h1n

1h12

1 h23

h24

sdot sdot sdot h2n

1h13

1h23

1 h34

sdot sdot sdot h3n

1h24

1h34

sdot sdot sdot sdot sdot sdot 1h1n

1h2n

1h3n

sdot sdot sdot sdot sdot sdot 1

(23)

Calculate multiplying vector of every row

M = [M1M2M3 Mn]T

Mi =nprodj=1

hij (i j = 1 2 3 n) (24)


Table 3 Comparison table

ij Equal Moderately Strongly Very Extremelyhij 1 3 5 7 9

Vehicle drivemodel

Vehicle vibrationmodel

SRM torquecontroller

Electromagneticsuspensioncontroller

SRM vertical forcemodel

Reference torque

Road

Vehicle vibrationresponse

+-Driving torque

Figure 3 Control diagram for the electromagnetic active suspension

Calculate nradicW andW

W = [W1W2W3 Wn]T

Wi = nradicMi (i = 1 2 3 n)

W = Wsumn

i=1Wi (i = 1 2 3 n)

(25)

where W is the subjective weighted coefficient

(2) Maximum Eigenvalue and Consistency Checking of MatrixH

120582max =nsumi=1

(HW)inWi

(i = 1 2 3 n) (26)

where 120582max is the maximum eigenvalue of HIf every element in matrix H satisfies the equations hij =1hij and hij = hiktimeshkj thematrixH is the consistencymatrix

The method of consistency checking is comparing randomconsistency ratio CR

CR = 120582max minus nRI (n minus 1) (i = 1 2 3 n) (27)

RI is the random consistency index When n is 14 RI is 1 59If CR is less than 1 H passes the consistency checking If CRis more than 1 H needs to be revised [24]

323 Weighted Coefficients Subjective weighted coefficientsof pitch angle airgap eccentricity tyre deformation andsuspension dynamic deflections can be calculated as follows

W1= Wi

120574i (28)

q1= 1

q2= 120573PA1205742

q3= 120573AEfl1205743

q4= 120573AEfr1205744

q5= 120573AErl1205745

q6= 120573AErr1205746

q7= 120573TDfl1205747

q8= 120573TDfr1205748

q9= 120573TDrl1205749

q10= 120573TDrr12057410

q11= 120573SDDfl12057411

q12= 120573SDDfr12057412

q13= 120573SDDrl12057413

q14 = 120573SDDrr12057414

(29)

33 LQG Controller Design The control diagram for theelectromagnetic active suspension is shown in Figure 3Vehicle body acceleration and pitch angle are chosen to bethe performance indexes for improving ride comfort andhandling stability Airgap eccentricity tyre deformation and


suspension dynamic deflections of each wheel are chosento be the performance indexes for reducing the verticalvibration of SRM

The performance function is defined as follows

J = 12 intinfin

0

q1z2b + q21205792 + q

3(zmsfl minus zufl)2

+ q4 (zmsfr minus zufr)2 + q5 (zmsrl minus zurl)2

+ q6(zmsrr minus zurr)2 + q

7(zufl minus qfl)2

+ q8 (zufr minus qf r)2 + q9 (zurl minus qrl)2

+ q10(zurr minus qrr) + q

11(z + cf120588 minus a120579 minus zmsfl)2

+ q12 (z minus cf120588 minus a120579 minus zmsfr)2

+ q13(z + cr120588 minus a120579 minus zmsrl)2

+ q14(z + cr120588 minus a120579 minus zmsrr)2 + Ru2] dt = 1

2sdot intinfin

0

YTQY + uTRu) dt

(30)

where q1is the weighted coefficient of body vertical accel-

eration q2is the weighted coefficient of pitch angle q

3 q4

q5 and q6 are the weighted coefficients of airgap eccentricityq7 q8 q9 and q

10are the weighted coefficients of tyre defor-

mation q11 q12 q13 and q

14are the weighted coefficients of

suspension dynamic deflections Q is the weight matrix ofthe state u is the control vector of Fc and R is the weightedcoefficient of u

Rewrite (30) as a standard form

J = 12 intinfin

0

[XTQ1015840X + 2XTNu + uTR1015840u] dt (31)

where

Q1015840 = CTQCN = CTQDR1015840 = R +DTQD

(32)

u = minusKX (33)

and the optimal control feedback matrix K can be givenby the Riccati equation

PA + ATP +Q minus (PB +N)Rminus1 (BTP +NT) = 0K = BTP +NT

(34)

It is easy to calculate feedback matrix K by using Matlabfunction as follows

[K S E] = lqr (ABQRN) (35)

0 2 4 6 8 10 12 14 16 18 20Time [S]

minus005

005

015

025

Road

[m

]

Figure 4 Effective road excitation

1 10 250Frequency [Hz]

PSD

of v

ehic

le b

ody

CG

passiveoptimal control

1 12 1403

04

05

10minus2

100

10minus4

10minus6

acc

[(m

Ｍ2)2

Hz]

Figure 5 Frequency response of vehicle body acceleration

4 Suppression of SRM Vertical Force andPromotion of Vehicle Dynamic Performance

SRM vibration and IWM-EV body movement influence eachother so it is difficult to improve the dynamic performance ofthe vehicle considering only the SRM structure and controllerdesign Therefore this study used electromagnetic activesuspension connecting body and wheels to reduce the SRMvibration and the negative influence on vehicle body

41 Frequency Response on Stochastic Roads For this simula-tion the road excitations at four tyres are assumed to be thesame only the front left in-wheel SRM response is presentedin this paper In order to study the effects of electromagneticactive suspension under urban condition and high-speedcondition vehicle responses are simulated at 60 kmh vehiclespeed on class C road and 100 kmh vehicle speed on class Croad

411 Response under Urban Condition Vehicle responses aresimulated at 60 kmh vehicle speed on class C road as shownin Figure 4

Responses of vehicle body acceleration airgap eccentric-ity SRM stator acceleration suspension dynamic deflectionsand tyre deformation at 60 kmh are shown in Figures 5ndash9

It can be seen that the electromagnetic active suspensioncan reduce the power spectral density (PSD) values of vehiclebody acceleration airgap eccentricity SRM stator accelera-tion suspension dynamic deflections and tyre deformationat their resonance frequency Specifically Figure 5 showsthat the resonance frequency of vehicle body accelerationis 1221Hz and the peak value of vehicle body accelerationdecreases from 05395 (ms2)2Hz to 04343 (ms2)2Hz and


1 10 300

Frequency [Hz]

PSD

of a

irgap

ecce

ntric

ity


90 100 110

10e-1115e-11

10minus16

10minus14

10minus12

10minus10

10minus8

[(m

2)2

Hz]

Figure 6 Frequency response of airgap eccentricity



90 100

5

10100

PSD

of s

tato

r CG

acc

[(m

Ｍ2)2

Hz]

Figure 7 Frequency response of stator acceleration


PSD

of s

uspe

nsio

n dy

nam

ic

defle

ctio

ns [

m2 H

z]

optimal controlpassive

1 12 148

10

12

10minus14

10minus8

10minus2

times10-5

Figure 8 Frequency response of suspension dynamic deflections

reduced by 195 This indicates that the electromagneticactive suspension can reduce the force acting between thewheel and the vehicle body and ride comfort improvedFigure 6 shows that the resonance frequency of airgapeccentricity is 9857Hz and the peak value of airgap eccen-tricity decreases from 1307eminus10m2Hz to 8339eminus11m2Hzand reduced by 362 Figure 7 shows that the resonancefrequency of stator acceleration is 9857Hz and the peakvalue of stator acceleration decreases from 8147 (ms2)2Hzto 5520 (ms2)2Hz and reduced by 322 Figures 6 and 7mean that electromagnetic active suspension conspicuouslysuppressed SRM vertical vibration and operating stabilityof SRM improved Furthermore SRMrsquos negative influenceon the vehicle reduced Figure 8 shows that the resonancefrequency of suspension dynamic deflections is 1221Hz andthe peak value of suspension dynamic deflections decreasesfrom 130eminus4m2Hz to 106eminus4m2Hz and reduced by 184


