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Rolling Stability Control Based on Electronic Stability Program for In-wheel-motor Electric Vehicle

EVS24

Stavanger,Norway,May13-16,2009

Rolling Stability Control Based on Electronic Stability Program for

In-wheel-motor Electric Vehicle

Kiyotaka Kawashima,Toshiyuki Uchida,Yoichi Hori

University of Tokyo,Tokyo,Japan,kawashima@horilab.iis.u-tokyo.ac.jp

Abstract

In this paper,a novel robust rolling stability control(RSC)based on electronic stability program(ESP)for electric vehicle(EV)is proposed.Since EVs are driven by electric motors,they have the following four remarkable advan-tages:(1)motor torque generation is quick and accurate;(2)motor torque can be estimated precisely;(3)a motor can be attached to each wheel;and(4)motor can output negative torque as a brake actuator.These advantages en-able high performance three dimensional vehicle motion control with a distributed in-wheel-motor system.RSC is designed using two-degree-of-freedom control(2-DOF),which achieves tracking capability to reference value and disturbance suppression.Generally,RSC and YSC are incompatible.Therefore,ESP,which is composed of estima-tion system(S1)and integrated vehicle motion control system(S2)is proposed.A distribution ratio of RSC and YSC is de?ned based on rollover index(RI)which is calculated in S1from rolling state information.The effectiveness of proposed methods are shown by simulation and experimental results.

Keywords:rolling stability control,electric vehicle,disturbance observer,two-degrees-of-freedom control,vehicle motion control, identi?cation

Nomenclature

a x,a y:Longitudinal and lateral acceleration

a yd:Lateral acceleration disturbance

a yth:Critical lateral acceleration

c f,c r:Front an

d rear tir

e cornering stiffness

C r:Combined roll damping coef?cient

d,d f,d r:Tread at CG,front and rear axle

F xfl,F xfr,F xrl,F xrr:Tire longitudinal forces

F yfl,F yfr,F yrl,F yrr:Tire lateral forces

F zfl,F zfr,F zrl,F zrr:Tire normal forces

g:Gravity acceleration

h c,h cr:Hight of CG and distance from CG to roll center

I r:Moment of inertia about roll axis(before wheel-lift-off) I r2:Moment of inertia about roll axis(after wheel-lift-off) I y:Moment of inertia about yaw axis

K r:Combined roll stiffness coef?cient

l,l f,l r:Wheelbase and distance from CG to front and rear axle

M,M s,M u,:Vehicle,sprung and unsprung mass

N:Yaw moment by differential torque

V,V w:Vehicle and wheel speed

β,γ:Body slip angle and yaw rate

δ:Tire steering angle

φ,˙φ:Roll angle and roll rate

φth,˙φth:Threshold of roll angle and roll rate 1Introduction

1.1In-wheel-Motor Electric Vehicle’s Advan-

tages and Application to Vehicle Motion

Control

Electric vehicles(EVs)with distributed in-wheel-motor systems attract global attention not only from the en-vironmental point of view,but also from the vehicle motion control.In-wheel-motor EVs can realize high performance vehicle motion control by utilizing advan-tages of electric motors which internal combustion en-gines do not have.The EV has the following four re-markable advantages[1]:

?Motor torque response is10-100times faster than internal combustion engine’s one.This property enables high performance adhesion control,skid prevention and slip control.

?Motor torque can be measured easily by observing motor current.This property can be used for road condition estimation.

?Since an electric motor is compact and inexpen-sive,it can be equipped in each wheel.This fea-

ture realizes high performance three dimensional vehicle motion control.

?There is no difference between acceleration and deceleration control.This actuator advantage en-ables high performance braking control.

Slip prevention control is proposed utilizing fast torque response[1].Road condition and skid detection meth-ods are developed utilizing the advantage that torque can be measured easily[1].Yawing stability control, side slip angle estimation and control methods are also proposed by utilizing a distributed in-wheel-motor sys-tem[2]-[4].

