2009-IE-Adaptive Control for Virtual Steering Characteristics on EV Using SBW

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 5, MAY 2009 1585

Adaptive Control for Virtual Steering Characteristicson Electric Vehicle Using Steer-by-Wire System

Yousuke Yamaguchi and Toshiyuki Murakami, Member, IEEE

Abstract—This paper describes an adaptive control to realizethe desired steering characteristics on a vehicle. As is well known,the steering characteristics indicate handling performance on avehicle and are important for safe driving. In this paper, a strategyto adjust it to a driver’s preference easily using a Steer-by-Wiresystem is proposed. The control system including the proposedmethod intervenes only when the front tire cornering stiffnessundergoes many changes. Then, the estimated self-aligning torqueis fed back to the steering wheel so that a driver can feel reactiontorque from the road. This is one of the remarkable features inthe proposed Steer-by-Wire system. Numerical simulation andexperiment are carried out to show the validity of the proposedmethod.

Index Terms—Parameter identification, steer-by-wire system,steering characteristics, steering control, vehicle state estimation.

I. INTRODUCTION

ADVANCED Cruise-Assist Highway Systems, AdvancedSafety Vehicle (ASV), and other development concepts

related to Intelligent Transport Systems are expected to supportthe reduction of burden imposed on the driver greatly andimprove vehicle dynamics control [1][15]. Some papers havereported estimation strategies of road condition [13], [14], [17].Safety driving for drivers has been analyzed in [16]. Moreover,several control strategies for stable vehicle motion have beenproposed in [17]–[22]. In the category of ASV, particularlyactive safety technology, many control methods have beenproposed to realize safe yaw motion of a vehicle. One approachfor yaw dynamics improvement is to control individual wheeldriving/braking force, thereby obtains the moment that is nec-essary to counteract the undesired yaw motion [2]. Moreover,some of these technologies are in practical use now. The otherapproach is to command additional steering angles to create thecounteracting moment [3]. Lately, X-by-Wire control systemshave begun to be used in this field [4]. X-by-Wire controlsystems in automotive applications refer to systems where theinput device used by the driver is connected to the actuationpower subsystem by electrical wires, as opposed to being con-nected by mechanical or hydraulic means. The “X” in the X-by-Wire is replaced by throttle, brake, steer, and so on. Fig. 1 showsa photograph of a Steer-by-Wire system used in this paper.

Manuscript received May 11, 2008; revised November 4, 2008. First pub-lished November 25, 2008; current version published April 29, 2009. Thiswork was supported in part by Grant in Aid for the 21st Century Center ofExcellence for “System Design: Paradigm Shift from Intelligence to Life” fromthe Ministry of Education, Culture, Sport, and Technology in Japan.

The authors are with the Department of System Design Engineering, KeioUniversity, Yokohama 223-8522, Japan (e-mail: [email protected];[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIE.2008.2010171

Fig. 1. Outline view of steer-by-wire system.

Recent advance of electric power steering systems make itpossible to realize intelligent assist of driver’s steering action[5], [6], [21]. In the Steer-by-Wire system, the direct connectionbetween the driver and wheel assembly is removed, and dualactuators are introduced to control the driver interface and thesteering system instead. In the conventional steering system,there is a mechanical linkage between the steering wheel andthe front-wheels, so active steering control is hard to applybecause of the interference with the driver. In addition, itrequires physical modification of its mechanism to changesteering characteristics of the vehicle.

On the other hand, the potential ability of Steer-by-Wiresystem has received considerable attention from the automotiveindustry. The advantage of the system brigs an important featureto control the steering wheel and the front-wheel steeringindependently. Therefore, it is possible to realize the desiredsteering characteristics without driver’s uncomfortable feeling.Furthermore, the relation between the steering wheel and thefront-wheel steering becomes more flexible, so various sophis-ticated design of power steering system can be expected [4].

Several ideas using Steer-by-Wire system have been pro-posed. Segawa et al. [7] implement lateral acceleration andyaw rate feedback control system to the vehicle with a Steer-by-Wire system and show more improved driving stabilitythan differential brake control. In [8], Yih and Gerdes proposea method for altering a vehicle’s handling characteristics byaugmenting the driver’s steering command with full vehiclestate feedback, which are chassis sideslip angle and yaw rate, byusing a combination of global positioning system and inertialnavigation system sensors. The aforementioned strategies arepowerful, but there are still several issues shown below.

