2011 International Conference on Electronic & Mechanical Engineering and Information Technology

Integrated Control of Variable Torque Distribution and Electronic Stability Program Based on Slip Angle Phase

Jianhua Guo, Liang Chu, Feikun Zhou, Libo Cao

State Key Laboratory of Automobile Dynamic Simulation, Jilin University, Changchun, China xhhmail@jlu.edu.cn

Abstract—In this paper, an integrated vehicle dynamics control system is designed to improve vehicle handling and stability by coordinating control of Variable Torque Distribution (VTD) and Electronic Stability Program (ESP). The control system includes a coordinated controller in the upper layer and two subsystems controller in the lower layer. The control algorithm is based on the slip angle (/?-/?) phase plan to identify the driving situations and a rule based integrated scheme is employed to determine and allocate the control tasks between two subsystems. The simulation results demonstrate that the proposed control strategy is able to increase the tracking performance of the reference yaw rate and improve the driving steer ability of the vehicle.

Keywords—Vehicle, Integrated Control, Variable Torque Distribution, Electronic Stability Program

I. INTRODUCTION

Recently, vehicle stability control system that prevent vehicles from spinning , drifting out and rolling over have been developed and commercialized by several automotive manufacturers[1].Those control systems aim to improve the vehicle stability by controlling its actuating mechanism.

v IESP

(a)Oversteer (b) Understeer Figure 1. Integrated control of VTD and ESP .

VTD systems utilize active differentials to independently control the drive torque distributed to each drive wheel and thus provide active control of both traction and yaw moment [2], as shown in Fig.l. The VTD system is generally suitable for work in the steady-state conditions of the vehicle. ESP systems maintain the rotational stability of vehicle by applying independently controlled brake forces on the individual wheel (Fig.l). ESP systems can improve vehicle dynamic stability even if tire lateral forces approach their limits. But ESP decreases steady-state value of yaw rate at high speed and adds the burden of the driver in cornering. If

ESP is used during vehicle acceleration, however, it reduces the acceleration of the vehicle and therefore may not provide the longitudinal response the driver needs [3]. A solution to this problem is the use of combination control of VTD and ESP. However, due to the different characteristics between subsystems, this often produces mutual interference and unable to fully exert the subsystems efficiency. This paper investigates the integrated control of AFS and ESP in vehicle to solute the problem and further improves the overall performance of vehicles.

II. COTROLLER DESIGN

A. ESP Controller Design In this paper, the model reference adaptive algorithm is

used to derive the control law for ESP controller. The 2DOF vehicle model is selected as the reference model [4]. The 2DOF vehicle model with small steering angle and constant forward speed assumptions can be shown in Eq. (1):

r a, a 21 a

hi r22 J

\K Ir.

+ V IAJ [*/]

(1)

Where, -(Paf+Car)

<hx= mVx

>

I C —IrC , r ar j af

c ,

m

al2 =

<•*-

lrCar-lfCaf

(llcf+l2c ) \ f af r ar /

IV,

Where, m is whole vehicle mass, Iz is vehicle yaw moment of inertia, r is the yaw rate, Vx is the longitudinal vehicle velocity, Vy is the lateral vehicle velocity, Sf is the steering angle, // is the distance from CG to front axle, lr is the distance from CG to rear axle, Caf, Car are the tire cornering stiffness.

The reference yaw rate yd can be solved in Eq. (1) by setting[y y~i = o, expressed as:

V-t<mSf Yd-

(2)

1 + rv* i V , \ V chj

978-l-61284-088-8/ll/$26.00 ©2011 IEEE 3777 12-14 August, 2011

C ,C r af ar Where, y 2 .

ch m(CJr-Caflf)

Considering the tire-road friction coefficient, yd must comply with the following conditions:

r < 0 . 8 5 ^ 0 ) / d y

X

Where / / is road friction coefficient. The reference slip angle fid can also be calculated based

on 2DOF, expressed as:

I A=-

M-lrVx2

c •/ (4)

1 + 2 ^

ch J Considering the tire-road friction coefficient, fid must

comply with the following conditions: A<atan(0.02/ /g) (5)

The yaw moment demand generated by the ESP controller can be expressed as:

Me={\-qa){KpX\yd-y\ + Kpl\Pd- p\) (6)

Where, KpX and Kp2 are the proportionality constants of ESP controller, qa is the coordinated control parameter.