PSD

of t

ire d

efor

mat

ion

[m2 H

z]


65 7112e-5

116e-5

10minus9

10minus7

10minus5

Figure 9 Frequency response of tyre deformation

0 2 4 6 8 10 12 14 16 18 20Time [S]

0

01

03

Road

[m

] 02



PSD

of v

ehic

le b

ody

CG

acc

[(m

s2)2

Hz]


11 12 13 14070809

10minus5

100


Figure 9 shows that the resonance frequency of tyre defor-mation is 6714Hz and the peak value of tyre deforma-tion decreases from 1154eminus5m2Hz to 1140eminus5m2Hz andreduced by 121 Because driving stability is related to sus-pension dynamic deflections and tyre deformation decreaseof them implies that electromagnetic active suspension canimprove vehicle safety Therefore compared with passivesuspension electromagnetic active suspension can availablyreduce values of body acceleration airgap eccentricity SRMstator acceleration and so on Ride comfort and safety underurban condition improved

412 Response underHigh-SpeedCondition Vehicle respons-es are simulated at 100 kmh vehicle speed on class C roadas shown in Figure 10 Vehicle body acceleration airgapeccentricity SRM stator acceleration tyre deformation andsuspension dynamic deflections responses at 100 kmh areshown in Figures 11ndash15

Under high-speed condition the power spectral density(PSD) values of vehicle body acceleration airgap eccentricity



PSD

of a

irgap

ecce

ntric

ity [

m2H

z]

104 105 106 107 108

12

16

2


10minus16

10minus12

10minus8

times10-10



PSD

of s

tato

r CG

acc [

(ms

2)2

Hz]

104 106 108

10

15


100



PSD

of s

uspe

nsio

n dy

nam

ic

defle

ctio

ns [

m2H

z]


09 1 11 12 1316

18

10minus14

10minus8

10minus2

times10-4


SRM stator acceleration suspension dynamic deflectionsand tyre deformation can be reduced at their resonancefrequency Figure 11 shows that the peak value of vehiclebody acceleration decreases from 09104 (ms2)2Hz to 08158(ms2)2Hz and reduced by 10 4 This means that evenunder high-speed conditions the electromagnetic activesuspension can still significantly reduce the vibration ofthe vehicle body and the ride comfort improved obviouslyAs can be seen from Figures 12 and 13 the peak valueof airgap eccentricity decreases from 1867eminus10m2Hz to1625eminus10m2Hz and reduced by 130 the peak value ofstator acceleration decreases from 1595 (ms2)2Hz to 1391(ms2)2Hz and reduced by 128 This indicates that thevibration of SRM under high-speed condition was reducedeffectively Figure 14 shows that the peak value of sus-pension dynamic deflections decreases from 224eminus4m2Hzto 202eminus4m2Hz and reduced by 98 Figure 15 showsthat the peak value of tyre deformation decreases from1902eminus5m2Hz to 1894eminus5m2Hz and reduced by 042


PSD

of t

ire d

efor

mat

ion

[m2H

z]


665 675188e-5

190e-5

10minus9

10minus7

10minus5


h

L

Figure 16 Bump road model

Therefore electromagnetic active suspension can improveride comfort and reduce SRM vibration under high-speedcondition Because decreases of suspension dynamic deflec-tions and tyre deformation can greatly enhance the driv-ing stability under high-speed condition the vehicle safetyimproved

The effects of electromagnetic active suspension underhigh-speed condition are weaker than effects under urbancondition because the weighted coefficients of LQG con-troller are more suitable for urban condition All the vehicleresponses at both 60 kmh and 100 kmh were shown inTable 4

42 Time Response on Representative Roads

421 Response on Bump Road In order to simulate thespeed bump bump road model is shown in Figure 16 Thesimplified model can be described as (36) where L h are thewidth and height of the bump and V is the vehicle speedSetting different vehicle speed or changing the width of thebump can easily adjust road excitation frequency To simulatethe ordinary low frequency speed hump excitation L=08mh=007m and V is 08ms Vehicle body acceleration pitchangle airgap eccentricity suspension dynamic deflectionsand tyre deformation responses on class C road are shownin Figures 17ndash21

Figure 17 shows the vehicle body acceleration responsesWhen t=1s the vehicle body starts to vibrate under theexcitation of bump road When t=216s the vehicle bodyacceleration reaches peak value and the peak value decreasesby 611 Figure 18 shows the response of pitch angle Whent=1s the bump road excitation starts to affect the vehicleWhen t=3s the vehicle system tends to be stable The peakvalue of pitch angle decreases by 316 Figures 17 and 18mean that the vertical vibration of the body was reduced andthe ride comfort improved because the vertical motion of theunsprung mass and its impact on vehicle body were reduced


Table 4 Vehicle responses

Frequencyresponse

Resonancefrequency (Hz) Units

60 kmh 100 kmh

Passive Optimalcontrol reduce by Passive Optimal

control reduce by

Vehicle bodyacceleration 1221 (ms2)2Hz 05395 04343 195 09104 08158 10 4

Airgapeccentricity 9857 m2Hz 1307eminus10 8339eminus11 362 1867eminus10 1625eminus10 130

Statoracceleration 9857 (ms2)2Hz 8147 5520 322 1595 1391 128

Suspensiondynamicdeflections

1221 m2Hz 130eminus4 106eminus4 184 224eminus4 202eminus4 98

Tyredeformation 6714 m2Hz 1154eminus5 1140eminus5 121 1902eminus5 1894eminus5 042

0 05 1 15 2 25 3 35 4 45 5Time [S]

minus3

minus2

minus1

0

1

2

3

Vehi

cle b

ody

acce

lera

tion

[ms

2]


Figure 17 Time history response of vehicle body acceleration

0 05 1 15 2 25 3 35 4 45 5Time [S]

minus002

minus001

0

001

Pitc

h an

gle

[rad

]


Figure 18 Time history response of pitch angle

As can be seen from Figures 19 and 20 the trend of airgapeccentricity is similar to vehicle body acceleration and thepeak value of airgap eccentricity decreases by 889 Whent=1s the suspension system starts to shrink When t=3sthe electromagnetic active suspension system approachessteady state that is faster than passive suspension systemat t=37s The peak value of suspension dynamic deflectiondecreases by 364 Figure 21 shows that the peak value oftyre deformation decreases by 744 This implies that theelectromagnetic active suspension can effectively reduce theairgap eccentricity suspension dynamic deflection and tyredeformation on bump road The unsprung mass had less

0 05 1 15 2 25 3 35 4 45 5Time [S]

minus2

minus1

0

1

2

Airg

ap ec

cent

ricity

[m

]


times10-4

Figure 19 Time history response of airgap eccentricity

0 05 1 15 2 25 3 35 4 45 5Time [S]

minus004

minus002

0

002

004

Susp

ensio

n dy

nam

ic d

eflec

tions

[m

]


Figure 20 Time history response of suspension dynamic deflec-tions

0 05 1 15 2 25 3 35 4 45 5Time [S]

minus001

minus0005

0

0005

001

Tyre

def

orm

atio

n [m

]


Figure 21 Time history response of tyre deformation


0 05 1 15 2 25 3 35 4 45 5Time [S]

minus006

0

006

Stee

ring

angl

e for

sing

le la

ne ch

ange

[ra

d]

Figure 22 Single lane change


0 05 1 15 2 25 3 35 4 45 5Time [S]

minus5

0

5

airg

ap ec

cent

ricity

[m

]

times10-4


influence on the body and can provide higher stability for thevehicle

zr = h (1 minus cos 2120587f t)2r

f = VL

(36)

422 Response on Single Lane Change In order to studythe effects of electromagnetic active suspension on handlingstability vehicle responses are simulated under single lanechange condition The steering angle model is shown inFigure 22 Airgap eccentricity roll angle sideslip angle andyaw rate responses at 100 kmh on class C road are shown inFigures 23ndash26