1) It is assumed that vehicle parameter is known in advance,and controller is sensitive against parameter uncertainties.

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1586 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 5, MAY 2009

2) There is no feedback to reflect variation of road surfaceto the steering wheel.

The improvement of the first issue is important. In particular,the tire cornering stiffness, which is one of important vehicleparameters, is affected by road condition, tire characteristics,and so on. This means that it is difficult to realize accuratevehicle yaw motion control by simple state feedback in thepractical implementation. The second issue is about vehiclemaneuverability. An adequate torque transmission from roadto the driver through steering wheel is very important for thedriver to achieve safety driving of the vehicle.

To address the aforementioned issues, this paper focuses on arealization of the desired steering characteristics independentlyof road condition. In order to modify the steering characteristicsaccording to the change of road surface, an adaptive controlmethod based on a Steer-by-Wire system is proposed. Theadaptive algorithm utilizes lateral acceleration observer withparameter identification. It is one of remarkable points of thispaper. The proposed method, which is active front steering, setsdriver definable front cornering stiffness and adjusts steeringcharacteristics by vehicle full state feedback control, so itrequires yaw rate and chassis sideslip angle which show vehiclelateral dynamics. Yaw rate is measurable easily by low-costgyro sensor. On the other hand, the chassis sideslip angle isestimated by an adaptive observer [9]. The control systemincluding the proposed method intervenes only when the fronttire cornering stiffness undergoes great changes that the vehiclemotion gets into a situation where it is difficult for the driverto handle. In the proposed approach, it possible to improvehandling performance of the vehicle according to such a criticalsituation. Moreover, self-aligning torque which is part of thetire force is estimated from information of steering motor andvehicle model, and is fed back to the Steer-by-Wire controlsystem for driver’s perception of road condition.

This paper is organized as follows. In Section II, the vehi-cle model and lateral dynamics is introduced. In Section III,adaptive control method for virtual steering characteristics isproposed. Then, motor control method in Steer-by-Wire systemis described in Section IV. In Sections V and VI, the numericaland experimental results are shown to verify the effectivenessof the proposed method. Finally, conclusions are described inSection VII.

II. VEHICLE DYNAMICS

A. Tire Force

Fig. 2 shows tire forces generated at front-left wheel. Param-eters of vehicle dynamics are shown in Table I. F x and F y aredriving force and lateral force. F y is generated by sideslippingof each tire. CF means cornering force. In the linear region oftire characteristics, CFfl is composed of cornering stiffness Cf

and αfl

CFfl = −Cfαfl. (1)

From Fig. 2, relation between F yfl and CFfl at front-left wheel

is represented as

F yfl =

CFfl

cos αfl. (2)

Fig. 2. Tire force at front-left wheel. (a) Tire forces. (b) Self-aligning torque.

TABLE IPARAMETERS OF VEHICLE DYNAMICS

Fig. 3. Vehicle model.

Moreover, while a vehicle is turning, tire force acting on thesteering system tends to resist steering motion away from thestraight-ahead position. This torque is tire self-aligning torque,which is a function of the steering geometry, particularly casterangle, and the manner in which the tire deforms to generatelateral force. In Fig. 2, ξc is the caster trail, the distance from thetire center to the point on the ground about that the tire pivotsas a result of the wheel caster angle, ξp is the pneumatic trail,the distance from the center of tire to the application of lateralforce. Self-aligning torque is given by

τSAT = (ξc + ξp) (F yfl + F y

fr) . (3)

B. Yaw Motion of a Vehicle

Vehicle dynamics in the horizontal plane is represented byfour-wheeled model, as shown in Fig. 3. From Figs. 2 and 3,tire sideslip angle at a front-left wheel is given as follows:

αfl = arctan

(V sinβ + lfγ

V cos β − L2 γ

)− δf . (4)

YAMAGUCHI AND MURAKAMI: ADAPTIVE CONTROL FOR VIRTUAL STEERING CHARACTERISTICS 1587

Fig. 4. Steering characteristics.