1.2Background and Purpose of the Research The purpose of this paper is to propose integrated rolling and yawing stability control(RSC and YSC). Rollover stability is important for all classes of light-vehicles such as light trucks,vans,SUVs and espe-cially,for EVs which have narrow tread and high CG because EV is suitable for relatively small vehicle and human height does not change.According to the data from NHTSA,ratio of rollover accidents of pick ups’and vans’crashes in2002was only3%against whole accidents.However,nearly33%of all deaths from pas-senger vehicle crashes are due to rollover accidents[5]. Therefore,RSC is very important not only for ride qual-ity but also for safety.

The RSC system has been developed by several auto-motive makers and universities[6][7].Rollover detec-tion systems,such as rollover index(RI)[8]and Time-to-rollover(TTR)[9]are proposed for mitigating criti-cal rolling motion.

Every system controls braking force on each wheel in-dependently and suppresses sudden increase of lateral acceleration or roll angle.However,since braking force is the average value by pulse width modulation con-trol of brake pad,brake system cannot generate precise torque or positive torque.In the case of in-wheel-motor, both traction and braking force can be realized quickly and precisely.

In addition to actuator advantages,RSC is designed by utilizing two-degrees-of-freedom(2-DOF)control based on disturbance observer(DOB)[10].For the ve-hicle motion control?eld,DOB is applied to vehicle yaw/pitch rate control[2][3]and2-DOF control is ap-plied to the electric power steering control[11].There are three reasons to utilize DOB:1)disturbance suppres-sion,2)nominalize lateral vehicle model and3)tracking capability to reference value.DOB loop that suppresses the effect of disturbance,is faster than outer loop that achieves tracking capability.Designing DOB for trac-tion force is not applicable for ICEV,because engine torque is not accurately known and long time delay ex-ists.Therefore,DOB is applicable only in case of EVs. The tracking capability and robustness for lateral accel-eration disturbance against such as side blast are real-ized by the proposed method.

However,roll and yaw stabilities are incompatible. High rolling stability makes vehicle behavior under steer.On the other hand,high yawing stability to avoid vehicle side slip,vehicle roll stability is not guaranteed. In the next section,electronic stability program(ESP) on EV is introduced using RI based on vehicle ge-ometry and dynamics model,which achieves integrated three dimensional vehicle motion control.2Electronic Stability Program for Electric Vehicle

2.1Introduction of Electronic Stability Pro-

gram

Fig.1shows concept of ESP for EV.ESP consists of two systems;vehicle/road state estimation system (S1)and integrated vehicle motion control system(S2). S1integrates information from sensors(accelerome-ter,gyro,GPS,suspension stroke and steering angle sensors)and estimates unknown vehicle parameters (mass),vehicle state variables(yaw rate,lateral accel-eration,roll angle,roll rate and normal forces on tires) and environmental state variables[7][12]. According to the information from S1,S2controls ve-hicle dynamics using RSC and YSC,pitching stability control(PSC)and anti-slip control(ASC).According to RI,which is calculated by S1,a proper stability control strategy(YSC,RSC or mixed)is determined.

RSC is based on DOB and nominal vehicle state is cal-culated by a controller.If there are errors between cal-culated and actual dynamics,it is compensated by dif-ferential torque.

Figure1:ESP based on DOB

2.2A Scheme of Integrated Vehicle Motion

Control

Lateral acceleration is composed of vehicle side slip, yaw rate and longitudinal speed.

a y=(˙β+γ)V(1)

If constant vehicle speed is assumed and lateral acceler-ation is suppressed,yaw rate is also suppressed as long as differentiation of side slip is not controlled.This physical constraint makes RSC and YSC incompatible. Therefore,rollover detection is necessary for integrated control.In order to detect rollover,Yi proposed RI (0

Control algorithm is simple and given by following equation.Fig.2shows block diagram of three dimen-sional integrated vehicle motion control.

N ?=f (RI,N RSC ,N Y SC ,N DOB )

=RI ?N RSC +(1?RI )?N Y SC +N DOB (2)

Figure 2:Block diagram of integrated vehicle motion control

3Estimation System

S1is composed of vehicle parameters,state variables and environmental state variables estimation system.In this section,vehicle state variable estimation system is mainly introduced.According to the estimated state variables,RI ,a distribution ratio of RSC and YSC is determined.

3.1Lateral Acceleration and Roll Angle Ob-server

Fig.3shows four wheel model and rolling model of electric

vehicle.

