线控转向系统有限时间鲁棒抗扰控制

doi:10.16182/j.issn1004731x.joss.24-1370

摘要/Abstract

摘要：

为了消除参数摄动和外部扰动对汽车线控转向(SbW)系统的车轮转角跟踪控制性能的影响，提出了一种基于有限时间扰动观测器的分数阶积分终端滑模控制策略。设计了一种基于滑模的二阶有限时间扰动观测器，实现了SbW系统总扰动的精确估计，并将估计的总扰动补偿到系统控制输入，降低车轮转角跟踪误差。为确保车轮转角跟踪误差的快速收敛和抖振抑制，设计了分数阶快速积分终端滑模控制策略。实验结果表明：所提控制策略在转角跟踪误差的MAE和RMSE上相比PI、FOFITSMC和NASTSMC策略均改善了25%以上，具有更好的控制精度和鲁棒性。本文设计的控制策略为实际工程中SbW系统控制器设计提供了理论参考。

关键词: 线控转向系统, 有限时间观测器, 分数阶, 终端滑模控制, 车轮转角跟踪

Abstract:

To eliminate the influence of parameter perturbations and external disturbances on the wheel angle tracking control performance of steer-by-wire (SbW) system, a fractional-order integral terminal sliding mode control scheme based on a finite-time disturbance observer is proposed. A sliding mode-based second order finite-time disturbance observer (FDO) is designed to precisely estimate the total disturbance of the SbW system, and the estimated total disturbance is compensated into the system control input to reduce the wheel angle tracking error. A fractional-order fast integral terminal sliding mode control (FOFITSMC) scheme is designed to ensure fast convergence of the wheel angle tracking error and achieve the suppression of chattering. Results demonstrate that the proposed control strategy improves the MAE and RMSE of angle tracking by over 25% compared to PI, FOFITSMC, and NASTSMC strategies, and has better control accuracy and robustness. The control scheme proposed in the paper provides theoretical reference for the design of SbW system controllers in actual engineering.

Key words: SbW system, finite-time observer, fractional order, terminal sliding mode control, wheel angle tracking

中图分类号:

TP391

张静宜,陈新,丁金刚等 . 线控转向系统有限时间鲁棒抗扰控制[J]. 系统仿真学报, 2025, 37(6): 1376-1387.

Zhang Jingyi,Chen Xin,Ding Jingang,et al . Finite-time Robust Anti-disturbance Control for Steer-by-wire System[J]. Journal of System Simulation, 2025, 37(6): 1376-1387.

图/表 12

图1

图2

图3

表1

SbW系统参数

参数	数值	参数	数值
$I d s / (k g ⋅ m 2)$	2.6	$B f s / ((N ⋅ m ⋅ s) / r a d)$	0.038
$B d s / ((N ⋅ m ⋅ s) / r a d)$	12	$m 2 / m 1$	3
$I f s / (k g ⋅ m 2)$	0.021 29	$η$	6

表1

表2

控制策略参数

参数	数值	参数	数值
$η 1$	391	$p$	19
$η 2$	16	$q$	13
$η 3$	0.95	$μ$	0.8
$ϕ$	270	$k$	0.7
$α$	17	$κ$	0.4