The brake pressure of front wheel can be expressed as:

pr.= -M.

cos<5- — + sin<5-/, \/B,

(7)

The brake pressure of rear wheel can be expressed as: -2-Ma

Tw-Bw

(8)

Where, Tw is the wheelbase and Bw is the braking effectiveness factor.

B. VTD Controller Design Unlike ESP, VTD systems utilize active differentials to

independently control the driving torque distributed to each drive wheel and thus provide active control of both traction and yaw moment . Table II shows the wheel selection rules of the VTD control. When the vehicle is over steer, the driving torque of wheel © is transferred to wheel © by torque transfer differential [5]. Likewise, the driving torque of wheel © is transferred to wheel © when the vehicle is understeer.

TABLE II. WHEEL SELECTION RULES OF VTD CONTROL

Ay = Yd-Y

Ay<0

A / > 0

A / < 0

Ar >o Ay = 0

Steer Angle

Sf-° Sf<0 Sf<0 Sf>0

—

Vehicle Status

Oversteer

Oversteer

Understeer

Understeer

—

Driving torque transfer direction

Wheel © to ©

Wheel © to ©

Wheel © t o ©

Wheel © t o ©

—

Figure 2. Steering Schemes of Vehicle.

The direct yaw moment control is generated by applying braking forces only at either left or right side of the vehicle. In this research, the braking torques is applied on the individual wheel base on detection of the understeer or oversteer driving situations (Fig.l). Fig.2 is the steering schemes of vehicle. When the vehicle is understeer, The braking force is applied on the inside rear wheel ©. Likewise, The braking force is applied on the outside front wheel© when the vehicle is oversteer. Table I shows the wheel selection rules of the ESP control.

TABLE I. WHEEL SELECTION RULES OF ESP CONTROL

Ay = Yd-Y A/<0

A / > 0

A / < 0

A / > 0

Af = 0

Steer Angle Sf>0

Sf<0 Sf<0 Sf>0

—

Vehicle Status Oversteer

Oversteer

Understeer

Understeer

—

Wheel Selected Wheel©

Wheel®

Wheel©

Wheel©

—

The yaw moment demand generated by the VTD controller can be expressed as:

K=<la(Kpi\ra-7i + KP2\fr-0\) (9> The driving torque transferred between wheel © and

wheel © can be expressed as:

2M r A T v_j_ (10)

Where, r is tires radius.

III. COORDINATED CONTROLLER DESIGN

The structure of proposed integrated control system is shown in Fig.3. It has a hierarchical structure consisting of two controlling layers [6]. The upper layer is the coordinated controller which is designed based on slip angle and slip angular velocity ( / ? - / ? ) phase plan technique. The output of the coordinated controller is coordinated control parameter qa which is used to modify the decision-making

of bottom controls. As discussed previously, the VTD system is generally

suitable for work in the steady-state conditions of the

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vehicle, while ESP controller is mainly used as the stability controller for emergency maneuvers and not active in normal driving situations. To avoid the conflict of different control objectives, individual subsystem should be activated according to driving situations and in sequence of control priorities. In this paper, the vehicle slip angle and its angular velocity ( p - p ) phase plan for is used to determine the driving situations.

Sfd

sensor

i {

r P

\ r

+ Signal processing

p\'P Coordinated controller

i* VTD controller

ArJ

\ r 1 " ^ \

r P

!

ESP controller

^k Whole vehicle system

Figure 3. Block Diagram of Integrated Control.

region (D) can be divided in the stable region ® and expressed as:

\BJ+P\<BVI2 (12)

Where, Bvt2 is positive constant. When vehicle states go inside the VTD control region,

the VTD controller is activated and ESP controller does not work.

The ESP control region (the region ©)which is divided outside the stable region ® can be expressed as:

\BJ + p\>Bes2 (13) Where Bes2 is positive constant.

When vehicle states go inside the ESP control region, the ESP controller work independently.

