车辆稳定域描述与求解的一种新方法

doi:10.19562/j.chinasae.qcgc.2025.03.008

Abstract

Abstract:

The vehicle stability region is an important aspect of research on vehicle stability analysis and control. For the problems of inaccurate description and difficult solution of stability region in existing research， a quadrilateral description and automatic solution method for vehicle stability region is proposed. A nonlinear two-degree-of-freedom vehicle model is established， and the ant colony algorithm is used to solve the equilibrium state of vehicle system. The Lyapunov indirect method is applied to determine the stability of the equilibrium state. Based on the phase plane of the sideslip angle-sideslip angle velocity of mass center， several phase trajectory feature points and the phase plane stability region boundary point search method are established to solve the stability region boundary points. According to the different distributions of the vehicle stability region， two types of stability regions are proposed， and corresponding judgment methods， stability region quadrilateral description and its automatic solution methods are established. Based on the proposed method， the stability region of vehicle under common medium speed driving condition is solved. The results are compared with the parallel line method and diamond method， and the correctness of the quadrilateral description is validated by CarSim sine wave simulation results. The results show that the proposed quadrilateral description of the vehicle stability region can better describe the boundary of the stability region than the parallel line method and diamond method， and automatic solution reduces the workload of stability region solution.

Key words: vehicle stability region, phase plane, equilibrium state, ant colony algorithm, the Lyapunov indirect method

Changwang Jia,Jie Li,Lingling Zheng,Qi Zhao. A New Method for Describing and Solving the Vehicle Stability Region[J].Automotive Engineering, 2025, 47(3): 460-469.

Figures/Tables 13

边界点	获得方法
$A 10$	使用稳定域边界点搜索法从不稳定平衡状态 $S r$ 垂直向下搜索得到的稳定域边界点
$l 12$	起点为 $A 10$ 、终点为 $S o$ 的相轨迹
$A 11$	相轨迹 $l 12$ 的拐点
$A 12$	相轨迹 $l 12$ 的左端点
$A 13$	使用稳定域边界点搜索法从不稳定平衡状态 $S l$ 垂直向上搜索得到的稳定域边界点
$l 11$	起点为 $A 13$ 、终点为 $S o$ 的相轨迹
$A 14$	相轨迹 $l 11$ 的拐点
$A 15$	相轨迹 $l 11$ 的右端点
$A 16$	直线 $A 14 A 15$ 与过 $A 10$ 水平线的交点
$A 17$	直线 $A 11 A 12$ 与过 $A 13$ 水平线的交点

边界点	获得方法
$A 20$	使用稳定域边界点搜索法从不稳定平衡状态 $S l$ 垂直向上搜索得到的稳定域边界点
$l 21$	起点为 $A 20$ 、终点为 $S o$ 的相轨迹
$A 21$	相轨迹 $l 21$ 的拐点
$A 22$	相轨迹 $l 22$ 的右端点
$A 23$	相轨迹 $l 22$ 下端点
$A 24$	相轨迹 $l 22$ 左端点
$A 25$	直线 $A 23 A 24$ 与过 $A 20$ 水平线的交点

参数	数值
汽车总质量 $m$ / kg	1 987.9
横摆转动惯量 $I z$ / （kg·m²）	2 703.7
质心到前轴距离 $a$ / m	1.347
质心到后轴距离 $b$ / m	1.531

前轴参数	数值	后轴参数	数值
$P C y f 1$	1.162	$P C y r 1$	1.314
$P E y f 1$	0.251	$P E y r 1$	0.041
$P E y f 2$	0.588	$P E y r 2$	0.321
$P E y f 3$	-0.024	$P E y r 3$	-0.132
$P K y f 1$	195.561	$P K y r 1$	29.072
$P K y f 2$	12.517	$P K y r 2$	1.697
$P K y f 4$	0.427	$P K y r 4$	0.597

项目	四边形法	平行线法	菱形法
$δ = 0$ rad	0.60	0.60	0.20
$δ = 0.05$ rad	0.75	0.70	0.25
$δ = 0.1$ rad	0.90	0.40	0.20
$δ = 0.15$ rad	0.90	0.60	0.30
平均值	0.79	0.58	0.24