(a)Four wheel model and

rotational direction

(b)Rolling model

Figure 3:Vehicle model

Vehicle motion is expressed as the following three lin-ear https://www.sodocs.net/doc/2513705253.html,teral motion:

MV (˙β

+γ)=F yfl +F yfr +F yrl +F yrr =?2c f (β+l f

V γ?δ)?2c r (β?l f V

γ)(3)

Yawing motion:

I y ˙γ=(F yfl +F yrl )l f ?(F yfr +F yrr )l r

=?2c f (β+l f V γ?δ)l f +2c r (β?l r

V γ)l r +N (4)

Rolling motion:

M s h cr a y =I r ¨φ

+C r ˙φ+K r φ?M s gh cr sinφ(5)(φ<φwheel ?lift ?off )

M s h cr a y =I r 2¨φ

?M s gh cr sinφ+M s g d 2

cosφ(6)

(φ>φwheel ?lift ?off )

Here,these motion equations need to be expressed as state equations to design observer.Observer gain ma-trix,however,becomes 2×4matrix if whole equations are combined.To reduce redundancy of designing gain matrix,tire dynamics and rolling dynamics are sepa-rated.A matrix,A rt connects two state equations.From eq.(3)and eq.(4),state equation is expressed as,

˙x t =A t x t +B t u ,(7)y t =C t x t +D t u .

(8)

It is noted that there is feedforward term in the transfer function from u to y t .Therefore,to eliminate feedfor-ward term and design stable observer,x t vector is de-?ned using differential torque and steering angle as the following equations,where,

x t = a y ?c 2δ˙a y ?c 2˙δ

?b 1N ?c 1δ

T ,y t =a y ,u = N δ T

,

A t =

01

?a 0?a 1

,

B t =

b 1

c 1

a 1

b 1+b 0a 1

c 1+c 0

,

C t

=

10 ,D t = 0c 2 .a 0=4c f c r l 2

MI y V 2?

2(c f l f ?c r l r )I y

,a 1=2M (c f l 2f +c r l 2r )+2I y (c f +c r

)MI y V

,

b 0=2(

c f +c r )

MI y ,b 1=?2(c f l f ?c r l r )MI y V

,

c 0=4c f c r l MI y ,c 1=4c f c r l r l MI y V ,c 2=2c f

N

,c 0

=c 0?a 0c 2,c 1=c

1?a 1c 2

From eq.(7),state space equation is,

˙x r =A r x r +A rt y t ,

(9)y r =C r x r ,

(10)

where,x r = φ˙φ

T ,y r =˙φ,A r = 01

?K r ?M s gh cr

I r ?C r I r ,A rt =

0M s h cr I r

,

C r = 01 .

These parameters are based on the experiment vehicle ”Capacitor-COMS1”developed in our research group.The method to evaluate the values of c f ,c r are referred to the paper [13],and rolling parameters to the paper [10]

It should be noted that lateral acceleration dynamics ex-pressed as eq.(8)is a linear time varying system de-pending on vehicle speed.The states are observable at various longitudinal speed except for a very low speed.In the following sections,for repeatability reason,ex-periment has been done under constant speed control.Observer gains are de?ned by pole assignment.

3.2Rollover Index

RI is a dimensionless number which indicates a danger of vehicle rollover.RI is de?ned using the following three vehicle rolling state variables;1)present state of roll angle and roll rate of the vehicle,2)present lateral acceleration of the vehicle and 3)time-to-wheel lift.RI is expressed as eq.(11),

RI =C 1 |φ|˙φth +|˙φ|φth φth ˙φth +C 2

|a y

|a yc ,+(1?C 1?C 2) |φ| φ2+˙φ2 ,if φ(˙φ

?k 1φ)>0,RI =0,else if φ(˙φ

?k 1φ)≤0,(11)where,C 1,C 2and k 1are positive constants (0

dynamics (eq.7).Fig.5shows phase plane plot under several initial condition (φ,˙φ)at critical lateral accel-eration.Consequently,φth and ˙φth are de?ned by the

analysis.

4Integrated Motion Control System 4.1Rolling Stability Control Based on Two-Degrees-of-Freedom Control In this section,RSC based on 2-DOF control which

achieves tracking capability to reference value and dis-turbance suppression is introduced.

