design of adaptive sliding mode controller for robust...

EVS26Los Angeles, California, May 6 - 9, 2012

Design of Adaptive Sliding Mode Controller for Robust Yaw

Stabilization of In-wheel-motor-driven Electric Vehicles

Kanghyun Nam1, Sehoon Oh1, Hiroshi Fujimoto2, and Yoichi Hori21Department of Electrical Engineering, Hongo Bunkyo-ku Tokyo 113-8656,

[email protected]; [email protected] of Advanced Energy, Kashiwa, Chiba, Japan 277-8561,

[email protected]; [email protected]

Abstract

A robust yaw stability control system is designed to stabilize the vehicle yaw motion. Since the vehiclesundergo changes in parameters and disturbances with respect to the wide range of driving condition,e.g., tire-road conditions, a robust control design technique is required to guarantee system stability. Inthis paper, a sliding mode control methodology is applied to make vehicle yaw rate to track its referencewith robustness against model uncertainties and disturbances. A parameter adaptation law is applied toestimate varying vehicle parameters with respect to road conditions and is incorporated into sliding modecontrol framework. The control performance of the proposed control system is evaluated through com-puter simulation using CarSim vehicle model which proved to give a good description of the dynamics ofan experimental in-wheel-motor-driven electric vehicle. Moreover, field tests were carried out to verifythe effectiveness of the proposed adaptive sliding mode controller.

Keywords: Adaptive sliding mode control, In-wheel motor-driven electric vehicle, Yaw stabilization

1 Introduction

Due to the increasing concerns about advancedmotion control of electric vehicles with in-wheelmotors, a great deal of research on dynamics con-trol for electric vehicles has been carried out [1]–[5]. Advanced motion control systems for elec-tric vehicles, slip prevention, spinout prevention,and excessive roll prevention, are referred to asyaw stability control and roll stability control, re-spectively. Compared with internal combustionengine vehicles, electric vehicles with in-wheelmotors have several advantages in the viewpointof motion control [1], [3].

1. The torque generation of driving motors isvery fast and accurate.

2. The driving torque can be easily measuredfrom motor current.

3. Each wheel with an in-wheel motor can beindependently controlled.

The purpose of vehicle motion controls is to pre-vent unintended vehicle behavior through activevehicle control and assist drivers in maintain-ing controllability and stability of vehicles. Themain goal of most motion control systems is tocontrol the yaw rate of the vehicles. In [6], di-rect yaw moment control based on side slip an-gle estimation was proposed for improving thestability of in-wheel-motor-driven electric vehi-cles (IWM-EV). A fuzzy-rule-based control andsliding mode control algorithms for vehicle sta-bility enhancement were proposed and evaluatedthrough experiments [7], [8]. A novel yaw sta-bility control method based on robust yaw mo-ment observer (YMO) design is presented andits practical effectiveness was verified throughvarious field tests [9]. Parameter uncertaintiesshown in a vehicle model and external distur-bances acting on vehicles are compensated by thedisturbance observer and yaw stabilization is re-alized through yaw rate feedback control. In thispaper, a sliding model control method with pa-