表2

图4

表3

图5

图6

图7

图8

表4

参考文献 34

1	杜文龙, 陈俐, 刘文通, 等. 考虑延迟的线控转向二自由度内模控制[J]. 中国机械工程, 2021, 32(16): 1904-1911, 1920.
	Du Wenlong, Chen Li, Liu Wentong, et al. 2DOF Internal Model Control for Steer-by-wire Systems with Time Delay[J]. China Mechanical Engineering, 2021, 32(16): 1904-1911, 1920.
2	Jiao Xiaohong, Li Guanghui, Wang Hui. Adaptive Finite Time Servo Control for Automotive Electronic Throttle with Experimental Analysis[J]. Mechatronics, 2018, 53: 192-201.
3	石琴, 刘鑫, 应贺烈, 等. 电液线控制动系统压力反步控制算法研究[J]. 汽车工程, 2022, 44(5): 747-755.
	Shi Qin, Liu Xin, Ying Helie, et al. Study on the Backstepping Control Algorithm for the Hydraulic Pressure in Electro-hydraulic Brake-by-wire System[J]. Automotive Engineering, 2022, 44(5): 747-755.
4	Jung DaeYi, Kim Seulgi. Hardware-in-the-loop Simulation of Synchronous Motion Control for Dual-motor Driving Steer-by-wire System Integrated with Optimal Finite Preview Path-tracking Control[J]. IEEE Transactions on Vehicular Technology, 2024, 73(3): 3311-3328.
5	Wang Yunlong, Liu Yan, Wang Yongfu, et al. Neural Output Feedback Control of Automobile Steer-by-wire System with Predefined Performance and Composite Learning[J]. IEEE Transactions on Vehicular Technology, 2023, 72(5): 5906-5921.
6	Luo Gang, Li Hongjuan, Ma Bingxin, et al. Event-triggered Adaptive Fuzzy Control for Automated Vehicle Steer-by-wire System with Prescribed Performance: Theoretical Design and Experiment Implementation[J]. Expert Systems with Applications, 2022, 195: 116458.
7	He Lin, Li Feilong, Guo Chaolu, et al. An Adaptive PI Controller by Particle Swarm Optimization for Angle Tracking of Steer-by-wire[J]. IEEE/ASME Transactions on Mechatronics, 2022, 27(5): 3830-3840.
8	Wang Yunlong, Wang Yongfu. Discrete-time Adaptive Neural Network Control for Steer-by-wire Systems with Disturbance Observer[J]. Expert Systems with Applications, 2021, 183: 115395.
9	Huang Chao, Naghdy F, Du Haiping. Delta Operator-based Fault Estimation and Fault-tolerant Model Predictive Control for Steer-by-wire Systems[J]. IEEE Transactions on Control Systems Technology, 2018, 26(5): 1810-1817.
10	Huang Chao, Naghdy F, Du Haiping. Observer-based Fault-tolerant Controller for Uncertain Steer-by-wire Systems Using the Delta Operator[J]. IEEE/ASME Transactions on Mechatronics, 2018, 23(6): 2587-2598.
11	Jia Huaiyuan, Shang Weiwei, Xie Fei, et al. Second-order Sliding-mode-based Synchronization Control of Cable-driven Parallel Robots[J]. IEEE/ASME Transactions on Mechatronics, 2020, 25(1): 383-394.
12	Hu Youhao, Wang Hai. Robust Tracking Control for Vehicle Electronic Throttle Using Adaptive Dynamic Sliding Mode and Extended State Observer[J]. Mechanical Systems and Signal Processing, 2020, 135: 106375.
13	Wang Hai, Liu Linfeng, He Ping, et al. Robust Adaptive Position Control of Automotive Electronic Throttle Valve Using PID-type Sliding Mode Technique[J]. Nonlinear Dynamics, 2016, 85(2): 1331-1344.
14	Wang Hai, Kong Huifang, Man Zhihong, et al. Sliding Mode Control for Steer-by-wire Systems with AC Motors in Road Vehicles[J]. IEEE Transactions on Industrial Electronics, 2014, 61(3): 1596-1611.
15	Do M T, Man Zhihong, Zhang Cishen, et al. Robust Sliding Mode-based Learning Control for Steer-by-wire Systems in Modern Vehicles[J]. IEEE Transactions on Vehicular Technology, 2014, 63(2): 580-590.
16	Sun Zhe, Zheng Jinchuan, Man Zhihong, et al. Robust Control of a Vehicle Steer-by-wire System Using Adaptive Sliding Mode[J]. IEEE Transactions on Industrial Electronics, 2016, 63(4): 2251-2262.
17	Wu Xiaodong, Zhang Mingming, Xu Min. Active Tracking Control for Steer-by-wire System with Disturbance Observer[J]. IEEE Transactions on Vehicular Technology, 2019, 68(6): 5483-5493.