Slip angle at each tire is calculated as well as (4). In this paper,driving force F x at each tire is supposed to be equal to zero.Therefore, the yaw motion equation for the vehicle model iswritten as follows:

My = (F yfl + F y

fr) cos δf + F yrl + F y

rr (5)

Jγ = lf cos δf (F yfl + F y

fr) +L

2sin δf (F y

fl − F yfr)

− lr (F yrl + F y

rr) (6)

where y is lateral acceleration at COG of vehicle. Then, underthe assumption that |V | ≈ 0 and |β|, |(Lγ/2V )| � 1, it is alsoassumed that tire force at left side, right side is the same [21].Therefore, (5) and (6) are rewritten as

My = − 2Cf

(β +

lfV

γ − δf

)− 2Cr

(β − lr

Vγ

)(7)

Jγ = − 2lfCf

(β +

lfV

γ − δf

)+ 2lrCr

(β − lr

Vγ

). (8)

Moreover, from Fig. 3, y is related to β and γ as follows:

y = (V sin β + V β cos β + V γ cos β)≈V (β + γ). (9)

Therefore, the state equation for vehicle model is given as(10) from (7)–(9)

x =Ax + bδf

x = [β γ ]T

A =[ −2Cf+Cr

MV −1 − 2 lfCf−lrCrMV 2

−2 lfCf−lrCrJ −2 l2f Cf+l2r Cr

JV

]

b = [ 2CfMV

2lfCfJ ]T . (10)

Equation (10) has state variables of vehicle here defined bychassis sideslip angle and yaw rate. lfCf − lrCr is called steer-ing characteristics and indicates vehicle motion behavior, asshown in Fig. 4. Then, the steering characteristics are classifiedbelow

lfCf − lrCr > 0 over steering

lfCf − lrCr < 0 under steering

lfCf − lrCr = 0 neutral steering. (11)

III. CONTROL FOR STEERING CHARACTERISTICS

An approach to change steering characteristics depending onthe driver’s preference is proposed. This method is composedof the following three parts. First, a linear observer of β isintroduced. Next, identification approach of cornering stiffness,which is a parameter that the observer and control method needfor adaptation to various driving conditions, is described. Atthe last part, cornering stiffness at front tire changing control isexplained.

A. Estimation of Chassis Sideslip Angle

Before now, linear observer using only γ as measurablestate variable has been used as a method to estimate chassissideslip angle. However, this method has a serious problem.When lfCf − lrCr is equal to zero, the system (10) falls intounobservable. Then, y is added to output equation and it isrewritten as follows:

y = cx + dδf

y = [ γ y ]T

c =[

0 1V a11 V (1 + a12)

]d = [ 0 V b1 ]T (12)

where a, b are elements of the matrix A, b. By (12), fullobservability is satisfied in any condition. The observer isdesigned as follows:

˙x = Ax + bδf + K(i) (y − y) . (13)

This observer is called Lateral Acceleration Observer (LAO)[10]. Here, using poles of the observer λ1, λ2, observer gainmatrix K(i) is decided as

K(1) =

[ Jλ1λ2(lfCf−lrCr)2CfCr(lf+lr)2

− 1 1V

−λ1 − λ2M(l2f Cf+l2r Cr)J(lfCf−lrCr)

]. (14)

When lfCf − lrCr = 0, K(i) changes to K(2) in order toimprove the problem that k

(1)22 , which is an element of K(1),

have to be set to ∞

K(2) =

[−λ1λ2 − 1 1

V

−λ1 − λ2 − JV

2(l2f Cf+l2r Cr) − M2(Cf+Cr)

]. (15)

Therefore, the estimated β converges to β even if lfCf − lrCr

is equal to zero.