Figure 23 shows that the airgap eccentricity responsedoes not have much relevance to steering angle but theelectromagnetic active suspension efficiently reduces theairgap eccentricity Figure 24 shows that the vehicle startsto roll at 05s The roll angle reaches peak value at 18sand decreases by 366 Figures 25 and 26 show that thetrends of sideslip angle and yaw rate are similar to steeringangle Although the contributions of the electromagneticactive suspension to sideslip angle and yaw rate under thiscondition are not very significant the electromagnetic activesuspension systemdoes have positive influences on the lateraldynamic performance

5 Conclusions

In order to reduce SRM vertical vibration and improve IWM-EV dynamic performance this paper used electromagneticactive suspension and LQG controller to suppress the SRM


1 2 3 4 5Time [S]

minus5

0

5

Roll

angl

e [r

ad]

times10-3

Figure 24 Time history response of roll angle


0 05 1 15 2 25 3 35 4 45 5Time [S]

minus002

0

002

Side

slip

angl

e [r

ad]

Figure 25 Sideslip angle

unbalanced radial force The controller based on optimalcontrol theory can efficiently match electromagnetic activesuspension In theory compared with the passive suspensionthis electromagnetic active suspension can reduce SRMvertical vibration and provide better dynamic performanceto the IWM-VE Based on the analyzed simulation results thefollowing 3 conclusions can be summarize

(1) This electromagnetic active suspension could effec-tively improve the ride comfort Vehicle body accelerationwas reduced on urban condition high-speed conditionand representative roads For urban condition the vehiclebody acceleration reduced by 195 near the vehicle bodyrsquosresonance frequency 122Hz For high-speed condition thevehicle body acceleration reduced by 104 near the vehiclebodyrsquos resonance frequency 122Hz

(2) This electromagnetic active suspension could effec-tively reduce the SRM vertical vibration SRM airgap eccen-tricity and stator acceleration were both reduced Specificallywhen the frequencies of the SRM airgap eccentricity andstator acceleration are near the statorrsquos resonance frequencyof 1074Hz the SRM vertical vibration shows a most obviousdrop

(3)This electromagnetic active suspension could improvethe safety Under both urban condition and high-speedcondition suspension dynamic deflection and tyre deforma-tion were reduced On representative roads electromagneticactive suspension reduced roll angle sideslip angle and yawrate It indicated that the electromagnetic active suspensioncan improve lateral dynamic performance and reduce SRMvertical vibration at the same time



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus04

0

04

yaw

rate

[ra

ds]

Figure 26 Yaw rate

In summary this paper used electromagnetic activesuspension and LQG controller to effectively improve theIWM-EV ride comfort and safety and also reduce the SRMvertical vibrationDue to limited research resource this paperdoes not construct an experimental platform to verify thesimulation results But we are preparing an experimentalplatform and will give introduction in the next work

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This research is supported by the National Natural ScienceFoundation of China (Grant No 51605390) Foundation ofEducational Commission of Sichuan Province (Grant No16ZA0161) the Open Research Subject of Key Laboratoryof Sichuan Provincial Automotive Engineering (Grant Noszjj2015-048) Foundation of the Science and TechnologyResearch and Development Program of Sichuan Province(Grant No 2017GZ0103)

References

[1] M Divandari and A Dadpour ldquoRadial force and torque rippleoptimization for acoustic noise reduction of SRM drives viafuzzy logic controlrdquo in Proceedings of the 2010 9th IEEEIASInternational Conference on Industry Applications INDUSCON2010 Brazil November 2010

[2] F L dos Santos J Anthonis and H Van der Auweraer ldquoMul-tiphysics thermal and NVHmodeling Integrated simulation ofa switched reluctance motor drivetrain for an electric vehiclerdquoin Proceedings of the 2012 IEEE International Electric VehicleConference (IEVC) pp 1ndash7 Greenville SC USA March 2012

[3] I Husain A Radun and J Nairus ldquoUnbalanced force calcu-lation in switched-reluctance machinesrdquo IEEE Transactions onMagnetics vol 36 pp 330ndash338 2000

[4] N K Sheth and K R Rajagopal ldquoVariations in overalldeveloped torque of a switched reluctance motor with airgap

nonuniformityrdquo IEEE Transactions on Magnetics vol 41 no 10pp 3973ndash3975 2005

[5] B M Ebrahimi J Faiz andM J Roshtkhari ldquoStatic- dynamic- and mixed-eccentricity fault diagnoses in permanent-magnetsynchronousmotorsrdquo IEEE Transactions on Industrial Electron-ics vol 56 no 11 pp 4727ndash4739 2009

[6] N K Sheth and K R Rajagopal ldquoEffects of nonuniform airgapon the torque characteristics of a switched reluctance motorrdquoIEEE Transactions on Magnetics vol 40 no 4 pp 2032ndash20342004

[7] E Afjei and H Torkaman ldquoAirgap eccentricity fault diagnosisin switched reluctance motorrdquo in Proceedings of the 1st PowerElectronics and Drives Systems and Technologies ConferencePEDSTC 2010 pp 290ndash294 Iran February 2010

[8] M C Ta and C Dufour ldquoReal-time simulation and control ofreluctance motor drives for high speed operation with reducedtorque ripplerdquo in Proceedings of the 37th Annual Conference ofthe IEEE Industrial Electronics Society IECON 2011 pp 4176ndash4181 Australia November 2011

[9] X D Xue K W E Cheng TW Ng and N C Cheung ldquoMulti-objective optimization design of in-wheel switched reluctancemotors in electric vehiclesrdquo IEEE Transactions on IndustrialElectronics vol 57 no 9 pp 2980ndash2987 2010

[10] H Chaozhi ldquoA Stator novel structure to decrease vibration ofswitched reluctance motorrdquo China Micro Motor vol 45 no 9pp 37ndash40 2017

[11] X Zhang X Wang Y Yang and B Wei ldquoVibration reductionof a switched reluctance motor using new rotor tooth with sloton each siderdquo Zhongguo Dianji Gongcheng XuebaoProceedingsof the Chinese Society of Electrical Engineering vol 35 no 6 pp1508ndash1515 2015

[12] P C Desai M Krishnamurthy N Schofield and A EmadildquoNovel switched reluctance machine configuration with highernumber of rotor poles than stator poles Concept to implemen-tationrdquo IEEE Transactions on Industrial Electronics vol 57 no2 pp 649ndash659 2010

[13] J Ye B Bilgin and A Emadi ldquoAn extended-speed low-rippletorque control of switched reluctance motor drivesrdquo IEEETransactions on Power Electronics vol 30 no 3 pp 1457ndash14702015

[14] P Song M Tomizuka and C Zong ldquoA novel integratedchassis controller for full drive-by-wire vehiclesrdquoVehicle SystemDynamics vol 53 no 2 pp 215ndash236 2015

[15] S Ko J Ko S Lee J Cheon and H Kim ldquoA study on theroad friction coefficient estimation and motor torque controlfor an in-wheel electric vehiclerdquo Proceedings of the Institution ofMechanical Engineers Part D Journal of Automobile Engineer-ing vol 229 no 5 pp 611ndash623 2015

[16] Y Wang P Li and G Ren ldquoElectric vehicles with in-wheelswitched reluctance motors Coupling effects between roadexcitation and the unbalanced radial forcerdquo Journal of Soundand Vibration vol 372 pp 69ndash81 2016

[17] Y-Y Wang Y-N Li W Sun and L Zheng ldquoEffect of theunbalanced vertical force of a switched reluctancemotor on thestability and the comfort of an in-wheel motor electric vehiclerdquoProceedings of the Institution of Mechanical Engineers Part DJournal of Automobile Engineering vol 229 no 12 pp 1569ndash1584 2015

[18] J Lin K W E Cheng Z Zhang and X Xue ldquoExperimentalinvestigation of in-wheel switched reluctance motor drivingsystem for future electric vehiclesrdquo in Proceedings of the 2009


3rd International Conference on Power Electronics Systems andApplications PESA 2009 China May 2009

[19] A Labak and N C Kar ldquoOuter rotor switched reluctancemotor design for in-wheel drive of electric bus applicationsrdquoin Proceedings of the 2012 XXth International Conference onElectrical Machines (ICEM) pp 418ndash423 Marseille FranceSeptember 2012