The integrated control region (the region (§)) which is divided between the VTD control region and ESP control region can be expressed as:

Bvl2<\Bj + j3\<Bes2 (14) In this region, two subsystems' working states are

switched. Then, the coordinated control parameter qa in Eq. (6)

and Eq. (9) can be calculated as:

= 1 \BYp + p\<Bvt

1 af(\B^+j3\-cf)

^ 2 < | A / ? + / ? | < ^ 2 (15)

l + e [qa = Q \Bj+p\>Ba2

In Eq.(15), the sigmoid function is used to avoid the impact of the subsystems switching.Where a/ and Cf are shape parameters of the sigmoid function. The calculation of the coordinated control parameter qa is shown in Fig.5.

Figure 5. Caculation of the coordinated control parameter qa.

Figure 4. Integrated control region in (J3-J8) phase plan.

As shown in Fig.4, the region ® between two stable boundary lines is defined as the stable region. When the vehicle states go inside this region, the vehicle can be easily control by the driver. The stable region can be expressed as:

\BlJ3 + fi\<B2 (11) Where Bx and B2 are positive constants.

Due to the VTD system generally works in the steady-state conditions of the vehicle. It's control region (the

IV. SIMULATION AND RESULTS

Computer simulations are carried out to evaluate the performance of the integrated control system. In the process of simulations, the performance of the integrated system, in comparison with non-control and VTD individual control, are also considered.

The simulation consists of tracking a reference yaw rate for a high lateral acceleration lane change maneuver. In this maneuver, vehicle runs at the initial velocity 90km/h on a road with friction coefficient ju=0A. The steering input and simulation results are shown in Fig.6 (a).

Fig.6 (b) shows the vehicle trajectories for non-control, individual VTD and integrated VTD/ESP. It can be seen that

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integrated VTD/ESP has a better ability to keep track of vehicle than individual ESP. Fig.6(c) shows the performance of individual VTD and integrated VTD /ESP in tracking reference yaw rate. It is seen that the integrated VTD /ESP tracks the reference yaw rate more accurate than individual ESP. Fig.6 (d) shows the / ? - / ? phase trajectory in the phase plane. There is most of the phase trajectory of integrated VTD /ESP in the stable region. It shows that the vehicle with the integrated AFS/ESP has better stability compared with individual control.

Figure 6. Results of computer simulations

V. CONCLUSION

In this paper, an integrated vehicle dynamics control system which coordinates the control actions of VTD and ESP is proposed to improve vehicle handling performance and stability. The proposed control system includes a coordinated controller in the upper layer and two subsystems controller in the lower layer. The proposed algorithm is based on the P - P phase plan to identify the driving situations and a rule based integrated scheme is employed to determine and allocate the control tasks between two subsystems. As the simulation results demonstrate, the proposed control system is able to increase the tracking performance of the reference yaw rate and improve the driving dynamics and steer ability of the vehicle.

REFERENCES

[1] W.M. Allan, Bonnick, Automotive Computer Controlled Systems, Butterworth-Heinemann, Oxford, Britain, 2001.

[2] Siqi Zhang, Tianxia Zhang, Vehicle Stability Control Strategy Based on Active Torque Distribution and Differential Braking, International Conference on MTMA, vol.09, April 2009.

[3] A. Allryne, "Improve Vehicle Performance Using Combined Suspension and Braking Forces", Proceeding of the American Control Conference, June 1995.

[4] Wu Yihu, Song Dandan, Hou Zhixiang, "A Fuzzy Control Method to Improve VehicleYaw Stability Based on Integrated Yaw Moment Control and Active Front Steering," Proc. IEEE Symp. International Conference on Mechatronics and Automation, IEEE Press, August. 2007, pp. 1508-1512.

[5] Junjie He, David A. Crolla, and Martin C.Levesley. "Integrated Active Steering and Variable Torque Distributuon Control for Improving Vehicle Handling and Stability", SAE Paper 2004-01-1071,March 2004.

[6] B. A. Guven, "Coordination of Steering and Individual Wheel Braking Actuated Vehicle Yaw Stability Control", IEEE conf, 2003.

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