Research on Control Algorithm for DYC and Integrated Control with 4WS

Zhu tianjun College of Mechanical and Electronic Engineering

Hebei University of Engineering Handan, China

E-mail: tianjun_zhu@yahoo.com.cn

Zong changfu State Key Laboratory of Automobile Dynamics

Simulation Jilin University

Changchun, China E-mail: ztj99@163.com

Abstract— The best advantage of the DYC is it can greatly improve vehicle handling and stability. It is proposed integrated control of four wheel steering systems (4WS) and direct yaw moment control. A desirable vehicle model is established with the best performance of side slip angle and yaw rate. The strategy of both the forward controller and feedback controller of tracking the desirable model is adopted and an optimal controller is designed. By the simulation, it is compared to only DYC and integrated control of 4WS and DYC. The simulation results indicated that integrated control could effectively control side slip angle and yaw rate tracking the desirable value.

Keywords-component; vehicle handling; four wheel steering; side slip angle;

I. INTRODUCTION Vehicle yaw dynamic may show unexpected dangerous

behavior in presence of unusual external conditions such as lateral wind force, different left-right side friction coefficients and steering steps needed to avoid obstacles. Vehicle active steering control systems aim to enhance driving comfort characteristics ensuring stability in critical situations. The research on active steering control was very active from the 1990’s due to the large number of systems under development. Extensive reviews on the development of active steering systems can be found in various articles [1].

On the vehicles, three main techniques were used to implement active steering control. One is to correct the driver’s steering by actuating the front road wheels. This technique is referred to as Front-Wheel steering control [2]. The second technique is to develop a steering moment by introducing difference in braking forces between the right and left sides of the vehicle. This asymmetric braking technique is referred to as Direct Yaw-moment Control (DYC) [3]. The third one is to generate an additional steering moment at the rear axle by steering the wheels according to the steering input at the front wheels, known as Rear-Wheel Steering (RWS) or 4 Wheel Steering (4WS)[4].

Now DYC system has become the most widely used active steering system during the last ten years. A DYC system developed by Bosch company, known as the ESP, has been produced for more than 10 millions sets since 1995[5]. One of the major advantages of DYC is its ease of implementation through the existing ABS actuators, since it can use the available functions of braking and traction

control components. DYC also has a superior performance in vehicle stabilization under limit driving conditions when the lateral tire force is near saturation or already saturates. However, the effect of DYC is limited under some commonly seen difficult driving situations, such as split-μdriving/braking, since the maximum braking forces on the two sides of the vehicle are different. In addition, a braking maneuver on low-friction surface may cause the vehicle to deviate from the driver’s intended direction. Among these three techniques, 4WS provides advantages in high-speed stability and low-speed maneuverability on low-friction surface.

This paper proposes an integrated chassis control system theoretically utilizing DYC system by using 4WS to improve vehicle handling and stability. The simulations are carried out to verify the effectiveness of the proposed integrated chassis control system on handling performance in lane-change tests, and stability against low-friction road.

II. VEHICLE MODEL This paper employs a 7DOF vehicle dynamic model as

shown in Fig.1 to describe the vehicle dynamics. The equations of motions can be expressed as follows:

b a( )1,2yF

( )1,2xF

( )1,2zM

( )2,2yF

( )2,2xF

( )2,2zMfdrd

( )1,1yF( )1,1xF

( )1,1zM

( )2,1yF( )2,1xF

( )2,1zM

swδ

β

r

v

u

V

WFFF o

X

Yswδ

b a( )1,2yF

( )1,2xF

( )1,2zM

( )2,2yF

( )2,2xF

( )2,2zMfdrd

( )1,1yF( )1,1xF

( )1,1zM

( )2,1yF( )2,1xF

( )2,1zM

swδ

β

r

v

u

V

WFFF o

X

Yswδ

Figure 1 Schematic of 7 DOF vehicle model

WFxx

yy

xx

FFFFFF

FFvruM

−−+

+−−+=⋅−

)2,2()1,2()sin()2,1()sin()1,1(

)cos()2,1()cos()1,1()(

21

21

δδδδ (1)