For RSC,lateral acceleration is selected as controlling

parameter because roll angle information is relatively

slow due to roll dynamics (about 100ms).

R o ll a n g le (ra d)

L a t e r a l a c c e l e r a t i o n (m /s /s )

a Figure 4:Equilibrium lateral acceleration in rollover of a sus-pended vehicle

11R o ll a n g le (d e g )

R o l l r a t e (d e g /s )

Figure 5:Phase plane plot of roll dynamics 4.1.1Lateral acceleration disturbance observer Based on ?g.6,transfer function from reference lateral

acceleration u ,δand a yd to a y is expressed as the fol-lowing equation.Roll moment is applied by differential torque N ?by right and left in-wheel-motors.Reference value of lateral acceleration is given by steering angle

and vehicle speed.a y =P a y N P n Na y

(K ff +K fb )1+P a y N P n Na y K fb u +P a y δ1+P a y N P n Na y K fb δ+11+P a y N P n Na y

K fb a yd .(12)Tracking capability and disturbance suppression are two important performances in dynamics system con-trol and can be controlled independently.On the other hand,one-degree-of-freedom (1-DOF)control such as PID controller loses important information at subtract-ing actual value from reference one.In the control,there is only one way to set feedback gain as high to im-prove disturbance suppression performance,however the gain makes the system unstable.

Hence 2-DOF control in terms of tracking capability and disturbance suppression is applied to RSC.Pro-posed lateral acceleration DOB estimates external dis-turbance to the system using information;V ,δ,N and a y .Fig.6shows the block diagram of lateral accelera-tion DOB.

Figure6:Block diagram of lateral acceleration

DOB

Figure7:Block diagram of2-DOF for RSC based on DOB Estimated lateral acceleration disturbance?a yd and a y are expressed as

?a yd=a y?P n a

y N N??P n a

δ,(13)

a y=P a

y N N?+P a

δ+a yd.(14)

?a yd=P n

Na y

P Na

y

P Na

y

P n

Na y

?1

a y+(P a

?P n a

)δ+a yd

.(15)

In eq.(15),the?rst and the second terms are modeling errors and the third term is lateral disturbance.If mod-eling error is small enough,a yth is approximately equal to actual lateral acceleration disturbance.

4.1.2Disturbance suppression and normalize of

roll model

Fig.7shows the proposed2-DOF control for RSC. Estimated lateral acceleration disturbance is fedback to lateral acceleration reference multiplied by?lter Q.

a?y=v?Q?a yd.(16) Filter Q is low pass?lter and expressed as the following equation[14].In this study,the cut-off frequency is set as63rad/s.

Q=1+

N?r

k=1

a k(τs)k

1+

N

k=1

a k(τs)k

,(17)

where r must be equal or greater than relative order of the transfer function of the nominal plant.Substituting eq.(16)to eq.(13),the following equation is de?ned.

a y=v+P n a

yδδ+(1?Q)?a yd.(18)

Disturbance,which is lower than the cut-off frequency

of Q and vehicle dynamics,is suppressed by DOB.In

addition to the function of disturbance rejection,the

plant is nearly equal to nominal model in lower fre-

quency region than the cut-off frequency.Therefore the

proposed RSC has the function of model following con-

trol.

4.2Yawing Stability Control

As?g.2shows,YSC is yaw rate control.Yaw rate

reference value is de?ned by steering angle and longi-

tudinal vehicle speed.Transfer function from yaw rate

reference and steering angle is expressed as the follow-

ing equation.

γ=

PγN P n

(K ff+K fb)

1+PγN P n

K fb

u+

Pγδ

1+PγN P n

K fb

δ.(19)

5Simulation Results

Three dimensional vehicle motion simulations have

been conducted with combination software of Car-

Sim7.1.1and MATLAB R2006b/Simulink.

At?rst,the effectiveness of RSC is veri?https://www.sodocs.net/doc/2513705253.html,t-

eral acceleration disturbance is generated by differen-

tial torque for repeatability reason of experiments.In

the simulation,lateral blast is generated at straight and

curve road driving,the proposed DOB suppresses the

disturbance effectively.