EVS26 International Battery, Hybrid and Fuel Cell Electric Vehicle Symposium 1

rameter adaptation is employed for robust yawstabilization of electric vehicles. The proposedcontrol structure employs a reference generator,which is designed from driver’s commands, asliding mode controller, and parameter adapta-tion laws. The sliding mode control techniqueis well-known robust control methodology par-ticularly suitable for dealing with nonlinear sys-tems with model uncertainties and disturbanceslike the considered vehicle systems. Since thevehicles operate under wide range of road con-ditions and speed, the controller should providerobustness against varying parameters and unde-sired disturbances all over the driving regions.In [10], a cascade vehicle yaw stability controlsystem was designed with the sliding mode andbackstepping control approaches. In [11], a vehi-cle yaw controller via second-order sliding modetechnique was designed to guarantee robust sta-bility in front of disturbances and model uncer-tainties.In order to compensate the disturbances andmodel uncertainties existing in control law, theadaptive sliding mode control method is applied.By combining with the defined sliding surface, asliding mode controller is re-designed such thatthe state (i.e., yaw rate) is moved from the out-side to inside of the region, and finally, it remainsinside the region even though there are model un-certainties and disturbances, which can be esti-mated and then rejected by adaptation law.In order to verify the control performances, thecomputer simulation is performed using a Car-Sim vehicle model, which proved to give agood description of the dynamics of an in-wheel-motor driven electric vehicle developed by theHori/Fujimoto research team (see [12] and [13]),as compared with test data. This paper is or-ganized as follows. A vehicle model for con-trol design is introduced in Section 2. A slidingmode controller combining parameter adaptationapproaches is proposed and the stability of botha sliding mode control law and an adaptation lawis proved in Section 3. The simulation and ex-periment results are presented and discussed inSection 4. Finally, conclusions and future worksare presented in Section 5.

2 Vehicle Modeling

In this section, a yaw plane model is introducedto describe the motion of an in-wheel-motordriven electric vehicle. The main difference withcommonly used vehicle dynamics is that the di-rect yaw moment is an additional input variable,which is generated by motor torque differencebetween each wheel. The yaw plane represen-tation with direct yaw moment is shown in Fig.1.From the linear single track vehicle model asshown in Fig. 1 (b), the governing equation foryaw motion is given by

Izγ = lfFyf cos δf − lrF

yr +Mz (1)

where γ is the yaw rate, Iz is the yaw momentof inertia, F y

f and F yr are the front and rear lat-

fl

rl

fδ

d

y

rrF

x

rrF

y

rlF

x

rlF

x

frFx

flF

X

Y

y

flFy

frFxv

yv γCG

y

fFfα

rαzM

y

rF

γzM

β

fδ fδ

β

CG

(a) (b)

Figure 1: Planar vehicle model: (a) Four wheelmodel, (b) Single track model (i.e., bicycle model).

eral tire forces, respectively, lf and lr are the dis-tance from vehicle center of gravity (CG) to frontand rear axles, δf is the front steering angle, andthe yaw moment Mz indicates a direct yaw mo-ment control input, which is generated by the in-dependent torque control of in-wheel motors andis used to stabilize the vehicle motion, and can becalculated as follows:

Mz =d

2(F x

rr − F xrl) +

d

2(F x

fr − F xfl) cos δf (2)

Here, longitudinal tire forces can be obtainedfrom a driving force observer (shown in Fig. 2),which is designed based on wheel rotational mo-tion [14], and the estimate of longitudinal tireforces is expressed as

F xi =

ωD

s+ ωD

(Tmi − Iωωis

r

)(3)

where F xi is the estimated longitudinal tire force

at ith wheel, Tmi is the motor torque acting on

each wheel, Iω is the wheel inertia, ωi is an an-gular velocity of the wheel, r is an effective tireradius, and ωD is a cutoff frequency of the ap-plied low-pass filter which rejects high frequencynoises cause by time derivative of ωi.In order to describe the vehicle motion, a lineartire model is used. For small tire slip angles, thelateral tire forces can be linearly approximated asfollows:

F yf = −2Cfαf = −2Cf

(β +

γlfvx− δf

)(4)

F yr = −2Crαr = −2Cr

(β − γlr

vx

)(5)

where β is a vehicle sideslip angle, vx is the vehi-cle speed, αf and αr are tire slip angles of front


m

iT

iω

r

x

iF

1

I sω

I sω

m

iT

D

Ds +

ω

ω

iω

x

iF1

r

+−

(a) (b)

DFO

Figure 2: (a) Wheel rotational motion, (b) Block dia-gram of a driving force observer (DFO) [14].

and rear tires, and Cf and Cr are the front andrear tire cornering stiffness, respectively.From (1), (4), and (5), yaw dynamics is ex-pressed as