)2,2()1,2()sin()2,1()sin()1,1(

)cos()2,1()cos()1,1()(

21

21

yy

xx

yy

FFFF

FFurvM

+++

++=⋅+

δδδδ (2)

2009 International Conference on Computational Intelligence and Natural Computing

978-0-7695-3645-3/09 $25.00 © 2009 IEEE

DOI 10.1109/CINC.2009.91

166

1 2

1 2 1

2 1 2

[ (1,1)sin( ) (1,2)sin( )] [ (1,1)

cos( ) (1,2)cos( )] [ (1,1)cos( )2

(1,2)cos( )] [ (1,1)sin( ) (1,2)sin( )]

[ (2,1) (2,2)] [ (2,1) (2,2)]2 2

(1,1) (1,2)

Z x x x

fx y

y y y

f ry y x x

Z Z

I r F F a Fd

F F

F a F Fd dF F b F F

M M

δ δ

δ δ δ

δ δ δ

= + ⋅ −

− + +

+ −

⋅ − + ⋅ − − ⋅

+ + (2,1) (2,2)Z ZM M+ +

(3)

( ) ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛⋅−⋅−⋅⋅⋅

+=

fggZ d

bhvhubgba

MF21

211,1

(4)

( ) ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛⋅+⋅−⋅⋅⋅

+=

fggZ d

bhvhubgba

MF21

212,1 (5)

( ) ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛⋅−⋅+⋅⋅⋅

+=

rggZ d

ahvhuagba

MF21

211,2 (6)

( ) ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛⋅+⋅+⋅⋅⋅

+=

rggZ d

ahvhuagba

MF21

212,2 (7)

Tire model is based on academician Guo Konghui tires model which is semi-empirical exponential model [7].

( )⎪⎪⎪

⎩

⎪⎪⎪

⎨

⎧

−+=

⋅+−−−−=

⋅+−−−−=

bxbxyz

yzyy

xzxx

YFXDFM

EEFuF

EEFuF

φφφφφ

φφφφφ

)))121(exp(1(

)))121(exp(1(

321

21

321

21

(8)

Where, ux 、 uy are longitudinal and lateral friction coefficient; xφ 、 yφ and φ are relative longitudinal slip rate, lateral slip rate, total slip rate. Dx is tire lag.

III. CONTROL SYSTEM DESIGN

A. 4WS Integrated controller design As shown in Fig.2, integrated controller is expressed as

the following. With the application of model matching control technique, the integrated control system consists of a feedforward compensator with respect to the steering angle and a feedback compensator to match the yaw rate and side slip angle to the desired value.

Feedforwardcontroller

Desired model

Feedbackcontroller

Vehiclemodel

＋ －

＋ －

＋ ＋

＋ ＋

βΔ γΔ

β

γ

fδ

MΔ rδΔ

rfδ

ffM

Figure 2 Block diagram of integrated controller

The deviation amplitude of yaw rate and side slip angle is expressed as the equation (9):

( ) ( )

( ) ( ) ( )

d

f d d d f

d d d d f

e X XAX BU E A X E

A X X BU A A X E Eδ δ

δ

= −= + + − +

= − + + − + −

(9)

Where, ( ) ( )fb d d d fBU BU A A X E E δ= + − + − (10)

The equation (9) can be written as follows: fbe Ae BU= + (11)

The steady state gain of the deviation can be obtained as the follows:

fbU Ke= − (12) Or it can be expressed as the follows:

11 12

21 22

r K KK KM

δ βγ

Δ Δ⎡ ⎤⎡ ⎤ ⎡ ⎤= − ⎢ ⎥⎢ ⎥ ⎢ ⎥Δ Δ⎣ ⎦ ⎣ ⎦⎣ ⎦

(13)

Where, K are the state gains.

