Journal of Jilin University(Engineering and Technology Edition) ›› 2024, Vol. 54 ›› Issue (8): 2141-2148.doi: 10.13229/j.cnki.jdxbgxb.20221380

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H∞ loop shaping robust control of vehicle tracking on variable curvature curve

Sheng CHANG1(),Hong-fei LIU2(),Nai-wei ZOU3   

  1. 1.School of Automotive Engineering，Changshu Institute of Technology，Suzhou 215500，China
    2.College of Transportation，Jilin University，Changchun 130022，China
    3.College of Mechanical Engineering，Ningbo University of Technology，Ningbo 315336，China
  • Received:2022-10-28 Online:2024-08-01 Published:2024-08-30
  • Contact: Hong-fei LIU E-mail:changsheng_jms@163.com;hongfeiliu@jlu.edu.cn

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Abstract:

To solve the problem of vehicle deviate from the planned trajectory caused by the changing radius of curvature of the route， a robust control approach based on H∞ loop shaping is proposed to improve the automated trajectory tracking performance. Firstly， the vehicle dynamics model is analyzed and processed to provide the generalized interference control system form， and then the function operation of transfer is used to indirectly obtain the required output variables. Secondly， the nominal plant is selected and the nominal condition is given， the system singular values of the plants can obtain desired shapes based on the robust controller and thus can meet the system performance index and robust stability requirements. Finally， the automated tracking ability of the vehicle on the variable curvature paths is tested. The results show that the vehicle has a stable anti-interference ability under the action of fixed order robust controller， when parameters change within a reasonable range， the lateral error of the vehicle can be controlled within 0.2 m， the goal of good automated tracking performance in multi-curvature routes of the vehicle has realized. Therefore， this control method has a widely potential applications prospect and is suitable for the development of intelligent vehicle path tracking lateral control and autonomous vehicle lane keeping control.

Key words: vehicle engineering, variable curvature curve （road）, trajectory tracking, H∞ loop shaping

CLC Number: 

  • U461.6

Table 1

Minimum radius of circular curve"

设计速度/（km·h-1）圆曲线最小半径（一般值）/m
2030
3065
40100
60200
80400
100700
1201 000

Fig.1

Variable curvature road"

Table 2

Radius of curves and vehicle speeds"

弯道路段曲率半径/m前进车速/（km·h-1）前行距离/m各段时间/s弯道产生的角速度/（rad·s-1）
15006017410.40.033
27001001836.60.040
3600801577.10.037
41 0001202096.30.033
5800901124.50.031
6200601056.30.083

Fig.2

Vehicles model built in ground coordinate"

Table 3

Vehicles parameters"

符号参数名称及单位车辆1车辆2车辆3
m总质量/kg1 0051 8203 020
ms悬挂质量（总质量82%）/kg8241 4922 460
a质心至前轴距/m0.951.171.84
b质心至后轴距/m1.421.771.88
k1前轮总侧偏刚度/（N·rad-1）-45 454-72 653-46 294
k2后轮总侧偏刚度/（N·rad-1）-67 041-121 449-76 636
Iz整车绕z轴的转动惯量/（kg·m2）2 1453 74610 437
Ix悬挂质量绕x轴转动惯量/（kg·m2）6571 1801 960
Ixz悬挂质量绕x、z轴惯性积/（kg·m2）000
hs侧倾力臂/m0.450.410.49
Ef前轮侧倾转向系数0.110.16-0.114
Er后轮侧倾转向系数0.100.100
C?f前悬架侧倾角刚度/（N·m·rad-1）29 67652 151100 548
C?r后悬架侧倾角刚度/（N·m·rad-1）23 54341 40032 732
Df前悬架侧倾角阻尼/（N·m·s·rad-1）2 7504 9803 430
Dr后悬架侧倾角阻尼/（N·m·s·rad-1）2 0003 6243 430

Fig.3

Generalized control system"

Fig.4

Loop shaping design procedure"

Fig.5

Singular values of the plants"

Fig.6

Lateral tracking errors"

Fig.7

Feedback control block diagrams"

Fig.8

Lateral tracking errors of roads"

Fig.9

Comparison diagram of vehicle roll angle"

Fig.10

Partial enlarged detail"

Fig.11

Comparison of lateral tracking error when mass of vehicle changed"

Fig.12

Simulation results for three vehicles with| different parameters"

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