Izγ = −2(l2fCf + l2rCr)

vxγ + 2lfCfδf +Mz

− 2β(lfCf − lrCr) +Md (6)

where Md is the yaw moment disturbance whichmay be caused by unstable road condition or sidewind etc., the yaw moment generated by vehiclesideslip, i.e.,−2β(lfCf− lrCr), is considered asa disturbance. In Md is defined as a lumped yawmoment disturbance and can be expressed as

Md = −2β(lfCf − lrCr) +Md (7)

Assumption: The lumped disturbance Md(t),which varies with tire-road condition and vehicleparameters, is bounded and satisfy the followingcondition

‖Md(t)‖ ≤ κ (8)

where κ is the upper bound of the disturbance.Thus, yaw dynamics equation (6) can be consid-ered as a time-varying two input and one outputsystem and rewritten as

Izγ = −Bγ + 2lfCfδf +Mz + Md (9)

where B is defined as a yaw damping coeffi-cient which varies with vehicle speed and tire-road condition.

3 Design of Adaptive Sliding

Mode Controller

3.1 Overall Control structure

The proposed control system is depicted in Fig.3. A reference generator makes a desired yawrate γd from driver’s steering command δcmd and

vehicle speed vx. The feedback controller is de-signed to make yaw moment to compensate yawrate tracking error (i.e., γd − γ) based on thestandard sliding mode control methodology. Fortreating model uncertainties and disturbances ex-isting in a feedback control law, parameters in adesigned sliding mode control law are updatedaccording to adaptation laws. The external inputMd accounts for yaw moment disturbance causedby lateral wind, unbalanced road conditions, andunbalanced tire pressure ,etc. With well-tunedcontrol parameters, a proposed controller con-tributes to keeping the vehicle yaw rate followingits target commanded by the driver.

3.2 Reference Generation: Desired Yaw

Response

The objective of the yaw stability control is toimprove the vehicle steadiness and transient re-sponse properties, enhancing vehicle handlingperformance and maintaining stability in thosecornering maneuvers, i.e., the yaw rate γ shouldbe close to desired vehicle responses (i.e., γd).The desired vehicle response is defined based ondriver’s cornering intention (e.g., driver’s steer-ing command and vehicle speed). Desired vehi-cle yaw rate response for given steering angle andvehicle speed is obtained as follows:

γd =K(vx)

1 + τs· δcmd

K(vx) =1

1 + kusv2x

vxl,

kus =m(lrCr − lfCf )

2l2CfCr(10)

where τ is a cutoff frequency of desired modelfilters, kus is a vehicle stability factor which ex-plains the steering characteristics of the vehicles.The sign of lrCr− lfCf in kus represents the ve-hicle motion behavior by steering action and thesteering characteristics are classified as follows:

lrCr − lfCf > 0 : under steeringlrCr − lfCf = 0 : neutral steeringlrCr − lfCf < 0 : over steering. (11)

3.3 Sliding Mode Control

It is well known that sliding mode control is arobust control method to stabilize nonlinear anduncertain systems which have attractive featuresto keep the systems insensitive to the uncertain-ties on the sliding surface [15]. The conventionalsliding mode control design approach consists oftwo steps. First, a sliding surface is designedsuch that the system trajectory along the surfaceacquires certain desired properties. Then, a dis-continuous control is designed such that the sys-tem trajectories reach the sliding surface in finitetime. A sliding mode control as a general design


cmdδ+

−

Adaptation law:

γ

ˆ2

x

B

v

dM

dγ zM

B

ˆf

C

p zk I

sgn( )s zk I ⋅ ⋅

( )

1

xK v

sτ+

zI s

ˆ2 f fl C

+

+ +

−

Adaptation law:

IWM

electric

vehicle

+

Figure 3: Block diagram of an adaptive sliding mode controller.

technique for control systems has been well es-tablished, the advantages of a sliding model con-trol method are:

• fast response and good transient perfor-mance

• its robustness against a large class of pertur-bations or model uncertainties

• the possibility of stabilizing some complexnonlinear systems which are difficult to sta-bilize by continuous state feedback laws.