[20] R Krishnan Switched Reluctance Motor Drives-Modeling Sim-ulation Analysis Design and Applications CRC Press BocaRaton Florida 2001

[21] E Bakker L Nyborg and H B Pacejka ldquoTyre modelling foruse in vehicle dynamics studiesrdquo SAE Technical Papers ArticleID 870421 pp 1ndash15 1987

[22] L Chai and T Sun ldquoThe design of LQG controller for activesuspension based on analytic hierarchy processrdquoMathematicalProblems in Engineering vol 2010 Article ID 701951 19 pages2010

[23] S-A Chen F Qiu R He and S-L Lu ldquoMethod for choosingweights in a suspension LQG controlrdquo Journal of Vibration andShock vol 27 no 2 pp 65ndash68 2008

[24] T Xiao and Y Shihua ldquoMethod of comparison matrix consis-tency adjustment based on AHPrdquo Ordnance Industry Automa-tion vol 27 no 4 2008

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018


Active and Passive Electronic Components

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of



Journal ofEngineeringVolume 2018

SensorsJournal of



RotatingMachinery


Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation


Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom


Table 1 The SRM parameter values

Definition Symbol Units ValueAirgap g m 000025Minimum inductance Lq H 00019Maximum inductance Ld H 00318Saturated inductance Ldsat H 00013Maximum flux linkage 120595m Wb 09

Figure 1 SRM vertical force

on stochastic roads and time responses on representativeroads are analyzed Conclusion shows that the electromag-netic active suspension can effectively reduce SRM vibrationand the negative influence on vehicle dynamic performance

2 IWM-EV Modeling

Two models were constructed for studying the effects ofelectromagnetic active suspension One is SRM vertical forcemodel that reflects the SRM vertical force exerting on thewheel another is full IWM-EV model that reflects theinfluence of electromagnetic active suspension force andunbalanced vertical force on vehicle

21 SRM Vertical Force Model Because of the geometricallybalanced motor structure the SRM radial force is alwaysconsidered zero But the vehicle load and road excitation [17]will yield SRM airgap eccentricity due to which the radialforce is always not zero In this study The primary objectiveis to reduce the vertical vibration of SRM and the negativeinfluence on vehicle dynamic performance the well-known64 outside-rotor SRM like [18 19] is shown in Figure 1TheSRMparameter values are listed in Table 1 According to [20]the difference magnetic pull between each pair of poles yields

the unbalanced radial force and the radial force of oppositestator poles can be described as follows


0)

gm minus ΔgT = minus r sin (1205790)gm minus Δg Ft (1)


0)

gm + ΔgT = minus r sin (1205790)gm + Δg Ft (2)

The unbalanced radial force is follows

Fr = F1minus F2 (3)

The vertical force that is the vertical component of theunbalanced radial force can be described as

Fv = Fr sin (1205791015840) (4)

where 1205790is the overlap angle of stator and rotor Ft is

tyre tangential force gm is airgap length of SRM Δg isthe airgap eccentricity and 1205791015840 is the angle between statorand wheel longitudinal axis Each pair of opposite statorwith eccentricity will yield unbalanced radial force for theconvenience of presentation only stators 1 and 4 are pickedout to investigate the influence of SRM vertical force on SRMvibration and vehicle dynamic performance When the 1205791015840 is90∘ SRM unbalanced radial force is equal to SRM verticalforce

22 Vehicle Model To simulate the effects of electromagneticactive suspension force on IWM-EV the required vehicledynamics model needs to reflect contributions of both elec-tromagnetic active suspension force and SRM vertical forceA vehicle model which has been proved reasonably well inprevious work [16 17] is developed as shown in Figure 2and the governing equations of the vehicle motions can bedescribed as

Mtx = minus (Fxfl + Fxfr) cos 120575 minus (Fyfl + Fyfr) sin 120575 minus Fxrl

minus Fxrr(5)


θv

2cf

Fc Fc

2cr


Fyfl

Fyfl

Fvrl Fvfl

Fxflksrl ksfl

kmsrl kmsfl

zmsrl zmsflMmsrl

Murl Mufl

Mmsfl

zurl zufl

qrl qflktrl ktfl

csrl csfl

FyfrFyrr

Fyfr

FyrlFxrl

FxrrFxfr

Mbay

Mbg

a b

v

CG

Z

α δ



+ Fyrr(6)


minus Fcrr(7)


(8)




(10)






(11)






(12)










(13)




Fxij (120582) = Dx


Fyij (120572) = Dy



CxDx

Cx = b0

Dx = a1F2z + a

2Fz

1000Ex = a

5Fz + a

6


CyDy

Cy = b0


Dy = b1F2z + b

2Fz

1000Ey = b

5Fz + b

6

(16)






X = AX + Bu + GQ (17)

Y = CX +Du (18)

where



u = Fc (21)





(22)




H = (hij)nxn =

1 h12

h13


1h12

1 h23

h24

sdot sdot sdot h2n

1h13

1h23

1 h34

sdot sdot sdot h3n

1h24

1h34


1h2n

1h3n


(23)


M = [M1M2M3 Mn]T

Mi =nprodj=1

hij (i j = 1 2 3 n) (24)




Vehicle drivemodel





Reference torque

Road


+-Driving torque



W = [W1W2W3 Wn]T


W = Wsumn

i=1Wi (i = 1 2 3 n)

(25)



120582max =nsumi=1

(HW)inWi

(i = 1 2 3 n) (26)






W1= Wi

120574i (28)

q1= 1

q2= 120573PA1205742

q3= 120573AEfl1205743

q4= 120573AEfr1205744

q5= 120573AErl1205745

q6= 120573AErr1205746

q7= 120573TDfl1205747

q8= 120573TDfr1205748

q9= 120573TDrl1205749

q10= 120573TDrr12057410

q11= 120573SDDfl12057411

q12= 120573SDDfr12057412

q13= 120573SDDrl12057413

q14 = 120573SDDrr12057414

(29)





J = 12 intinfin

0

q1z2b + q21205792 + q




7(zufl minus qfl)2







2sdot intinfin

0

YTQY + uTRu) dt

(30)



3 q4







J = 12 intinfin

0

[XTQ1015840X + 2XTNu + uTR1015840u] dt (31)

where


(32)

u = minusKX (33)



(34)



0 2 4 6 8 10 12 14 16 18 20Time [S]

minus005

005

015

025

Road

[m

]



PSD

of v

ehic

le b

ody

CG


1 12 1403

04

05

10minus2

100

10minus4

10minus6

acc

[(m

Ｍ2)2

Hz]









1 10 300

Frequency [Hz]

PSD

of a

irgap

ecce

ntric

ity


90 100 110

10e-1115e-11

10minus16

10minus14

10minus12

10minus10

10minus8

[(m

2)2

Hz]




90 100

5

10100

PSD

of s

tato

r CG

acc

[(m

Ｍ2)2

Hz]



PSD

of s

uspe

nsio

n dy

nam

ic

defle

ctio

ns [

m2 H

z]


1 12 148

10

12

10minus14

10minus8

10minus2

times10-5




PSD

of t

ire d

efor

mat

ion

[m2 H

z]


65 7112e-5

116e-5

10minus9

10minus7

10minus5


0 2 4 6 8 10 12 14 16 18 20Time [S]

0

01

03

Road

[m

] 02



PSD

of v

ehic

le b

ody

CG

acc

[(m

s2)2

Hz]


11 12 13 14070809

10minus5

100







PSD

of a

irgap

ecce

ntric

ity [

m2H

z]

104 105 106 107 108

12

16

2


10minus16

10minus12

10minus8

times10-10



PSD

of s

tato

r CG

acc [

(ms

2)2

Hz]

104 106 108

10

15


100



PSD

of s

uspe

nsio

n dy

nam

ic

defle

ctio

ns [

m2H

z]


09 1 11 12 1316

18

10minus14

10minus8

10minus2

times10-4




PSD

of t

ire d

efor

mat

ion

[m2H

z]