To show the effectiveness of ESP,lateral acceleration

response and trajectory at curving are compared.It

is shown that lateral acceleration is unnecessarily sup-

pressed only with RSC,however,tracking capability to

yaw rate reference is achieved by ESP.

5.1Effectiveness of RSC

5.1.1Vehicle Stability under Crosswind Distur-

bance

Vehicle stability of RSC under crosswind disturbance is

demonstrated.At?rst,the vehicle goes straight and a

driver holds steering angle(holding steering wheel

as0

deg).Under20km/h vehicle speed control,crosswind

is applied during3-6sec.Fig.8shows the simulation

results.

-1

-0.5

L

a

t

e

r

a

l

a

c

c

e

l

e

r

a

t

i

o

n

(

m

/

s

/

s

)

(a)Lateral acceleration

-0.2

-0.1

Y

a

w

r

a

t

e

(

r

a

d

)

(b)Yaw rate

Figure8:Simulation result of RSC:Disturbance suppression

at straight road drive

When proposed RSC is activated,the proposed lateral acceleration DOB detects the lateral acceleration distur-bance and suppresses it.

Then,disturbance is applied at curve road driving.Un-der 20km/h constant speed control as well,180deg step steering is applied with roll moment disturbance dur-ing 3-6sec.Fig.9shows decrease of lateral accelera-tion since disturbance is rejected perfectly by differen-tial torque with RSC.The robustness of RSC is veri?ed with simulation results.

-1-0.5L a t e r a l a c c e l e r a t i o n

(a)Lateral acceleration Y a w r a t e

(b)Yaw rate

Figure 9:Simulation result of RSC:Disturbance suppression

at curving

5.1.2Tracking capability to reference value In this section,tracking capability of RSC to reference value is veri?ed with simulation results.Under 20km/h vehicle speed control,180deg sinusoidal steering is ap-plied and reference value of lateral acceleration is 80%of nominal value.Fig.10shows that lateral accelera-tion follows reference value with RSC.

5.2Effectiveness of ESP

Rollover experiment can not be achieved because of

safety reason.Under 20km/h constant speed control,240deg step steering is applied.From ?g.16,with only RSC case,even though the danger of rollover is not so high,lateral acceleration is strongly suppressed and trajectory of the vehicle is far off the road.On the other hand,with ESP case,the rise of lateral accelera-tion is recovered and steady state yaw rate is controlled so that it becomes close to no control case.

6Experimental Results

6.1Experimental setup

A novel one seater micro EV named ”Capacitor COMS1”is developed for vehicle motion control exper-iments.The vehicle equips two in-wheel motors in the rear tires,a steering sensor,an acceleration sensor and gyro sensors to detect roll and yaw motion.An upper micro controller collects sensor information with A/D converters,calculates reference torques and outputs to the inverter with DA converter.In this system,sampling time is 1(msec).

Fig.12shows the vehicle control system and TABLE I shows the speci?cations of the experimental vehicle.

-6-4

-2

T i me (s )

L a t e r a l a c c e e l r a t i o n (m /s /s )

Figure 10:Simulation result of RSC:tracking capability to

reference

L a t e r a l a c c e l e r a t i o n (m s /s /s )

-0.010.0.02

0.0.04R o l l a n g l e (r a d )

(b)Roll angle

Y a w r a t e (r a d /s )

(c)Yaw rate 111Y (m )

(d)Trajectory

Figure 11:Simulation result of ESP:Step steering maneuver

At ?rst,disturbance suppression performance and tracking capability to reference value are veri?ed with experimental results.Then,effectiveness of ESP is demonstrated.In the experiment,since vehicle rollover experiment is not possible due to safety reason,step re-sponse of lateral acceleration and yaw rate are evalu-ated.

6.2Effectiveness of RSC

6.2.1Vehicle Stability under Crosswind Distur-bance For repeatability reason,roll moment disturbance is generated by differential torque.Under 20km/h con-stant speed control,roll moment disturbance is applied from 1sec.The disturbance is detected by DOB and compensated by differential torque of right and left in-wheel motors.Here,the cut-off frequency of the low pass ?lter is 63rad/s.