B. Identification of Cornering Stiffness

Parameter uncertainty of a vehicle is not considered whenLAO described in the above is applied to the system. Therefore,the estimation error remains in β. In order to solve this problem,parameter identification method is incorporated into LAO. Themost important parameter is tire cornering stiffness, becausethe value changes often depending on driving condition. Here,identification method of cornering stiffness at front/rear tirebased on the weighted recursive least-squares (RLS) algorithm


[9] is applied. The conventional method [9] is based on yawmoment equation (8). Then, the output equation is as follows:

y1 =θT1 η1

y1 =Jγ

θ1 = [Cf Cr ]T

η1 =

⎡⎣−2lf

(β + lf

V γ − δf

)2lr

(β − lr

V γ)

⎤⎦ (16)

where β is the chassis sideslip angle estimated by LAO. How-ever, the moment of vehicle inertia J and γ used in (16) aredifficult to measure with high accuracy. The low-cost yawrate sensor is available, but yaw rate accelerations sensor isexpensive. Then, the time differentiation of the yaw rate may becalculated, but the sensor noise is emphasized in the controller.This is confirmed by experiments shown in the latter part. Toimprove this issue, this paper proposes the parameter identifica-tion method based on lateral motion equation (7) instead of (8)

y2 =θT2 η2

y2 =My

θ2 = [Cf Cr ]T

η2 =

⎡⎣−2

(β + lf

V γ − δf

)−2

(β − lr

V γ)

⎤⎦ . (17)

The advantage of this method is that the measured variabley is directly available by acceleration sensor. If yaw momentequation is used, it is necessary to differentiate measured γ forobtaining γ. Additionally, mass M is measurable very easily incase load on the vehicle changes. However, it is more difficultto know true value of vehicle inertia J in that case. Here,weighted RLS algorithm is used. The error E(i) is defined as

E(i) = yres2 (i) − θT

2 (i)η2(i). (18)

In addition, evaluation function J(θ) is set as follows:

J(θ) =k∑

i=0

σk−i (E(i))2 (19)

where σ is forgetting factor that is a weighting gain of past datain parameter identification process. In order to minimize J(θ),θ(k) is calculated by

θ(k) =Q(k)Z(k) (20)

Q(k) =

{k∑

i=0

σk−iη2(i)ηT2 (i)

}−1

(21)

Z(k) =

{k∑

i=0

σk−iη2(i)y2(i)

}. (22)

Then, the relation between Q(k) and Q(k − 1) is computed asfollows:

Q(k) =1σ

{Q(k − 1) − Q(k − 1)η2η

T2 Q(k − 1)

σ + ηT2 (k)Q(k − 1)η2(k)

}.

(23)

Moreover, the relation between Z(k) and Z(k − 1) isexpressed as

Z(k) = σZ(k − 1) + η2(k)y2(k). (24)

Finally, the identified cornering stiffness θ(k) is derived from(23) and (24) as

θ(k) = θ(k − 1) +Q(k − 1)η2

{y2(k) − ηT

2 θ(k − 1)}

σ + ηT2 (k)Q(k − 1)η2(k)

.

(25)

Then, LAO updating θ is restructured as follows:

˙x = A( ˆtheta)x + b(θ)δf + K(i)(θ)(y − y) (26)

y = c(θ)x + d(θ)δf . (27)

C. Adaptive Control for Virtual Steering Characteristics

The control law based on [8] which realizes the desiredcornering stiffness at front tire by active front steering isproposed. First, reference value of cornering stiffness at fronttire is defined as

Cf,th = Cf(1 + κ) (28)

where κ is the evaluation index of Cf . The controller intervenesonly when absolute value |κ| is more than κth which is the limitvalue of κ. In other words, κ shows acceptable variation ratioof the cornering stiffness to guarantee the desired steering char-acteristics. This constraint means the controller assists steeringonly when the vehicle motion gets into a situation where it isdifficult for the driver to handle. The steering angle input isdesigned as

δf = Kββ + Kγγ + Kswθresu (29)

where θresu is the response of steering wheel angle, Kβ , Kγ ,

Ksw are feedback gains. Then, the desired front corneringstiffness Cf is set as

Cf = Cf(1 + κ) (30)

and the gains as

Kβ = −κ Kγ = − lfV

κ Ksw =1 + κ

Grp(31)

where κ is the desired change factor in identified front corneringstiffness Cf , Grp is rack-and-pinion gear ratio. Substituting thefeedback law (29) into (10) yields the state space equationwith the new cornering stiffness Cf . By setting κ in advance,adaptive control to meet the original cornering stiffness rea-sonably is realized. Because vehicles steering characteristics


Fig. 5. Steer-by-Wire system model.

are directly influenced by tire cornering stiffness, this changecan make handling performance of the vehicle oversteering orundersteering depending on the value of κ.