Based on above advantages, sliding mode con-trol has been applied to vehicle control systems[10] and [11]. As usual in the sliding modecontrol technique, the control forces the sys-tem evolution on a certain surface which guar-antees the achievement of the control require-ments. In order to achieve control objective, i.e.,limt→∞S(t) = 0, the sliding surface S(t) is de-fined as

S = γ − γd (12)

Here we can see that the sliding condition S(t) =0 means a zero tracking error.By designing a satisfactory dynamics feedbackcontrol law, the trajectory of the closed-loop sys-tem can be driven on the sliding surface (12)and evolve along it, and yaw stabilization canbe achieved. In order to achieve control require-ments, a following reaching condition to be sat-isfied is designed as

S = −kPS − kS · sgn(S) (13)

where the kP > 0 is a control parameter whichdetermines the convergence rate of a tracking er-ror, the kS > 0 is a control parameter whichshould be tunned according to bound of uncer-tainties and disturbances.

From (6), (12), and (13), we can apply standardsliding mode control method [15] and thereby thefollowing control law can be obtained

Mz(t) = Izγd(t) +2B

vx(t)γ(t)− 2lfCfδf (t)

− kP IzS − kSIz · sgn(S) (14)

We can prove that the sliding mode controllaw (14) makes the closed-loop control systemasymptotically stable by introducing followingpositive definite Lyapunov function

V =1

2S2 (15)

The time derivative of (15) is

V = SS = S(γ − γd)

= S

[−2(l2fCf + l2rCr)

Izvxγ +

2lfCfδfIz

+Mz

Iz− γd

]= S(−kPS − kS · sgn(S))

= −kPS2 − kS |S| < 0. (16)

Thus, the control objective, i.e., S(t)→ 0 as t→∞, can be achieved by the control law (14).Remark 1: In (14), the sliding mode switchinggain kS is selected considering uncertainty anddisturbance bound. From assumption (8), kSshould be determined by considering the distur-bance bound. Moreover, the maximum kS whichcan be selected is limited by the maximum torquethat an in-wheel motor generates. By properlytuning kP and kS , the chattering in control law isalso reduced.


3.4 Sliding Mode Control with Parame-

ter Adaptation

For treating the disturbance and inertia uncer-tainty existing in the control law (14), adaptivecontrol method is a natural choice and has beenwidely applied. Combing with the defined slid-ing surface, a sliding mode controller can be de-signed such that the system state is moved fromthe outside to the inside of the region, and finallyremains inside the region in spite of the uncer-tainty and disturbance which can be estimatedand then rejected under the help of adaptive law.Thus, based on above analysis, the control law(14) is modified as

Mz(t) = Izγd(t) +2B

vx(t)γ(t)− 2lf Cfδf (t)

− kP IzS − kSIz · sgn(S) (17)

where the adaptation law for the estimated pa-rameter B and Cf are chosen as

˙B(t) = − 2k1

Izvx(t)γ(t)S − η1k1B (18)

˙Cf (t) = −2lfk2

Izδf (t)S − η2k2Cf . (19)

Here B = B(t)−B, Cf = Cf (t)−Cf , k1 and k2are adaptation gains which determine the updaterate, η1 and η2 are positive constant values.Remark 2: The main objective of parameteradaptation is to compensate parameter uncer-tainty and disturbance which varies with tire-road conditions. The adaptation law (18), (19)consists of a tracking error (i.e., S(t)) correctionterm. An adaptation law is rewritten in terms ofLaplace transform as follows:

B(s) =η1k1

s+ η1k1B +

(2k1Izvx

)1

s+ η1k1γS

(20)

