Journal of Jilin University(Engineering and Technology Edition) ›› 2022, Vol. 52 ›› Issue (10): 2225-2233.doi: 10.13229/j.cnki.jdxbgxb20210294

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Stability control of distributed electric vehicle based on Popov hyperstability

You-qun ZHAO(),Yu-hao LI,Hui-fan DENG,Tao LIN,Fen LIN   

  1. College of Energy and Power Engineering，Nanjing University of Aeronautics and Astronautics，Nanjing 210016，China
  • Received:2021-07-03 Online:2022-10-01 Published:2022-11-11

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Abstract:

In consideration of the terrible real-time performance and adaptability in vehicle stability control for distributed electric vehicles， a model reference adaptive control strategy based on hierarchical control structure was proposed in this paper. The upper controller was a model reference adaptive yaw moment controller based on Popov hyperstability. The adaptive feedforward and feedback gain was calculated by solving the Popov integral inequality. It had the advantages of small computational burden， excellent self-adaptability， and ensured hyperstability of the controller. The lower controller distributed differential wheel torques according to the desired yaw moment via quadratic programming. Actually， The distribution of wheel torques was exactly the solution of a weighted minimum square problem， which was solved by the active-set method. The proposed hierarchical stability control strategy was verified by the Carsim/Simulink co-simulation platform under the condition of fish hook in a low road adhesion coefficient. The simulation results show that the peaks of yaw rate and sideslip angle decrease 44.81%， 88.68%， respectively， compared with no control. The peaks of yaw rate and sideslip angle decrease 30.48%， 55.72%， respectively， compared with PID control. The proposed stability control strategy can significantly improve vehicle handling and stability performance， and increase stability of vehicles under extreme conditions.

Key words: vehicle engineering, distributed electric vehicle, stability control, Popov hyperstability, torque distribution

CLC Number: 

  • U461.6

Fig.1

Two-degree-of-freedom vehicle model"

Fig.2

Equivalent nonlinear time-varying feedback system"

Table 1

Vehicle parameters"

汽车参数数值
汽车质量m/kg2110
绕z轴转动惯量Iz /（kg·m2）2031.4
质心至前轴距离lf/m1.04
质心至后轴距离lr/m1.56
传动比i19.3
轮距d/m1.48
车轮滚动半径R/m0.468
电机峰值转矩Tmax/（N·m-1）400
前轮侧偏刚度Kf/（N·rad-1）-116 900
后轮侧偏刚度Kr/（N·rad-1）-112 700

Table 2

Parameters of controller"

控制器参数数值
对称正定矩阵 P求解Lyapunov方程
正定积分核 K?［30.5］
正定矩阵 G?［5.1］
半正定时变矩阵K?*(t)［11.3t］
半正定时变矩阵G?*(t)［13.2t］
正定积分核 Kφ［0.2］
正定矩阵 Gφ［0.5］
半正定时变矩阵Kψ*(t)［0.3t］
半正定时变矩阵Gψ*(t)［0.4t］
比例系数Kp500
积分系数Ki10
微分系数Kd0.5

Fig.3

Hook working-condition"

Fig.4

Curve of yaw rate"

Fig.5

Curve of sideslip angle"

Fig.6

Phase diagram of “yaw rate-sideslip angle”"

Fig.7

Response curve of yaw moment"

Fig.8

Curve of vehicle speed"

Fig.9

Curve of four wheel torque"

Table 3

Real-time state comparison of control strategies"

控制策略

Popov MRAC+

二次规划

Popov MRAC

无二次规划

仿真时长/s1010
程序耗时/s6.70.8
CPU占用率/%3621
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