IV. IMPEDANCE CONTROL FOR STEERING WHEEL

Fig. 5 shows the schematic of the Steer-by-Wire system. Thissystem has no mechanical linkage between the steering wheeland the front-wheels. τh is input torque of the driver, τu andτl are the torques generated by the steering wheel actuator andfront-wheels actuator, respectively. Moreover, θu and θl meanthe rotation angle of actuators.

In general, the response from the tire is important informa-tion for the driver to know the road condition. However, thetorque from the front-wheels is not transmitted to the driver ina conventional Steer-by-Wire control system.

In this paper, the estimated self-aligning torque is fed backto the steering wheel so that a driver can feel reaction torquefrom the road. Using lateral acceleration y, lateral forces areexpressed as

F yfl + F y

fr = 2(

M

Cry − 1

V(lf + lr) + δf

)CfCr

Cf + Cr. (32)

Substituting (32) and identified cornering stiffness Cf , Cr

into (3) yields

τSAT = 2(ξc + ξp)(

M

Cr

y − 1V

(lf + lr) + δf

)CfCr

Cf + Cr

.

(33)

Besides, impedance control law is applied to the steeringsystem in order to combine power assist for driver’s inputtorque via steering wheel and active return of self-aligningtorque smoothly. The concept of active return is simple andis essentially a control loop producing a component of overalltorque demand, which acts to power the steering back to thecenter position. Fig. 6 shows the block diagram of impedancecontrol system. Under the assumption that friction torque in theeach steering actuator is canceled by disturbance observer [11],angular acceleration reference θref

u at steering wheel actuator isdesigned as follows:

θrefu =

1Jc

{− Dcθ

resu − Kcθ

resu + (Khumτh − KSATτSAT)

}(34)

Fig. 6. Impedance control for the steering wheel.

where Jc, Dc, Kc are impedance gains, Khum, KSAT are scalefactors for power assist and perception of road condition. Thelarger Khum, the more the power assist works. The largerKSAT, the more the driver feels change of the road condition.The driver’s input torque τh is obtained by reaction torqueestimation observer [12] at steering actuator. Moreover, self-aligning torque is calculated by (33). By (34), transient re-sponse of upper motor is adjustable by selecting Kc, Dc, whichis related to both comfort of driving and driver’s perception ofroad condition. If θref

u is equivalent to the response of angularacceleration θres

u , the transfer function is calculated as

θresu (s) =

ω2n

s2 + 2ζωn + ω2n

Khumτh − KSATτSAT

Kc(35)

ζ =Dc

2√

JcKc

ωn =√

Kc

Jc(36)

where ζ and ωn are damping ratio and natural angular fre-quency, respectively. By selecting ζ, ωn appropriately, it is pos-sible to adjust sensitivity of driver’s perception against changeof road condition such as oscillation due to Shimmy effect. Thewhole control system of vehicle is summarized in Fig. 7. Asshown in this figure, the impedance control is employed in thesteering wheel actuator, and adaptive control for virtual steeringcharacteristics is applied to the front-wheels actuator. Thesetwo controllers are realized separately by using Steer-by-Wiresystem. This is an important point in the proposed approach.

V. SIMULATION

To verify the validity of the proposed estimation methodof vehicle parameters and control method for virtual steeringcharacteristics, two kinds of simulation are carried out. One isthe parameter identification of vehicle. The other is a realizationof the desired steering characteristics. The parameters and gainsused in simulation are summarized in Table II.

A. Estimation of Vehicle Parameters

First, the proposed parameter identification method is com-pared to the following two conventional methods, LAO inwhich vehicle parameters are constant and LAO using Cf , Cr

based on yaw moment equation. Here, the driver’s input θresu in

each case is shown in Fig. 8(a). In this figure, the upper motorresponse θres

u and the lower motor response θresl well coincide

with θresu by the disturbance observer-based motor control.

Here, the velocity of vehicle V is set as 5 m/s. The corneringstiffness Cf , Cr identified by the conventional approach and theproposed method are shown in Fig. 8(b) and (c), respectively.This result shows that the proposed method based on (7) aswell as the conventional approach based on (8) estimates the


Fig. 7. Steering control system.