Cf (s) =η2k2

s+ η2k2Cf +

(2k2lfIz

)1

s+ η2k2δfS

(21)

where the small s is a Laplace variable.Theorem. Considering vehicle yaw dynamicswith designed sliding surface, the trajectory ofthe closed-loop control system can be driven onto the sliding surface S(t) = 0 with the proposedadaptive control law and adaptation update law,and finally converge to the pre-defined referencetrajectory.Proof: Consider the following positive definiteLyapunov function:

V =1

2S2 +

1

2k1B2 +

1

2k2Cf

2. (22)

The time derivative of (22) is as follows:

V = SS +1

k1B

˙B +

1

k2Cf

˙Cf

= S

[2γ

IzvxB − 2lfδf

IzCf − kPS

− kS · sgn(S)]+

1

k1B

˙B +

1

k2Cf

˙Cf .

(23)

With the adaptation law, this can be rewritten asfollows:

V = SS +1

k1B

˙B +

1

k2Cf

˙Cf

= S

[2γ

IzvxB − 2lfδf

IzCf − kPS

− kS · sgn(S)]

+1

k1B

(− 2k1Izvx

γS − η1k1B

)

+1

k2Cf

(−2lfk2

Izδf (t)S − η2k2Cf

)= −kPS2 − kS |S| − η1B

2 − η2C2f < 0.

(24)

This shows that the tacking error S(t) asymptot-ically converges to zero and the yaw stabilizationis achieved.Remark 3: The control parameters kP and kS incontrol law (14) play a important role in controlsystem. These parameters determine the conver-gence rate of the sliding surface. It is noted thata larger kP will force the yaw rate to converge tothe desired yaw rate trajectory with a high speed.However, in practice, a compromise between theresponse speed and control input should be made.Since a too big kP will require a very high con-trol input, which is always bounded in reality.Therefore, the control parameter kP can not beselected too large.Remark 4: The control law (14) is discontinu-ous when crossing the sliding surface S(t) =0, which may lead to the undesirable chatteringproblem due to the measurement noise and someactuator delay. This problem can be eliminatedby replacing a discontinuous switching function(i.e., sgn(S)) with a saturation function sat(S)with the boundary layer thickness Φ as the con-tinuous approximation of a signum function

sgn(S) ≈ sat(S

Φ

)

=

⎧⎪⎪⎨⎪⎪⎩

S

Φ, if |S

Φ| < 1

sgn(S

Φ

), otherwise

(25)


Thus, this offers a continuous approximation tothe discontinuous sliding mode control law in-side the boundary layer and guarantees the mo-tion within the neighborhood of the sliding sur-face.

3.5 In-wheel-motor Torque Distribution

The control yaw moment Mz is distributed to tworeal in-wheel motors based on following equa-tions [9].

Mz =d

2(F x

rr − F xrl) (26)

Tcmd = Tmrr + Tm

rl (27)

where it is assumed that the vehicle is rear wheeldriving, the torque control commands to two rearin-wheel motors are calculated as Tm

rr = rF xrr

and Tmrl = rF x

rl, respectively.

4 Simulation and Experiment

4.1 Simulation Study

Computer simulations were performed to eval-uate the proposed control system. Based onspecifications of an experimental electric vehicle,the simulation vehicle model was obtained usingCarSim. Simulation environment using CarSimmodel and Matlab/simulink were constructed forimplementation of proposed control algorithms.The proposed stability control system was evalu-ated through cosimulation for double lane changeand step steering tests. A double lane changetest was performed at vx=60 km/h on a high-μroad (i.e., μ=0.9). Fig. 4 shows the simulationresults. Fig. 4(a) and (b) represent updated pa-rameters by defined adaptation laws. It can beseen that parameters (i.e., B and Cf ) stay closeto nominal values when the sliding surface is al-most the same as zero, on the other hand, param-eters are adapted when the tracking error exists.Fig. 4 (c),(d) indicates the control law Mz andcontrol torque command of in-wheel motors, re-spectively. From Fig. 4 (e) and (f), we can seethat the vehicle with a proposed controller welltracks the desired vehicle response with a smalltracking error.Fig. 5 shows the results of a step steering test.In order to verify the robustness of a proposedcontroller, the external yaw moment disturbance(Md = 300 Nm) is intentionally inserted at timeinstant t =12 sec.As can be seen from Fig. 5(e), if the control is setoff, the vehicle shows the spin-out, which causesthe vehicles to lose stability and unable to accom-plish the desired vehicle motion. From simula-tion results Fig. 4(c) and Fig. 5(c), we can seethat the control law could avoid undesirable chat-tering through the continuous approximation of asignum function.