665 675188e-5

190e-5

10minus9

10minus7

10minus5


h

L









Frequencyresponse


60 kmh 100 kmh


control reduce by







0 05 1 15 2 25 3 35 4 45 5Time [S]

minus3

minus2

minus1

0

1

2

3

Vehi

cle b

ody

acce

lera

tion

[ms

2]



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus002

minus001

0

001

Pitc

h an

gle

[rad

]




0 05 1 15 2 25 3 35 4 45 5Time [S]

minus2

minus1

0

1

2

Airg

ap ec

cent

ricity

[m

]


times10-4


0 05 1 15 2 25 3 35 4 45 5Time [S]

minus004

minus002

0

002

004

Susp

ensio

n dy

nam

ic d

eflec

tions

[m

]



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus001

minus0005

0

0005

001

Tyre

def

orm

atio

n [m

]




0 05 1 15 2 25 3 35 4 45 5Time [S]

minus006

0

006

Stee

ring

angl

e for

sing

le la

ne ch

ange

[ra

d]



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus5

0

5

airg

ap ec

cent

ricity

[m

]

times10-4




f = VL

(36)



5 Conclusions



1 2 3 4 5Time [S]

minus5

0

5

Roll

angl

e [r

ad]

times10-3



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus002

0

002

Side

slip

angl

e [r

ad]








0 05 1 15 2 25 3 35 4 45 5Time [S]

minus04

0

04

yaw

rate

[ra

ds]

Figure 26 Yaw rate


Data Availability




Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



θv

2cf

Fc Fc

2cr


Fyfl

Fyfl

Fvrl Fvfl

Fxflksrl ksfl

kmsrl kmsfl

zmsrl zmsflMmsrl

Murl Mufl

Mmsfl

zurl zufl

qrl qflktrl ktfl

csrl csfl

FyfrFyrr

Fyfr

FyrlFxrl

FxrrFxfr

Mbay

Mbg

a b

v

CG

Z

α δ



+ Fyrr(6)


minus Fcrr(7)


(8)




(10)






(11)






(12)










(13)




Fxij (120582) = Dx


Fyij (120572) = Dy



CxDx

Cx = b0

Dx = a1F2z + a

2Fz

1000Ex = a

5Fz + a

6


CyDy

Cy = b0


Dy = b1F2z + b

2Fz

1000Ey = b

5Fz + b

6

(16)






X = AX + Bu + GQ (17)

Y = CX +Du (18)

where



u = Fc (21)





(22)




H = (hij)nxn =

1 h12

h13


1h12

1 h23

h24

sdot sdot sdot h2n

1h13

1h23

1 h34

sdot sdot sdot h3n

1h24

1h34


1h2n

1h3n


(23)


M = [M1M2M3 Mn]T

Mi =nprodj=1

hij (i j = 1 2 3 n) (24)




Vehicle drivemodel





Reference torque

Road


+-Driving torque



W = [W1W2W3 Wn]T


W = Wsumn

i=1Wi (i = 1 2 3 n)

(25)



120582max =nsumi=1

(HW)inWi

(i = 1 2 3 n) (26)






W1= Wi

120574i (28)

q1= 1

q2= 120573PA1205742

q3= 120573AEfl1205743

q4= 120573AEfr1205744

q5= 120573AErl1205745

q6= 120573AErr1205746

q7= 120573TDfl1205747

q8= 120573TDfr1205748

q9= 120573TDrl1205749

q10= 120573TDrr12057410

q11= 120573SDDfl12057411

q12= 120573SDDfr12057412

q13= 120573SDDrl12057413

q14 = 120573SDDrr12057414

(29)





J = 12 intinfin

0

q1z2b + q21205792 + q




7(zufl minus qfl)2







2sdot intinfin

0

YTQY + uTRu) dt

(30)



3 q4







J = 12 intinfin

0

[XTQ1015840X + 2XTNu + uTR1015840u] dt (31)

where


(32)

u = minusKX (33)



(34)



0 2 4 6 8 10 12 14 16 18 20Time [S]

minus005

005

015

025

Road

[m

]



PSD

of v

ehic

le b

ody

CG


1 12 1403

04

05

10minus2

100

10minus4

10minus6

acc

[(m

Ｍ2)2

Hz]









1 10 300

Frequency [Hz]

PSD

of a

irgap

ecce

ntric

ity


90 100 110

10e-1115e-11

10minus16

10minus14

10minus12

10minus10

10minus8

[(m

2)2

Hz]




90 100

5

10100

PSD

of s

tato

r CG

acc

[(m

Ｍ2)2

Hz]



PSD

of s

uspe

nsio

n dy

nam

ic

defle

ctio

ns [

m2 H

z]


1 12 148

10

12

10minus14

10minus8

10minus2

times10-5




PSD

of t

ire d

efor

mat

ion

[m2 H

z]


65 7112e-5

116e-5

10minus9

10minus7

10minus5


0 2 4 6 8 10 12 14 16 18 20Time [S]

0

01

03

Road

[m

] 02



PSD

of v

ehic

le b

ody

CG

acc

[(m

s2)2

Hz]


11 12 13 14070809

10minus5

100







PSD

of a

irgap

ecce

ntric

ity [

m2H

z]

104 105 106 107 108

12

16

2


10minus16

10minus12

10minus8

times10-10



PSD

of s

tato

r CG

acc [

(ms

2)2

Hz]

104 106 108

10

15


100



PSD

of s

uspe

nsio

n dy

nam

ic

defle

ctio

ns [

m2H

z]


09 1 11 12 1316

18

10minus14

10minus8

10minus2

times10-4




PSD

of t

ire d

efor

mat

ion

[m2H

z]


665 675188e-5

190e-5

10minus9

10minus7

10minus5


h

L









Frequencyresponse


60 kmh 100 kmh


control reduce by







0 05 1 15 2 25 3 35 4 45 5Time [S]

minus3

minus2

minus1

0

1

2

3

Vehi

cle b

ody

acce

lera

tion

[ms

2]



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus002

minus001

0

001

Pitc

h an

gle

[rad

]




0 05 1 15 2 25 3 35 4 45 5Time [S]

minus2

minus1

0

1

2

Airg

ap ec

cent

ricity

[m

]


times10-4


0 05 1 15 2 25 3 35 4 45 5Time [S]

minus004

minus002

0

002

004

Susp

ensio

n dy

nam

ic d

eflec

tions

[m

]



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus001

minus0005

0

0005

001

Tyre

def

orm

atio

n [m

]




0 05 1 15 2 25 3 35 4 45 5Time [S]

minus006

0

006

Stee

ring

angl

e for

sing

le la

ne ch

ange

[ra

d]



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus5

0

5

airg

ap ec

cent

ricity

[m

]

times10-4




f = VL

(36)



5 Conclusions



1 2 3 4 5Time [S]

minus5

0

5

Roll

angl

e [r

ad]

times10-3



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus002

0

002

Side

slip

angl

e [r

ad]








0 05 1 15 2 25 3 35 4 45 5Time [S]

minus04

0

04

yaw

rate

[ra

ds]

Figure 26 Yaw rate


Data Availability




Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









(13)




Fxij (120582) = Dx


Fyij (120572) = Dy



CxDx

Cx = b0

Dx = a1F2z + a

2Fz

1000Ex = a

5Fz + a

6


CyDy

Cy = b0


Dy = b1F2z + b

2Fz

1000Ey = b

5Fz + b

6

(16)






X = AX + Bu + GQ (17)

Y = CX +Du (18)

where



u = Fc (21)





(22)




H = (hij)nxn =

1 h12

h13


1h12

1 h23

h24

sdot sdot sdot h2n

1h13

1h23

1 h34

sdot sdot sdot h3n

1h24

1h34


1h2n

1h3n


(23)


M = [M1M2M3 Mn]T

Mi =nprodj=1

hij (i j = 1 2 3 n) (24)




Vehicle drivemodel





Reference torque

Road


+-Driving torque



W = [W1W2W3 Wn]T


W = Wsumn

i=1Wi (i = 1 2 3 n)

(25)