TABLE IIPARAMETERS AND GAINS IN SIMULATION AND EXPERIMENT

cornering stiffness well. Fig. 8(d)–(f) shows the responses oftrue and estimated vehicle state variables. In case the observerwith fixed-parameter is used, it is found that the influenceof parameter uncertainty causes the error between the truevalue and estimated one in β response. On the other hand,the estimated chassis sideslip angle β by the use of LAO withidentified cornering stiffness shows the smooth convergence tothe true value. These results show that the proposed parameteridentification based on (8) is effective.

B. Control for Steering Characteristics

Next, in order to confirm the validity of adaptive controlfor virtual steering characteristics, alternative simulation isimplemented. In this simulation as well as previous one, thesame θcmd

u shown in Fig. 8(a) is assumed as driver’s input. Here,the value of κth which defines the range of application to thesteering system is 0.3 and κ has the same value. Because κ ispositive, the desired front cornering stiffness Cf is bigger thanactual Cf .

The results are shown in Fig. 9. As shown in Fig. 9(a),rotational angle of lower actuator in Steer-by-Wire systemθcmd

l , that is δf , is bigger than θresu because the controlled

input is added so that virtual front cornering stiffness becomesbigger than actual. Fig. 9(c) is the vehicle responses under theproposed control. Fig. 9(d) shows the vehicle behavior when

the actual front cornering stiffness Cf is equal to the desiredfront cornering stiffness Cf . From these results, it is found thatthe desired responses of both chassis sideslip angle β and yawrate γ are realized according to the desired cornering stiffnessby the proposed control method.

VI. EXPERIMENT

In this section, the experimental results of impedance controlfor the Steer-by-Wire system, the estimation method of thevehicle parameters, and adaptive control for virtual steeringcharacteristics are shown. Fig. 10 shows the experimental ve-hicle and the road condition which is dry asphalt. Moreover,the configuration of the vehicle is shown in Fig. 11. Parametersused in the experiment as well as simulation is shown inTable II.

A. Impedance Control for Steer-by-Wire System

In order to confirm the validity of the proposed control forthe Steer-by-Wire system, a slalom of the vehicle is carriedout. Here, ζ and ωn is set as 1.22 and 0.90, respectively. Thevehicle velocity V is 6.0 m/s. The response of each steeringactuator and the estimated self-aligning torque are shown inFig. 12. As described before, the self-aligning torque is part oftire force that is related to the reaction torque τ reac

l . Here, τ reacl

is estimated by the use of reaction torque estimation observeras comparison value of self-aligning torque. In Fig. 12, τSAT

calculated from (33) has similar tendency of τ reacl response.

This means that the calculation of τSAT is effective for thefeedback to realize the driver’s perception of road conditionfrom a viewpoint of practical implementation. In addition,it is confirmed that stable response of rotational angle andangular velocity of upper motor are achieved by the proposedcontrol method. In Fig. 13 which indicates relation betweenthe driver input torque and steering wheel angle, the estimatedhuman input torque τh decreases stably according to a decreaseof absolute value θres

u by the impedance control. From theseresults, it is verified that transmission of road condition andpower assist is realized by the proposed impedance controlmethod.


Fig. 8. Simulation: results of system identification and estimation. (a) Rotational angles response in Steer-by-Wire system. (b) Cf , Cr identification based onJγ. (c) Cf , Cr identification based on My. (d) LAO with fixed parameter. (e) LAO with Cf , Cr based on Jγ. (f) LAO with Cf , Cr based on My.


Fig. 9. Simulation: Result of adaptive control for virtual steering characteristics (κth: 0.3, κ: 0.3). (a) Controlled steering angle. (b) Cf , Cr. (c) Controlledvehicle behavior (Cf : 3800, Cr: 4500). (d) Vehicle behavior (Cf : 4920, Cr: 4500).

Fig. 10. Experimental setup and driving condition. (a) Experimental vehicle.(b) Road condition.