4.2 Experimental Verification

The proposed adaptive sliding mode controllerwas implemented on the experimental in-wheel-motor-driven electric vehicle shown in Fig. 6.An experimental electric vehicle which was de-veloped by the Hori/Fujimoto research team isequipped with direct-drive motors in each wheel.Fig.7 illustrates the driving motor installed ineach wheel. The specification of an experimentalelectric vehicle used in field tests is presented inTable I.

Figure 6: Experimental in-wheel-motor-driven elec-tric vehicle.

Figure 7: In-wheel motor.

Table 1: Specification of an experimental electric ve-hicle

Total weight

Wheel base

Track width

Yaw moment of inertia

Spin inertia for each wheel

In-wheel motor

Max. Power

Max. Torque

Max. Speed

Controller

Steering system

Suspension system

875 kg

1.715 m

1.3 m

617 kg·m²

1.26 kg·m²

PMSM (outer rotor type )

20.0 kW (for one front motor)

500 Nm (for one front motor )

1113 rpm

AutoBox-DS1103

Steer-by-Wire

Double wishbone type

Battery Lithium-ion


0 5 10 15 200

1

2

3

4

5x 10

4

Time [sec](a)

Par

amet

er a

dap

tati

on

: B

[m

2N

/rad

]

0 5 10 15 200

0.5

1

1.5

2x 10

4

Time [sec](b)

Par

amet

er a

dap

tati

on

: C

f [N

/rad

]

0 5 10 15 20-1000

-500

0

500

1000

Time [sec](c)

Co

ntr

ol

law

: M

z [N

m]

0 5 10 15 20-100

-50

0

50

100

150

Time [sec](d)

In-w

hee

l m

oto

r to

rqu

e [N

m]

Rear left

Rear right

0 5 10 15 20

-20

0

20

Time [sec](e)

Yaw

rat

e [d

egre

e/s]

Desired yaw rate

Without control

ASMC

0 5 10 15 20

-10

-5

0

5

Time [sec](f)

Sli

din

g s

urf

ace:

tra

ckin

g e

rro

r [d

egre

e/se

c]

Without control

ASMC

Figure 4: Simulation result of a sine steering test on high-μ: (a) Estimated parameter: B, (b) Estimated parameter:Cf , (c) Control law: Mz , (d) Control torque of In-wheel motor, (e) Yaw rate, (f) Sliding surface: tracking error.

0 5 10 15 200

1

2

3

4

5x 10

4

Time [sec](a)

Par

amet

er a

dap

tati

on

: B

[m

2N

/rad

]

0 5 10 15 200

0.5

1

1.5

2x 10

4

Time [sec](b)

Par

amet

er a

dap

tati

on

: C

f [N

/rad

]

0 5 10 15 20

-500

0

500

Time [sec](c)

Co

ntr

ol

law

: M

z [N

m]

0 5 10 15 20-100

-50

0

50

100

150

Time [sec](d)

In-w

hee

l m

oto

r to

rqu

e [N

m]

Rear left

Rear right

0 5 10 15 20

0

20

40

60

Time [sec](e)

Yaw

rat

e [d

egre

e/s]

Desired yaw rate

Without control

ASMC

0 5 10 15 20-10

-5

0

5

10

Time [sec](f)S

lid

ing

su

rfac

e: t

rack

ing

err

or

[deg

ree/

sec]

Without control

ASMC

Figure 5: Simulation result of a step steering test on high-μ: (a) Estimated parameter: B, (b) Estimated parameter:Cf , (c) Control law: Mz , (d) Control torque of In-wheel motor, (e) Yaw rate, (f) Sliding surface: tracking error.