120582max =nsumi=1

(HW)inWi

(i = 1 2 3 n) (26)






W1= Wi

120574i (28)

q1= 1

q2= 120573PA1205742

q3= 120573AEfl1205743

q4= 120573AEfr1205744

q5= 120573AErl1205745

q6= 120573AErr1205746

q7= 120573TDfl1205747

q8= 120573TDfr1205748

q9= 120573TDrl1205749

q10= 120573TDrr12057410

q11= 120573SDDfl12057411

q12= 120573SDDfr12057412

q13= 120573SDDrl12057413

q14 = 120573SDDrr12057414

(29)





J = 12 intinfin

0

q1z2b + q21205792 + q




7(zufl minus qfl)2







2sdot intinfin

0

YTQY + uTRu) dt

(30)



3 q4







J = 12 intinfin

0

[XTQ1015840X + 2XTNu + uTR1015840u] dt (31)

where


(32)

u = minusKX (33)



(34)



0 2 4 6 8 10 12 14 16 18 20Time [S]

minus005

005

015

025

Road

[m

]



PSD

of v

ehic

le b

ody

CG


1 12 1403

04

05

10minus2

100

10minus4

10minus6

acc

[(m

Ｍ2)2

Hz]









1 10 300

Frequency [Hz]

PSD

of a

irgap

ecce

ntric

ity


90 100 110

10e-1115e-11

10minus16

10minus14

10minus12

10minus10

10minus8

[(m

2)2

Hz]




90 100

5

10100

PSD

of s

tato

r CG

acc

[(m

Ｍ2)2

Hz]



PSD

of s

uspe

nsio

n dy

nam

ic

defle

ctio

ns [

m2 H

z]


1 12 148

10

12

10minus14

10minus8

10minus2

times10-5




PSD

of t

ire d

efor

mat

ion

[m2 H

z]


65 7112e-5

116e-5

10minus9

10minus7

10minus5


0 2 4 6 8 10 12 14 16 18 20Time [S]

0

01

03

Road

[m

] 02



PSD

of v

ehic

le b

ody

CG

acc

[(m

s2)2

Hz]


11 12 13 14070809

10minus5

100







PSD

of a

irgap

ecce

ntric

ity [

m2H

z]

104 105 106 107 108

12

16

2


10minus16

10minus12

10minus8

times10-10



PSD

of s

tato

r CG

acc [

(ms

2)2

Hz]

104 106 108

10

15


100



PSD

of s

uspe

nsio

n dy

nam

ic

defle

ctio

ns [

m2H

z]


09 1 11 12 1316

18

10minus14

10minus8

10minus2

times10-4




PSD

of t

ire d

efor

mat

ion

[m2H

z]


665 675188e-5

190e-5

10minus9

10minus7

10minus5


h

L









Frequencyresponse


60 kmh 100 kmh


control reduce by







0 05 1 15 2 25 3 35 4 45 5Time [S]

minus3

minus2

minus1

0

1

2

3

Vehi

cle b

ody

acce

lera

tion

[ms

2]



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus002

minus001

0

001

Pitc

h an

gle

[rad

]




0 05 1 15 2 25 3 35 4 45 5Time [S]

minus2

minus1

0

1

2

Airg

ap ec

cent

ricity

[m

]


times10-4


0 05 1 15 2 25 3 35 4 45 5Time [S]

minus004

minus002

0

002

004

Susp

ensio

n dy

nam

ic d

eflec

tions

[m

]



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus001

minus0005

0

0005

001

Tyre

def

orm

atio

n [m

]




0 05 1 15 2 25 3 35 4 45 5Time [S]

minus006

0

006

Stee

ring

angl

e for

sing

le la

ne ch

ange

[ra

d]



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus5

0

5

airg

ap ec

cent

ricity

[m

]

times10-4




f = VL

(36)



5 Conclusions



1 2 3 4 5Time [S]

minus5

0

5

Roll

angl

e [r

ad]

times10-3



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus002

0

002

Side

slip

angl

e [r

ad]








0 05 1 15 2 25 3 35 4 45 5Time [S]

minus04

0

04

yaw

rate

[ra

ds]

Figure 26 Yaw rate


Data Availability




Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Dy = b1F2z + b

2Fz

1000Ey = b

5Fz + b

6

(16)






X = AX + Bu + GQ (17)

Y = CX +Du (18)

where



u = Fc (21)





(22)




H = (hij)nxn =

1 h12

h13


1h12

1 h23

h24

sdot sdot sdot h2n

1h13

1h23

1 h34

sdot sdot sdot h3n

1h24

1h34


1h2n

1h3n


(23)


M = [M1M2M3 Mn]T

Mi =nprodj=1

hij (i j = 1 2 3 n) (24)




Vehicle drivemodel





Reference torque

Road


+-Driving torque



W = [W1W2W3 Wn]T


W = Wsumn

i=1Wi (i = 1 2 3 n)

(25)



120582max =nsumi=1

(HW)inWi

(i = 1 2 3 n) (26)






W1= Wi

120574i (28)

q1= 1

q2= 120573PA1205742

q3= 120573AEfl1205743

q4= 120573AEfr1205744

q5= 120573AErl1205745

q6= 120573AErr1205746

q7= 120573TDfl1205747

q8= 120573TDfr1205748

q9= 120573TDrl1205749

q10= 120573TDrr12057410

q11= 120573SDDfl12057411

q12= 120573SDDfr12057412

q13= 120573SDDrl12057413

q14 = 120573SDDrr12057414

(29)





J = 12 intinfin

0

q1z2b + q21205792 + q




7(zufl minus qfl)2







2sdot intinfin

0

YTQY + uTRu) dt

(30)



3 q4







J = 12 intinfin

0

[XTQ1015840X + 2XTNu + uTR1015840u] dt (31)

where


(32)

u = minusKX (33)



(34)



0 2 4 6 8 10 12 14 16 18 20Time [S]

minus005

005

015

025

Road

[m

]



PSD

of v

ehic

le b

ody

CG


1 12 1403

04

05

10minus2

100

10minus4

10minus6

acc

[(m

Ｍ2)2

Hz]









1 10 300

Frequency [Hz]

PSD

of a

irgap

ecce

ntric

ity


90 100 110

10e-1115e-11

10minus16

10minus14

10minus12

10minus10

10minus8

[(m

2)2

Hz]




90 100

5

10100

PSD

of s

tato

r CG

acc

[(m

Ｍ2)2

Hz]



PSD

of s

uspe

nsio

n dy

nam

ic

defle

ctio

ns [

m2 H

z]


1 12 148

10

12

10minus14

10minus8

10minus2

times10-5




PSD

of t

ire d

efor

mat

ion

[m2 H

z]


65 7112e-5

116e-5

10minus9

10minus7

10minus5


0 2 4 6 8 10 12 14 16 18 20Time [S]

0

01

03

Road

[m

] 02



PSD

of v

ehic

le b

ody

CG

acc

[(m

s2)2

Hz]


11 12 13 14070809

10minus5

100







PSD

of a

irgap

ecce

ntric

ity [

m2H

z]

104 105 106 107 108

12

16

2


10minus16

10minus12

10minus8

times10-10



PSD

of s

tato

r CG

acc [

(ms

2)2

Hz]

104 106 108

10

15


100



PSD

of s

uspe

nsio

n dy

nam

ic

defle

ctio

ns [

m2H

z]


09 1 11 12 1316

18

10minus14

10minus8

10minus2

times10-4




PSD

of t

ire d

efor

mat

ion

[m2H

z]


665 675188e-5

190e-5

10minus9

10minus7

10minus5


h

L









Frequencyresponse


60 kmh 100 kmh


control reduce by







0 05 1 15 2 25 3 35 4 45 5Time [S]

minus3

minus2

minus1

0

1

2

3

Vehi

cle b

ody

acce

lera

tion

[ms

2]



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus002

minus001

0

001

Pitc

h an

gle

[rad

]