B. Desired Model In this paper, the desired model response can be

expressed as the follows: fddd EXAX δ+= (14)

Where, dd

d

Xβγ⎡ ⎤

= ⎢ ⎥⎣ ⎦

0 0

10dAγτ

⎡ ⎤⎢ ⎥= ⎢ ⎥−⎢ ⎥⎣ ⎦

0

d kE γ

γτ

⎡ ⎤⎢ ⎥= ⎢ ⎥⎢ ⎥⎣ ⎦

0

1

dd f

d

kXs

γ

γ

βδ

γτ

⎡ ⎤⎡ ⎤ ⎢ ⎥= =⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎢ ⎥+⎣ ⎦

The transfer function from the steering wheel angle to the yaw rate and side slip angle can be expressed as follows:

21 22 11 22 1 11 22 11 22 212

11 22 11 22 12 21 11 22 12 21 11 22

( )( ) ( )( ) ( )

a a b b e a a b b e s fs ss a a s a a a a b b a a a a

γ δ− +=⎡ ⎤− + + − − +⎣ ⎦

(15)

[ ]11 12 21 22 11 1 12 2 22 12

11 22 11 22 12 21

12 12 22 22 122

11 22 11 22 12 21

( ) ( ) ( ) ( )( )

( )( ) ( ) +

( )

r fb s a b a b s e s a e a e sS

s a a s a a a ab s a b a b M s

s a a s a a a a

δ δβ

+ − + + −=

− + + −+ −

− + + −

(16)

IV. SIMULATION RESULTS This section will discuss the validity of the proposed

chassis control system on handling and stability as described in the previous section by simulation.

A. Step input on high-friction road The vehicle ran on the high-friction road at the velocity

of 100km/h. The control effect of vehicle handling by using integrated controller was investigated in step input test on high-friction road. Fig.3 shows the steering wheel angle during test. Fig.4-6 shows the lateral acceleration response, yaw rate response, side slip angle respectively during the test. It is found that, the overshoot of the yaw rate and the time reaching the steady state are significantly reduced during test, compared to the case without control and only DYC control. In the Fig.6, it is shown that the integrated controller using 4WS can effectively make the yaw rate and side slip angle match the desired value. Moreover, it is conformed that the

167

4WS integrated control system is realized by controlling the yaw rate and side slip angle to achieve desired value.

0 1 2 3 4 5

0

5

10

15

20

25

30

Stee

ring

Whe

el A

ngle

(deg

)

Time(s) 0 1 2 3 4 5

0

1

2

3

4

5

6

No control Only DYC control 4WS and DYC control

Late

ral a

ccel

erat

ion(

m/s2 )

Time(s) Figure 3 Steer wheel angle Figure 4 Lateral acceleration

0 1 2 3 4 5-2

02

468

1012

14

Yaw

Rat

e(de

g/s)

Time(s)

No control Only DYC control 4WS and DYC control Desired value

0 1 2 3 4 5-2.0

-1.5

-1.0

-0.5

0.0

No control Only DYC control 4WS and DYC control Desired value

Side

slip

ang

le(d

eg)

Time(s) Figure 5 Yaw rate Figure 6 Side slip angle

B. Lane-change test on high-friction road The Fig.7 is shown that the path setting of ISO 3881

lane-change test.

s 1 s 2 s 3 s 4 s 5

B1 B2

B3B

t=0 t=tn Figure 7 Path setting of ISO 3881

The vehicle ran on the high-friction road ( 1μ = ) at the

velocity of 80km/h. Fig.8 shows the vehicle driving path during test. Fig.9-11 shows the lateral acceleration response, yaw rate response, side slip angle respectively during the test. It is shown that the side slip angle is significantly reduced during test, compared to the case without control and only DYC control. At the same time, the integrated control system can effectively make the yaw rate match the desired yaw rate. It is shown putting into evidence the significant control effect provided by the integrated controller.