Fig.13shows disturbance suppression during straight road driving.Step disturbance roll moment (equivalent

Figure 12:Control system of experimental vehicle

Table 1:Drive train speci?cation of experimental vehicle

Motor

Category IPMSM

Phase/Pole 3/12Rating power/Max 0.29kW/2kW Max torque 100Nm Max velocity 50km/h

Inverter

Switching Hardware MOS FET Control method PWM vector control

to 0.5m/s 2?h c r )is applied around 1sec.In the case

without any control and only with FB control of RSC,lateral acceleration is not eliminated and vehicle trajec-tory is shifted in a wide range.On the other hand,in the case with DOB,disturbance is suppressed and vehicle trajectory is maintained.

Fig.14shows the experimental results of disturbance suppression at curve road driving.Under 20km/h con-stant speed control,240deg steering is applied and dis-turbance is applied at around 2.5sec.In this case,data is normalized by maximum lateral acceleration.In the case with RSC DOB,whole effect of disturbance is

sup-pressed as no disturbance case.In the case without RSC,lateral acceleration decreases about 25%and ve-hicle behavior becomes unstable.

6.2.2Tracking capability to reference value In the previous section,since it was assured that the in-ner DOB loop is designed properly,tracking capability to reference value is veri?ed with experimental results.180deg sinusoidal steering is applied and reference lat-eral acceleration is 80%of nominal value.The outer loop is designed with pole root loci method.Fig.15

-1.5-1

-0.5

L a t e r a l a c c e l e r a t i o n (m /s /s )

(a)Lateral acceleration

-0.2-0.15-0.1

-0.050.0.Y a w r a t e (r a d /s )

(b)Yaw rate

Figure 13:Experimental result of RSC:Disturbance suppres-sion at straight road drive

T i me (s )

N o r m a l i z e d l a t e r a l a c c e l e r a t i o n

(a)Lateral acceleration T ime(s)

N o r m a l i z e d y a w r a t e

(b)Yaw rate

Figure 14:Experimental result of RSC:Disturbance suppres-sion at curve road driving

shows that in the case with RSC,tracking capability to

reference value is achieved.

6.3Effectiveness of ESP

Effectiveness of ESP is demonstrated by experiments.For safety reason,rollover experiment is impossible.Therefore,experimental condition is the same as 5.2.Under 20km/h constant speed control,180deg step steering is applied.

Fig.16shows that in the case with only RSC,lateral acceleration and yaw rate are strongly suppressed.On the other hand,in the case with ESP,yaw rate is recov-ered close to reference value.In addition,the rise of lateral acceleration is also recovered and stable corner-ing is achieved with ESP.

7Conclusion

In this paper,a novel RSC based on ESP utilizing dif-ferential torque of in-wheel-motor EV is proposed.Ef-fectiveness of novel RSC designed by 2-DOF control is veri?ed with simulation and experimental results.Then incompatibility of RSC and YSC is described and ESP is proposed to solve the problem utilizing RI which is calculated using estimated value of estimation sys-tem of ESP.Experimental results validates the proposed ESP.

Acknowledgments

The author and the work are supported by Japan Society for the Promotion of Science.

T i me (s )

L a t e r a l a c c e l e r a t i o n (m /s /s )

Figure 15:Experimental result of RSC:tracking capability

to reference

L a t e r a l a c c e l e r a t i o n (m /s /s )

(a)Lateral

acceleration

0.02

0.04

0.06

0.08

R o l l a n g l e (r a d )

(b)Roll

angle

-0.22

4

68

Y a w r a t e (r a d /s )

(c)Yaw rate

-51015

20

Y (m )(d)Trajectory

Figure 16:Experimental result of ESP:Step steering maneu-ver

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Authors

He received B.C.and M.S.degrees in E.E.department,the University of Tokyo in 2004and 2006,and pro-ceeded to Ph.D.course,the University of Tokyo.He is now researching the motion control of electric vehicle.

He is working as a engineering of?cial in E.E.department,the University of Tokyo

He received Ph.D degree in E.E.from the UT in 1983and became a Profes-sor in 2000.IEEE Fellow.He is now an AdCom member of IEEE-IES.He is the President of IEE-Japan IAS in 08’-09’.His research ?elds are control the-ory and its industrial application to EV ,mechatronics,robotics,etc.

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