0 05 1 15 2 25 3 35 4 45 5Time [S]

minus2

minus1

0

1

2

Airg

ap ec

cent

ricity

[m

]


times10-4


0 05 1 15 2 25 3 35 4 45 5Time [S]

minus004

minus002

0

002

004

Susp

ensio

n dy

nam

ic d

eflec

tions

[m

]



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus001

minus0005

0

0005

001

Tyre

def

orm

atio

n [m

]




0 05 1 15 2 25 3 35 4 45 5Time [S]

minus006

0

006

Stee

ring

angl

e for

sing

le la

ne ch

ange

[ra

d]



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus5

0

5

airg

ap ec

cent

ricity

[m

]

times10-4




f = VL

(36)



5 Conclusions



1 2 3 4 5Time [S]

minus5

0

5

Roll

angl

e [r

ad]

times10-3



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus002

0

002

Side

slip

angl

e [r

ad]








0 05 1 15 2 25 3 35 4 45 5Time [S]

minus04

0

04

yaw

rate

[ra

ds]

Figure 26 Yaw rate


Data Availability




Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





Vehicle drivemodel





Reference torque

Road


+-Driving torque



W = [W1W2W3 Wn]T


W = Wsumn

i=1Wi (i = 1 2 3 n)

(25)



120582max =nsumi=1

(HW)inWi

(i = 1 2 3 n) (26)






W1= Wi

120574i (28)

q1= 1

q2= 120573PA1205742

q3= 120573AEfl1205743

q4= 120573AEfr1205744

q5= 120573AErl1205745

q6= 120573AErr1205746

q7= 120573TDfl1205747

q8= 120573TDfr1205748

q9= 120573TDrl1205749

q10= 120573TDrr12057410

q11= 120573SDDfl12057411

q12= 120573SDDfr12057412

q13= 120573SDDrl12057413

q14 = 120573SDDrr12057414

(29)





J = 12 intinfin

0

q1z2b + q21205792 + q




7(zufl minus qfl)2







2sdot intinfin

0

YTQY + uTRu) dt

(30)



3 q4







J = 12 intinfin

0

[XTQ1015840X + 2XTNu + uTR1015840u] dt (31)

where


(32)

u = minusKX (33)



(34)



0 2 4 6 8 10 12 14 16 18 20Time [S]

minus005

005

015

025

Road

[m

]



PSD

of v

ehic

le b

ody

CG


1 12 1403

04

05

10minus2

100

10minus4

10minus6

acc

[(m

Ｍ2)2

Hz]









1 10 300

Frequency [Hz]

PSD

of a

irgap

ecce

ntric

ity


90 100 110

10e-1115e-11

10minus16

10minus14

10minus12

10minus10

10minus8

[(m

2)2

Hz]




90 100

5

10100

PSD

of s

tato

r CG

acc

[(m

Ｍ2)2

Hz]



PSD

of s

uspe

nsio

n dy

nam

ic

defle

ctio

ns [

m2 H

z]


1 12 148

10

12

10minus14

10minus8

10minus2

times10-5




PSD

of t

ire d

efor

mat

ion

[m2 H

z]


65 7112e-5

116e-5

10minus9

10minus7

10minus5


0 2 4 6 8 10 12 14 16 18 20Time [S]

0

01

03

Road

[m

] 02



PSD

of v

ehic

le b

ody

CG

acc

[(m

s2)2

Hz]


11 12 13 14070809

10minus5

100







PSD

of a

irgap

ecce

ntric

ity [

m2H

z]

104 105 106 107 108

12

16

2


10minus16

10minus12

10minus8

times10-10



PSD

of s

tato

r CG

acc [

(ms

2)2

Hz]

104 106 108

10

15


100



PSD

of s

uspe

nsio

n dy

nam

ic

defle

ctio

ns [

m2H

z]


09 1 11 12 1316

18

10minus14

10minus8

10minus2

times10-4




PSD

of t

ire d

efor

mat

ion

[m2H

z]


665 675188e-5

190e-5

10minus9

10minus7

10minus5


h

L









Frequencyresponse


60 kmh 100 kmh


control reduce by







0 05 1 15 2 25 3 35 4 45 5Time [S]

minus3

minus2

minus1

0

1

2

3

Vehi

cle b

ody

acce

lera

tion

[ms

2]



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus002

minus001

0

001

Pitc

h an

gle

[rad

]




0 05 1 15 2 25 3 35 4 45 5Time [S]

minus2

minus1

0

1

2

Airg

ap ec

cent

ricity

[m

]


times10-4


0 05 1 15 2 25 3 35 4 45 5Time [S]

minus004

minus002

0

002

004

Susp

ensio

n dy

nam

ic d

eflec

tions

[m

]



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus001

minus0005

0

0005

001

Tyre

def

orm

atio

n [m

]




0 05 1 15 2 25 3 35 4 45 5Time [S]

minus006

0

006

Stee

ring

angl

e for

sing

le la

ne ch

ange

[ra

d]



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus5

0

5

airg

ap ec

cent

ricity

[m

]

times10-4




f = VL

(36)



5 Conclusions



1 2 3 4 5Time [S]

minus5

0

5

Roll

angl

e [r

ad]

times10-3



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus002

0

002

Side

slip

angl

e [r

ad]








0 05 1 15 2 25 3 35 4 45 5Time [S]

minus04

0

04

yaw

rate

[ra

ds]

Figure 26 Yaw rate


Data Availability




Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





J = 12 intinfin

0

q1z2b + q21205792 + q




7(zufl minus qfl)2







2sdot intinfin

0

YTQY + uTRu) dt

(30)



3 q4







J = 12 intinfin

0

[XTQ1015840X + 2XTNu + uTR1015840u] dt (31)

where


(32)

u = minusKX (33)



(34)



0 2 4 6 8 10 12 14 16 18 20Time [S]

minus005

005

015

025

Road

[m

]



PSD

of v

ehic

le b

ody

CG


1 12 1403

04

05

10minus2

100

10minus4

10minus6

acc

[(m

Ｍ2)2

Hz]









1 10 300

Frequency [Hz]

PSD

of a

irgap

ecce

ntric

ity


90 100 110

10e-1115e-11

10minus16

10minus14

10minus12

10minus10

10minus8

[(m

2)2

Hz]




90 100

5

10100

PSD

of s

tato

r CG

acc

[(m

Ｍ2)2

Hz]



PSD

of s

uspe

nsio

n dy

nam

ic

defle

ctio

ns [

m2 H

z]


1 12 148

10

12

10minus14

10minus8

10minus2

times10-5




PSD

of t

ire d

efor

mat

ion

[m2 H

z]


65 7112e-5

116e-5

10minus9

10minus7

10minus5


0 2 4 6 8 10 12 14 16 18 20Time [S]

0

01

03

Road

[m

] 02



PSD

of v

ehic

le b

ody

CG

acc

[(m

s2)2

Hz]


11 12 13 14070809

10minus5

100







PSD

of a

irgap

ecce

ntric

ity [

m2H

z]

104 105 106 107 108

12

16

2


10minus16

10minus12

10minus8

times10-10



PSD

of s

tato

r CG

acc [

(ms

2)2

Hz]

104 106 108

10

15


100



PSD

of s

uspe

nsio

n dy

nam

ic

defle

ctio

ns [

m2H

z]


09 1 11 12 1316

18

10minus14

10minus8

10minus2

times10-4




PSD

of t

ire d

efor

mat

ion

[m2H

z]


665 675188e-5

190e-5

10minus9

10minus7

10minus5


h

L









Frequencyresponse


60 kmh 100 kmh


control reduce by







0 05 1 15 2 25 3 35 4 45 5Time [S]

minus3

minus2

minus1

0

1

2

3

Vehi

cle b

ody

acce

lera

tion

[ms

2]



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus002

minus001

0

001

Pitc

h an

gle

[rad

]




0 05 1 15 2 25 3 35 4 45 5Time [S]

minus2

minus1

0

1

2

Airg

ap ec

cent

ricity

[m

]


times10-4


0 05 1 15 2 25 3 35 4 45 5Time [S]

minus004

minus002

0

002

004

Susp

ensio

n dy

nam

ic d

eflec

tions

[m

]



