Research on Stability Control and Optimal Algorithm of Regeneration

for Distributed Drive Four-wheel Drive Vehicles

YUEHANG DONG, YUANYUAN YANG, HONGJUN ZHAI, CHANGMING ZHAO

Ningbo Geely Automobile Research and Development Co., Ltd,

No. 918 Binhai 4th Rd, Hangzhou Bay New District, Ningbo, Zhejiang

CHINA

energy recovery. Finally, the effectiveness of the strategy is verified by the actual vehicle tests under pylon course

slalom and double-shift conditions.

Key-Words: - distributed drive, four-wheel drive, regenerative braking, yaw velocity, side slip angle, handling

stability, I curve, ECE R13 regulation

Received: July 24, 2022. Revised: April 19, 2023. Accepted: May 25, 2023. Published: July 6, 2023.

1 Preface

process, while there are few kinds of research on

brake process stability control and optimal brake

energy feedback. There needs to be more discussion,

especially for the combination of optimal braking

energy feedback and anti-slip braking during the

braking process, which meets the requirements of

ECE R13 regulations. This article discusses the

control strategy and calculation formula for

calculating the optimal braking feedback of

distributed four-wheel drive vehicles equipped with

actual vehicle testing to verify the effectiveness of the

strategy. Literature, [3], takes the two-axle

four-wheel drive electric vehicle as the research

object and develops the braking energy recovery

strategy, [3], based on the I-curve braking force

distribution. The description of braking strategy after

ESP needs to be described, and the vehicle speed

prediction strategy in literature, [3], is not defined.

Literature, [4], describes driver intention

identification based on the brake pedal, [4], only

prediction algorithms for future velocity and

acceleration, and there aren’t control algorithms for

vehicle stability control. In this paper, based on the

comprehensive consideration of the braking process

and the vehicle stability control, the slip rate, motor

fault state constraints, and front and rear load

constraints, the optimal feedback braking function is

formulated, and the practicability of the control

strategy is verified through the actual vehicle test.

The layout of four-wheel drive and two-drive

Fig. 2: Four-wheel drive power system layout of

REEV

control the four wheels, and achieve control of

vehicle stability, thereby achieving the dual goals of

optimal braking feedback energy and vehicle stability

control, [9], [10].

2.2 Determination of Vehicle Stable Yaw

Moment based on Fuzzy Control Theory

Based on the fuzzy control theory, [11], the fuzzy

controller of the expected yaw moment, [12], is

designed, as shown in Figure 5.

Fig. 7: Membership function of centroid sideslip

angle error

2) Fuzzy reasoning:

fuzzy reasoning is the core of fuzzy controller, that is

to use fuzzy language to describe the logical

relationship between input and output variables after

fuzzing, see Table 2 for details.

moment controller

front axle in the Y- axis direction, (m) is the

driving force of the left wheel of the front axle in the

X-axis direction, (m) is the driving force in the

Y-axis direction of the right wheel of the front axle,

of the right wheel of the front axle. (m) is the

distance from the rear axle to the vehicle

centroid,(m) is the distance from the front axle to

the vehicle centroid, ɼ (rad/s) is the yaw rate, β (rad) is

the sideslip angle of the vehicle centroid.

formula is obtained:

Z is the braking strength, and g is the acceleration of

gravity.

The coordinate of point A is ,  is the

intersection point of the ECE curve and axis.

6: The straight line formula of the AB section is： The

AB linear equation is:

Moreover, it is noticed that Figure 12 presents the

Where  is the braking torque of the front left

wheel after the stability yaw moment intervention,

stability yaw moment is involved,  is the

9：Driving force limit, corresponding to the driving

force limit layer in Figure 4:

charge and discharge power of the battery.

3) The driving or charging torque of a single motor

cannot exceed the limit value given by each motor

controller.   , where is the

motor torque demand sent by the vehicle controller to

each motor controller,  is the

maximum torque each motor can output, which is

sent by the controller.

4): Each wheel’s driving or braking force shall meet

2.5 Braking Anti-Skid Control Strategy

6) Based on the above strategy, braking torque will be

The estimation of longitudinal speed plays a very

critical role in vehicle anti-skid control. The

estimation of vehicle speed is inaccurate, and the

vehicle anti-skid will lose its foundation. According

shown in Table 3 (see Appendix). Based on the above

information, this paper uses a fusion algorithm to

calculate the current vehicle speed using the Kalman

filter under low-speed conditions. It uses acceleration

based on odorless transformation. Theoretically, the

tasteless conversion can approximate the posterior

mean and covariance of any nonlinear Gaussian

system state with at least third-order Taylor precision.

When the nonlinear degree of the target object is

improved to a certain level, UKF will have higher

accuracy, does not need to linearize the system, and

does not need to calculate the Jacobian matrix of the

system during the operation process, which can

improve the efficiency and stability of the estimation.

1: initialize

2: Time update section

1） Generate 2n sigma sampling points, which are

(38)