B. Estimation of Vehicle Parameters

Experiments of the vehicle slalom are carried out for vehicleparameter identification. As well as simulation, the proposedmethod is compared with conventional methods. The vehiclevelocity in each experiment is 6 m/s. Fig. 14 shows the results ofconventional parameter identification. The results of proposedparameter identification are shown in Fig. 15. In Fig. 14(d),the value of γ is obtained by the time differentiation of

Fig. 11. Configuration of the vehicle.

measured γ. Here, the true value of β in each experiment is sup-posed to be the value of simulation results. These simulationsare carried out according to the experimental data δf , steady-state value of Cf , Cr, and vehicle velocity V by using (10).


Fig. 12. Experiment: responses of steering actuators.

Fig. 13. Experiment: relation between τh and steering wheel angle.

Fig. 14. Experiment: conventional parameter identification and estimation(based on yaw moment equation). (a) Front-wheels actuator angle. (b) Cf , Cr

identification. (c) Response of β. (d) Measured γ.

In these experiments, LAO with fixed-parameter always hasestimation error because of model error. In Fig. 14(b), thereare some sharp fluctuations in the estimation values. Thisestimation method is based on moment of vehicle inertia J andγ, however, the obtained γ has significant noise, as shown inFig. 14(d). Therefore, the noise is thought to be aftereffectsof identification of cornering stiffness. It is contemplated thatthis fluctuations leads estimation error of β. On the other hand,the proposed method realizes better identification of corneringstiffness, as shown in Fig. 15(b) because the value of measuredy is smooth, as shown in Fig. 15(d). The aforementioned results

Fig. 15. Experiment: proposed parameter identification and estimation (basedon lateral motion equation). (a) Front-wheels actuator angle. (b) Cf , Cr

identification. (c) Response of β. (d) Measured y.

Fig. 16. Experiment: result of adaptive control for virtual steering charac-teristics (κth: 0.3, κ: 0.05). (a) Responses of steering actuators. (b) Cf , Cr

identification and κ. (c) Response of y. (d) Response of β. (e) Response of γ.(f) Vehicle velocity.

show that the proposed parameter identification strategy basedon the lateral motion equation (8) is effective for practicalimplementation.

C. Control for Steering Characteristics

In this section, the experimental results of adaptive control ofvirtual steering characteristics are shown. The value of κth is setas 0.3, the value of κ is 0.05. Fig. 16(a) shows the response ofrotational angle at each steering actuator. Fig. 16(b) shows Cf ,Cr and the evaluation index κ. In these figures, the intervention


of controller is observed after κ is over κth, and the controllerinput is added so that front cornering stiffness becomes biggerdue to κ. The vehicle behavior is shown in Fig. 16(c)–(e). Thesimulation results are obtained according to the experimentaldata δf , steady-state value of Cf , Cr and vehicle velocity V byusing (10). They are supposed to be true or desired values aswell as previous experiments. In Fig. 16(d), accurate estimationof chassis sideslip angle is realized. Moreover, experimentalresults of γ and y are pretty close to simulation results of them.Therefore, it would appear that steering characteristics of thisexperimental vehicle become desired.

VII. CONCLUSION

In this paper, an application to design steering wheel charac-teristics via a Steer-by-Wire system and a control method whichhelps the driver recognition of the road condition have beenproposed. The former is equivalent to physically changing thecornering stiffness at front tires, so very easy to realize the steer-ing characteristics depending on the factor κ. Additionally, bylimiting the range of the application, this control is performedonly when needed and the range is able to be adjusted with κth

very simply. The latter method realizes at the same time thefollowing three things, driver’s perception of road condition,power assist for the driver input torque, and active return ofself-aligning torque.

The validity of the proposed method were confirmed bysimulations and experiments.

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Yousuke Yamaguchi received the B.E. and M.E.degrees from Keio University, Yokohama, Japan, in2005 and 2007, respectively.

His research interests include intelligent vehiclesand motion control.

Toshiyuki Murakami (M’93) received the B.E.,M.E., and Ph.D. degrees in electrical engineeringfrom Keio University, Yokohama, Japan, in 1988,1990, and 1993, respectively.

Since 1993, he has been with Keio University,where he was first with the Department of ElectricalEngineering and is currently with the Departmentof System Design Engineering as a Professor. From1999 to 2000, he was a Visiting Researcher withthe Institute for Power Electronics and ElectricalDrives, Aachen University of Technology, Aachen,

Germany. His research interests include robotics, intelligent vehicles, mobilerobots, and motion control.

Documents

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