0 160 320 480 640 800 960-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5 No control Only DYC control 4WS and DYC control Desired path

Vehi

cle

driv

ing

path

(m)

distance(m)0 2 4 6 8 10 12

-3

-2

-1

0

1

2

3

No control Only DYC control 4WSandDYC control

Late

ral a

ccel

erat

ion(

m/s

2 )

Time(s)

Figure 8 Vehicle driving path Figure 9 Lateral acceleration

0 2 4 6 8 10 12-8

-6

-4

-2

0

2

4

6

8

Yaw

Rat

e(de

g/s)

Time(s)

No control Only DYC control 4WS and DYC control Desired value

0 2 4 6 8 10 12-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

side

slip

ang

le(d

eg)

Time(s)

No control BP network PID control 4WS and DYC control Desired value

Figure10 Yaw rate Figure11 Side slip angle

C. Lane-change test on low-friction road The vehicle ran on the high-friction road ( 0.2μ = ) at the

velocity of 60km/h. Fig.12 shows the vehicle driving path during test. Fig.13-14 shows side slip angle response, yaw rate response respectively during the test. Fig.15 shows the Yaw moment on the vehicle during the test. It is clearly shown that the vehicle without control run off the road during the test. The yaw rate of integrated control system is much smaller than the ones of the DYC control and no control. And the yaw moment on the integrated control vehicle is significantly reduced than the only DYC control.

0 160 320 480 640 800 960

-6

-4

-2

0

2

4

Vehi

cle

driv

ing

Pat

h(m

)

Distance(m)

No control Only DYC control 4WS and DYC control Desired path

0 2 4 6 8 10 12-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

Side

slip

ang

le(d

eg)

Time(s)

Only DYC control 4WS and DYC control Desired value

Figure 12 Vehicle driving path Figure13 Side slip angle

0 2 4 6 8 10 12

-8

-6

-4

-2

0

2

4

6

8

Yaw

Rat

e(de

g/s)

Time(s)

Only DYC control 4WS and DYC control Desired value

0 2 4 6 8 10 12-400

-300

-200

-100

0

100

200

300

400

Yaw

mom

ent(N

*m)

Time(s)

Only DYC control 4WS and DYC control

Figure14 Yaw rate Figure15 Yaw moment

V. CONCLUSION This paper proposes an integrated chassis control system

theoretically utilizing DYC system by using 4WS to improve vehicle handling and stability. It is proposed integrated control of four wheel steering systems (4WS) and direct yaw moment control. A desirable vehicle model is established with the best performance of side slip angle and yaw rate. The strategy of both the forward controller and feedback controller of tracking the desirable model is adopted and an

168

optimal controller is designed. The simulations are carried out to verify the effectiveness of the proposed integrated chassis control system on handling performance in lane-change tests, and stability against low-friction road.

REFERENCES

[1] Yoshimi Furukawa, Masato Abe, “Advanced Chassis Control Systems for Vehicle Handling and Active Safety,” Vehicle System Dynamics, vol. 28, pp. 59–86, August 1997, doi: 10.1080/00423119708969350.

[2] Mammar S., and Koenig D., “Vehicle Handling Improvement by Active Steering,” Vehicle System Dynamics, vol. 38, pp. 211–242, September 2002, doi: 10.1076/vesd.38.3.211.8288.

[3] Kojo, T., Suzumura, M., , “Development of active front steering control system.,” SAE 2005-01-0404, pp. 346–352, August 2005 .

[4] O. Mokhiamar, M. Abe, “Active wheel and Yaw moment control combination to maximize stability as well as vehicle responsiveness during quick lane change for Active vehicle handling safety,” Proceeding of the Institution of Mechanical Engineers,Part D: Journal of Automobile Engineering , Vol.216, Dec. 2002, pp. 115-124, doi: 10.1243/0954407021528968.

[5] Liebemann, E. K., Meder, K., Schuh, J., and Nenninger, G.,“Safety and performance enhancement: the Bosch ectronic stability control (ESP).,” SAE 2005-0471-0, pp. 540–549, August 2005 .

169