# 基于横摆力矩的轮胎侧向力估计算法 ………………………………

## 赵林峰 杨 军 张荣芸等（

China Mechanical Engineering - - 中国机械工程 -

1.合肥工业大学汽车与交通工程学院，合肥， 230009

2.安徽工程大学机械与汽车工程学院，芜湖， 241000

DOI：10.3969/j.issn.1004⁃132X.2018.19.003 开放科学(资源服务)标识码(OSID)：

Estimation Algorithm Tire Lateral Forces by Yaw Moments

ZHAO Linfeng1 YANG Jun1 ZHANG Rongyun2 CHEN Wuwei1

1.School of Automotive and Transportation Engineering，Hefei University of Technology，Hefei，230009 2.School of Mechanical and Automotive Engineering，Anhui Polytechnic University，

Wuhu，Anhui，241000

Abstract： A tire lateral force estimation algorithm was proposed based on yaw moments via the analysis of the nonlinear vehicle dynamic model . Three basic steps were used to estimate the tire lateral forces. Firstly，the yaw moments of lateral forces were estimated based on the disturbance observers. Then the sums of the lateral forces of the two front wheels and the two rear wheels were estimated by us⁃ ing the least squares method. Finally，an empirical method of proportional distribution for vertical loads was adopted to estimate each tire lateral forces. The tire lateral force estimation system was simulated based on the MATLAB/Simulink software. The results were compared with the ones of CarSim dynam⁃ ics simulation software，and the hardware in ⁃ loop simulation platform was used to verify the tests. The results show that the proposed estimation algorithm may accurately estimate the tire lateral forces，the applications of complex tire models and the dependences on ground adhesion coefficient are avoided.

Key words： yaw moment；tire lateral force；disturbance observer；estimation

0 引言随着人们对汽车操纵性和安全性要求的日益提高，汽车侧向主动安全控制系统得到了极大的关注与发展。轮胎侧向力是汽车主动安全控制系统对汽车进行稳定性控制的一个关键参数，该参数的准确与否能够直接影响主动安全控制系统如电子稳定性程序（ electronic stability program， ESP）的性能。目前，轮胎侧向力传感器高昂的成

［］ 1⁃5个非常复杂的物理量，对其进行描述的数学模型主要有 Magic formula 轮胎模型、Fila 轮胎模型和Dugoff轮胎模型等 。但在运用上述模型时，需要

［］ 6在线实时检测路面附着系数，即便对轮胎模型做了大量简化（如LuGre轮胎模型 ），其结果还是呈

［］ 7现非线性，从而导致估计器及控制器的控制算法设计变得十分复杂。此外，轮胎的侧向力与纵向力之

1 汽车动力学以及横摆模型

1.1 汽车动力学模型

1.2 横摆动力学模型

MO2 =+ I Z γ̇ maX e + maY lf = TXO2 + TYO2

TXO2 = 2e ( FXfr cosδ + FXrr )

TYO2 = -2eFYfr sinδ - ( FYfl + FYrr ) (+ lf lr )

（ 4）右前轮旋转中心横摆力矩：

MO3 =- I Z γ̇ maX e - maY lf = TXO3 + TYO3

TXO3 = -2e ( FXfl cosδ + FXrl )

TYO3 = 2eFYfl sinδ - ( FYrl + FYrr ) (+ lf lr )

（ 5）右后轮旋转中心横摆力矩：

MO4 =- I Z γ̇ maX e + maY lr = TXO4 + TYO4

TXO4 = -2e ( FXfl cosδ + FXrl ) +( FXfl + FXfr ) (+ lf lr ) sinδ

TYO4 = 2eFYflsinδ + ( FYfl + FYfr ) (+ lf lr ) cosδ

1.3 基于干扰观测器的侧向力横摆力矩估计