References 21

1	杨秀建，王增才，彭伟利，等. 极限工况下周期转向汽车侧向动力稳定性及分岔分析［J］. 公路交通科技， 2009， 26（11）： 141-145，152.
	YANG X J， WANG Z C， PENG W L， et al. Analysis on lateral dynamics stability and bifurcation of vehicle periodic steering under critical condition ［J］. Journal of Highway and Transportation on Research and Development， 2009， 26（11）： 141-145，152.
2	钟龙飞，彭育辉，江铭，等. 基于相平面的分布式驱动电动汽车稳定性控制［J］. 汽车工程， 2021， 43（5）：721-729，738.
	ZHONG L F， PENG Y H， JIANG M， et al. Stability control of distributed driven electric vehicle based on phase plane ［J］. Automotive Engineering， 2021， 43（5）：721-729，738.
3	LI Q T， ZHANG J， LI L， et al. Coordination control of maneuverability and stability for four-wheel-independent-drive EV considering tire sideslip ［J］. IEEE Transactions On Transportation Electrification， 2022， 8（3）： 3111-3126.
4	HUANG Y W， LIANG W， CHEN Y. Stability regions of vehicle lateral dynamics： estimation and analysis ［J］. Journal of Dynamic Systems Measurement and Control， 2021， 143（5）： 1-12.
5	ALVES J A V， CHINELATO C I G， ANGELICO B A. Vehicle lateral stability regions for control applications ［J］. IEEE Access， 2022， 10（1）： 87787-87802.
6	彭涛，关志伟，张荣辉，等. 半挂汽车列车高速变道稳定域估计［J］. 交通运输工程学报， 2018， 18（4）： 90-102.
	PENG T， GUAN Z W， ZHANG R H， et al. Stability region estimation of lane change on highway for tractor-semitrailer ［J］. Journal of Traffic and Transportation Engineering， 2018， 18（4）： 90-102.
7	RIBEIRO A M， FIORAVANTI A R， MOUTINHO A， et al. Nonlinear state-feedback design for vehicle lateral control using sum-of-squares programming ［J］. Vehicle System Dynamics， 2022， 60（3）： 743-769.
8	HU X， CHEN H， REN Q， et al. Estimation and expansion of vehicle stability region with sums of squares programming ［J］. IEEE Transactions on Mechatronics， 2023， 1（1）： 1-12.
9	李静，王子涵，王宣锋. 基于相平面法的制动方向稳定性分析［J］. 汽车工程， 2014， 36（8）： 974-979.
	LI J， WANG Z H， WANG X F. An analysis on braking directional stability based on phase-plane technique ［J］. Automotive Engineering， 2014， 36（8）： 974-979.
10	LIU J， SONG J， LI H J， et al. Direct yaw-moment control of vehicles based on phase plane analysis ［J］. Proceedings of the Institution of Mechanical Engineers， Part D-Journal of Automobile Engineering， 2022， 236（10-11）： 2459-2474.
11	赵轩，王姝，马建，等. 分布式驱动电动汽车底盘集成控制技术综述［J］. 中国公路学报， 2023， 36（4）： 221-248.
	ZHAO X， WANG S， MA J， et al. Review of chassis integrated control technology for distributed drive electric vehicles ［J］. Chinese Journal of Highway and Transport， 2023， 36（4）： 221-248.
12	CHEN W W， LIANG X T， WANG Q D， et al. Extension coordinated control of four wheel independent drive electric vehicles by AFS and DYC ［J］. Control Engineering Practice， 2020， 101（1）： 1-12.
13	CHUNG T， YI K. Design and evaluation of side slip angle-based vehicle stability control scheme on a virtual test track ［J］. IEEE Transactions on Control Systems Technology， 2006， 14（2）： 224-234.
14	刘飞，熊璐，邓律华，等. 基于相平面法的车辆行驶稳定性判定方法［J］. 华南理工大学学报（自然科学版）， 2014， 42（11）： 63-70.
	LIU F， XIONG L， DANG L H， et al. Vehicle stability criterion based on phase plane method［J］. Journal of South China University of Technology （Natural Science Edition）， 2014， 42（11）： 63-70.
15	熊璐，曲彤，冯源，等. 极限工况下车辆行驶的稳定性判据［J］. 机械工程学报， 2015， 51（10）： 103-111.
	XIONG L， QU T， FENG Y， et al. Stability criterion of vehicle traveling under extreme working conditions ［J］. Journal of Mechanical Engineering， 2015， 51（10）： 103-111.
16	MASTINU G， PREVIATI G， DELLA R F， et al. How drivers lose control of the car ［J］. SAE Int. J. Veh. Dyn.， Stab.， and NVH， 2024， 8（1）：99-121.
17	DELLA R F， MASTINU G. Analysis of the lateral dynamics of a vehicle and driver model running straight ahead ［J］. Nonlinear Dynamics， 2018， 92（1）： 97-106.
18	李杰，高雄，王维，等. 基于UniTire模型的平顺性和操纵稳定性协同研究［J］. 汽车工程， 2018， 40（2）： 127-132.
	LI J， GAO X， WANG W， et al. A collaborative study on ride comfort and handling stability based on UniTire models ［J］. Automotive Engineering， 2018， 40（2）： 127-132.
19	PACEJKA H B. Tyre and vehicle dynamic（the third edition）［M］. Oxford： Butterworth-Heinemann， 2012.
20	DORIGO M. Optimization learning and natural algorithms ［D］. Italy： Politecnico di Milano， 1992.
21	李小雨. 复合工况下分布式驱动电动汽车失稳机理及操纵稳定性控制研究［D］. 长春：吉林大学， 2020.

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A New Method for Describing and Solving the Vehicle Stability Region

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