To demonstrate the performance and effective-ness of the proposed adaptive sliding mode con-troller, field tests were carried out with follow-ing driving conditions; 1) constant vehicle speed,i.e., vx=20 km/h; 2) step steering command, i.e.,δcmd=0.2 rad; 3) a proposed controller begins towork by enabling the manual control switch; 4)front-wheel driving mode; 5) dry asphalt.

0 5 10 15 20 250

1

2

3

4x 10

4

Para

met

er a

dapt

atio

n: B

[m

2 N/r

ad]

Time [sec]

control on

control off control off

(a)

0 5 10 15 20 250

5000

10000

15000

20000

Para

met

er a

dapt

atio

n: C

f [N

/rad

]

Time [sec]

control on

control off control off

(b)

0 5 10 15 20 250

500

1000

1500

Time [sec]

Yaw

mom

ent [

Nm

]

Control law: Mz

(c)

0 5 10 15 20 25−400

−300

−200

−100

0

100

200

300

Time [sec]

Mot

or to

rque

[N

m]

Driver torque commandIn−wheel motor torque: Front leftIn−wheel motor torque: Front right

(d)

Figure 8: Experimental results of a step steering testat vx=20 km/h on dry asphalt: (a) Estimated parame-ter: B. (b) Estimated parameter: Cf . (c) Control law:Mz . (d) Control torque of In-wheel motor.

0 5 10 15 20 250

5

10

15

20

Time [sec]

Yaw

rat

e [d

egre

e/se

c]

Desired yaw rateMeasured yaw rate: Gyro sensor

control off

control on

control off

(a)

0 5 10 15 20 25−2

−1

0

1

2

3

4

5

Yaw

rat

e [d

egre

e/se

c]

Time [sec]

Sliding surface: tracking error

(b)

Figure 9: Experimental results of a step steering testat vx=20 km/h on dry asphalt: (a) Yaw rate. (b) Slid-ing surface: tracking error.

Fig. 8 shows the experimental results for the pro-posed adaptive sliding mode controller. A con-troller begins to work when the control switch(see the thick gray line in Fig. 8 (a),(b)) is turnedon by a driver. That is, at t=11.5 sec, a proposedcontroller begins to work. A step steering in-put has been commanded by a driver at t=5 secand an steering motor controller has worked fortracking the driver’s steering command. Fig. 8(a) and (b) represent the results of estimated pa-rameters which are defined in section 3.4. Fig. 8(c) shows the control law Mz which is the out-put of an adaptive sliding mode controller. Thiscontrol law is allocated to front left and right mo-tors based on (2). In this field tests, front drivingmotors are used for yaw moment control and fol-lowing equation is used for control torque distri-bution.

Mz =d

2(F x

fr − F xfl) cos δf (28)

Measured torques of front left and right in-wheelmotors are illustrated in Fig. 8 (d).Fig. 9 represents the results for yaw rate control.We can confirm that the proposed adaptive slid-ing mode controller stabilizes the vehicle motionfrom the result of Fig. 9 (a). At t=11.5 sec, thecontroller begun to work and an actual vehicleyaw rate well tracks the desired yaw rate with-out a noticeable tracking error. Even though fieldtests are performed at low speed, the effective-ness of the proposed adaptive sliding mode con-troller is verified through experimental results of


Gyro sensor

control oncontrol

G

ng errorn

Fig. 9. The sliding surface S(t), which indi-cates a tracking error of the yaw rate, has con-verged to zero as shown in Fig. 9. Through the-oretical and experimental verification, it is con-firmed that tracking performances and stabilityof the proposed adaptive sliding mode controllerare achieved.