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus001

minus0005

0

0005

001

Tyre

def

orm

atio

n [m

]




0 05 1 15 2 25 3 35 4 45 5Time [S]

minus006

0

006

Stee

ring

angl

e for

sing

le la

ne ch

ange

[ra

d]



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus5

0

5

airg

ap ec

cent

ricity

[m

]

times10-4




f = VL

(36)



5 Conclusions



1 2 3 4 5Time [S]

minus5

0

5

Roll

angl

e [r

ad]

times10-3



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus002

0

002

Side

slip

angl

e [r

ad]








0 05 1 15 2 25 3 35 4 45 5Time [S]

minus04

0

04

yaw

rate

[ra

ds]

Figure 26 Yaw rate


Data Availability




Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



1 10 300

Frequency [Hz]

PSD

of a

irgap

ecce

ntric

ity


90 100 110

10e-1115e-11

10minus16

10minus14

10minus12

10minus10

10minus8

[(m

2)2

Hz]




90 100

5

10100

PSD

of s

tato

r CG

acc

[(m

Ｍ2)2

Hz]



PSD

of s

uspe

nsio

n dy

nam

ic

defle

ctio

ns [

m2 H

z]


1 12 148

10

12

10minus14

10minus8

10minus2

times10-5




PSD

of t

ire d

efor

mat

ion

[m2 H

z]


65 7112e-5

116e-5

10minus9

10minus7

10minus5


0 2 4 6 8 10 12 14 16 18 20Time [S]

0

01

03

Road

[m

] 02



PSD

of v

ehic

le b

ody

CG

acc

[(m

s2)2

Hz]


11 12 13 14070809

10minus5

100







PSD

of a

irgap

ecce

ntric

ity [

m2H

z]

104 105 106 107 108

12

16

2


10minus16

10minus12

10minus8

times10-10



PSD

of s

tato

r CG

acc [

(ms

2)2

Hz]

104 106 108

10

15


100



PSD

of s

uspe

nsio

n dy

nam

ic

defle

ctio

ns [

m2H

z]


09 1 11 12 1316

18

10minus14

10minus8

10minus2

times10-4




PSD

of t

ire d

efor

mat

ion

[m2H

z]


665 675188e-5

190e-5

10minus9

10minus7

10minus5


h

L









Frequencyresponse


60 kmh 100 kmh


control reduce by







0 05 1 15 2 25 3 35 4 45 5Time [S]

minus3

minus2

minus1

0

1

2

3

Vehi

cle b

ody

acce

lera

tion

[ms

2]



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus002

minus001

0

001

Pitc

h an

gle

[rad

]




0 05 1 15 2 25 3 35 4 45 5Time [S]

minus2

minus1

0

1

2

Airg

ap ec

cent

ricity

[m

]


times10-4


0 05 1 15 2 25 3 35 4 45 5Time [S]

minus004

minus002

0

002

004

Susp

ensio

n dy

nam

ic d

eflec

tions

[m

]



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus001

minus0005

0

0005

001

Tyre

def

orm

atio

n [m

]




0 05 1 15 2 25 3 35 4 45 5Time [S]

minus006

0

006

Stee

ring

angl

e for

sing

le la

ne ch

ange

[ra

d]



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus5

0

5

airg

ap ec

cent

ricity

[m

]

times10-4




f = VL

(36)



5 Conclusions



1 2 3 4 5Time [S]

minus5

0

5

Roll

angl

e [r

ad]

times10-3



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus002

0

002

Side

slip

angl

e [r

ad]








0 05 1 15 2 25 3 35 4 45 5Time [S]

minus04

0

04

yaw

rate

[ra

ds]

Figure 26 Yaw rate


Data Availability




Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




PSD

of a

irgap

ecce

ntric

ity [

m2H

z]

104 105 106 107 108

12

16

2


10minus16

10minus12

10minus8

times10-10



PSD

of s

tato

r CG

acc [

(ms

2)2

Hz]

104 106 108

10

15


100



PSD

of s

uspe

nsio

n dy

nam

ic

defle

ctio

ns [

m2H

z]


09 1 11 12 1316

18

10minus14

10minus8

10minus2

times10-4




PSD

of t

ire d

efor

mat

ion

[m2H

z]


665 675188e-5

190e-5

10minus9

10minus7

10minus5


h

L









Frequencyresponse


60 kmh 100 kmh


control reduce by







0 05 1 15 2 25 3 35 4 45 5Time [S]

minus3

minus2

minus1

0

1

2

3

Vehi

cle b

ody

acce

lera

tion

[ms

2]



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus002

minus001

0

001

Pitc

h an

gle

[rad

]




0 05 1 15 2 25 3 35 4 45 5Time [S]

minus2

minus1

0

1

2

Airg

ap ec

cent

ricity

[m

]


times10-4


0 05 1 15 2 25 3 35 4 45 5Time [S]

minus004

minus002

0

002

004

Susp

ensio

n dy

nam

ic d

eflec

tions

[m

]



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus001

minus0005

0

0005

001

Tyre

def

orm

atio

n [m

]




0 05 1 15 2 25 3 35 4 45 5Time [S]

minus006

0

006

Stee

ring

angl

e for

sing

le la

ne ch

ange

[ra

d]



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus5

0

5

airg

ap ec

cent

ricity

[m

]

times10-4




f = VL

(36)



5 Conclusions



1 2 3 4 5Time [S]

minus5

0

5

Roll

angl

e [r

ad]

times10-3



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus002

0

002

Side

slip

angl

e [r

ad]








0 05 1 15 2 25 3 35 4 45 5Time [S]

minus04

0

04

yaw

rate

[ra

ds]

Figure 26 Yaw rate


Data Availability




Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Frequencyresponse


60 kmh 100 kmh


control reduce by







0 05 1 15 2 25 3 35 4 45 5Time [S]

minus3

minus2

minus1

0

1

2

3

Vehi

cle b

ody

acce

lera

tion

[ms

2]



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus002

minus001

0

001

Pitc

h an

gle

[rad

]




0 05 1 15 2 25 3 35 4 45 5Time [S]

minus2

minus1

0

1

2

Airg

ap ec

cent

ricity

[m

]


times10-4


0 05 1 15 2 25 3 35 4 45 5Time [S]

minus004

minus002

0

002

004

Susp

ensio

n dy

nam

ic d

eflec

tions

[m

]



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus001

minus0005

0

0005

001

Tyre

def

orm

atio

n [m

]




0 05 1 15 2 25 3 35 4 45 5Time [S]

minus006

0

006

Stee

ring

angl

e for

sing

le la

ne ch

ange

[ra

d]



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus5

0

5

airg

ap ec

cent

ricity

[m

]

times10-4




f = VL

(36)



5 Conclusions



1 2 3 4 5Time [S]

minus5

0

5

Roll

angl

e [r

ad]

times10-3



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus002

0

002

Side

slip

angl

e [r

ad]








0 05 1 15 2 25 3 35 4 45 5Time [S]

minus04

0

04

yaw

rate

[ra

ds]

Figure 26 Yaw rate


Data Availability




Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus006

0

006

Stee

ring

angl

e for

sing

le la

ne ch

ange

[ra

d]



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus5

0

5

airg

ap ec

cent

ricity

[m

]

times10-4




f = VL

(36)



5 Conclusions



1 2 3 4 5Time [S]

minus5

0

5

Roll

angl

e [r

ad]

times10-3



0 05 1 15 2 25 3 35 4 45 5Time [S]

minus002

0

002

Side

slip

angl

e [r

ad]








0 05 1 15 2 25 3 35 4 45 5Time [S]

minus04

0

04

yaw

rate

[ra

ds]

Figure 26 Yaw rate


Data Availability




Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




0 05 1 15 2 25 3 35 4 45 5Time [S]

minus04

0

04

yaw

rate

[ra

ds]

Figure 26 Yaw rate


Data Availability




Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia












RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Documents

Suppression of Switched Reluctance Motor Vibration of In ...downloads.hindawi.com/journals/jcse/2018/1689690.pdfSwitched reluctance motor (SRM) has achieved good per-formance due to