5 Conclusion and Future Works

This paper has presented an adaptive slidingmode control method for yaw stability enhance-ment of in-wheel-motor-driven electric vehicles.The proposed control structure is composed ofa reference generator, a feedback controller (i.e.,sliding mode controller), and parameter adapta-tion laws. The sliding mode control method,that is capable of guaranteeing robust stabilityin the presence of model uncertainties and dis-turbances, is used to stabilize the vehicle yawmotion. The proposed controller has been veri-fied through computer simulation using CarSim.The obtained results show the effectiveness of theproposed control scheme. Moreover, field testsusing an experimental electric vehicle are car-ried out and its effectiveness is verified. In futureworks, optimal motor torque distribution meth-ods are presented and incorporated into the pro-posed adaptive sliding mode controller.

Acknowledgments

This work was supported in part by the IndustrialTechnology Research Grant Program from NewEnergy and Industrial Technology DevelopmentOrganization (NEDO) of Japan.

References

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Authors

Mr. Kanghyun Nam receivedthe B.S.degree in mechanical engi-neering from Kyungpook NationalUniversity, Daegu, Korea, in 2007and the M.S.degree in mechanicalengineering from Korea AdvancedInstitute of Science and Technol-ogy (KAIST), Daejeon, Korea, in2009. He is currently working to-ward the Ph.D.degree in electricalengineering with The University ofTokyo. His research interests in-clude vehicle dynamics and con-trol, state estimation and motioncontrol for electric vehicles, androbust control.

Dr. Sehoon Oh received the B.S.,M.S., and Ph.D. degrees in elec-trical engineering from The Uni-versity of Tokyo, Tokyo, Japan,in 1998, 2000, and 2005, respec-tively. He is currently a projectresearch professor in the Depart-ment of Electrical Engineering,The University of Tokyo. His re-search fields include the develop-ment of human friendly motioncontrol algorithms and assistive de-vices for people.

Dr. Hiroshi Fujimoto received thePh.D. degree in the Departmentof Electrical Engineering from theUniversity of Tokyo in 2001. In2001, he joined the Departmentof Electrical Engineering, NagaokaUniversity of Technology, Niigata,Japan, as a research associate.From 2002 to 2003, he was avisiting scholar in the School ofMechanical Engineering, PurdueUniversity, U.S.A. In 2004, hejoined the Department of Electricaland Computer Engineering, Yoko-hama National University, Yoko-hama, Japan, as a lecturer and hebecame an associate professor in2005. He is currently an asso-ciate professor of the University ofTokyo since 2010. His interestsare in control engineering, motioncontrol, nano-scale servo systems,electric vehicle control, and motordrive.

Dr. Yoichi Hori received eceivedB.S., M.S., and Ph.D. degrees inElectrical Engineering from theUniversity of Tokyo, Tokyo, Japan,in 1978, 1980, and 1983, respec-tively. In 1983, he joined theDepartment of Electrical Engineer-ing, The University of Tokyo, asa Research Associate. He laterbecame an Assistant Professor, anAssociate Professor, and, in 2000,a Professor at the same univer-sity. In 2002, he moved to the In-stitute of Industrial Science as aProfessor in the Information andSystem Division, and in 2008, tothe Department of Advanced En-ergy, Graduate School of Fron-tier Sciences, the University ofTokyo. From 1991-1992, he wasa Visiting Researcher at the Uni-versity of California at Berkeley.His research fields are control the-ory and its industrial applicationsto motion control, mechatronics,robotics, electric vehicles, etc.Prof. Hori is an IEEE Fellow andan AdCom member of IES. He isa member of the Society of In-strument and Control Engineers;Robotics Society of Japan; JapanSociety of Mechanical Engineers;and the Society of Automotive En-gineers of Japan. He is the Pres-ident of Capacitors Forum, andthe Chairman of Motor Technol-ogy Symposium of Japan Manage-ment Association (JMA) and theDirector on Technological Devel-opment of SAE-Japan (JSAE).


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