18	Sun Zhe, Zheng Jinchuan, Man Zhihong, et al. Nested Adaptive Super-twisting Sliding Mode Control Design for a Vehicle Steer-by-wire System[J]. Mechanical Systems and Signal Processing, 2019, 122: 658-672.
19	Hou Qiankang, Ding Shihong. GPIO Based Super-twisting Sliding Mode Control for PMSM[J]. IEEE Transactions on Circuits and Systems II: Express Briefs, 2021, 68(2): 747-751.
20	Xu Jian, Wang Man, Qiao Lei. Dynamical Sliding Mode Control for the Trajectory Tracking of Underactuated Unmanned Underwater Vehicles[J]. Ocean Engineering, 2015, 105: 54-63.
21	Yan Zheping, Wang Man, Xu Jian. Robust Adaptive Sliding Mode Control of Underactuated Autonomous Underwater Vehicles with Uncertain Dynamics[J]. Ocean Engineering, 2019, 173: 802-809.
22	Hu Youhao, Wang Hai, He Shuping, et al. Adaptive Tracking Control of an Electronic Throttle Valve Based on Recursive Terminal Sliding Mode[J]. IEEE Transactions on Vehicular Technology, 2021, 70(1): 251-262.
23	Chiu C S. Derivative and Integral Terminal Sliding Mode Control for a Class of MIMO Nonlinear Systems[J]. Automatica, 2012, 48(2): 316-326.
24	Qiao Lei, Zhang Weidong. Adaptive Non-singular Integral Terminal Sliding Mode Tracking Control for Autonomous Underwater Vehicles[J]. IET Control Theory & Applications, 2017, 11(8): 1293-1306.
25	Qiao Lei, Zhang Weidong. Double-loop Integral Terminal Sliding Mode Tracking Control for UUVs with Adaptive Dynamic Compensation of Uncertainties and Disturbances[J]. IEEE Journal of Oceanic Engineering, 2019, 44(1): 29-53.
26	Jia Shiyuan, Shan Jinjun. Continuous Integral Sliding Mode Control for Space Manipulator with Actuator Uncertainties[J]. Aerospace Science and Technology, 2020, 106: 106192.
27	Dong Xubin, Zhao Dingxuan, Yang Bin, et al. Fractional-order Control of Active Suspension Actuator Based on Parallel Adaptive Clonal Selection Algorithm[J]. Journal of Mechanical Science and Technology, 2016, 30(6): 2769-2781.
28	Zhang Bitao, Pi Youguo, Luo Ying. Fractional Order Sliding-mode Control Based on Parameters Auto-tuning for Velocity Control of Permanent Magnet Synchronous Motor[J]. ISA Transactions, 2012, 51(5): 649-656.
29	Mousavi Yashar, Alfi Alireza. A Memetic Algorithm Applied to Trajectory Control by Tuning of Fractional Order Proportional-integral-derivative Controllers[J]. Applied Soft Computing, 2015, 36: 599-617.
30	Li Haitao, Ning Xin, Han Bangcheng. Composite Decoupling Control of Gimbal Servo System in Double-gimbaled Variable Speed CMG Via Disturbance Observer[J]. IEEE/ASME Transactions on Mechatronics, 2017, 22(1): 312-320.
31	Zhang Longbin, Li Zhijun, Yang Chenguang. Adaptive Neural Network Based Variable Stiffness Control of Uncertain Robotic Systems Using Disturbance Observer[J]. IEEE Transactions on Industrial Electronics, 2017, 64(3): 2236-2245.
32	Razmjooei Hamid, Palli Gianluca, Abdi E, et al. Design and Experimental Validation of An Adaptive Fast-finite-time Observer on Uncertain Electro-hydraulic Systems[J]. Control Engineering Practice, 2023, 131: 105391.
33	Razmjooei Hamid, Palli Gianluca, Janabi-Sharifi F, et al. Adaptive Fast-finite-time Extended State Observer Design for Uncertain Electro-hydraulic Systems[J]. European Journal of Control, 2023, 69: 100749.
34	Shtessel Y B, Shkolnikov I A, Levant A. Smooth Second-order Sliding Modes: Missile Guidance Application[J]. Automatica, 2007, 43(8): 1470-1476.

控制策略	MAE	RMSE
FDO-FOFITSMC	0.003 0	0.003 5
FOFITSMC	0.004 1	0.004 7
NASTSMC	0.004 6	0.005 5
PI	0.005 9	0.006 7

工况	控制策略	MAE	RMSE
Ⅰ	FDO-FOFITSMC	0.001 1	0.001 4
	FOFITSMC	0.002 7	0.003 2
	NASTSMC	0.001 3	0.001 5
	PI	0.003 0	0.003 7
Ⅱ	FDO-FOFITSMC	0.001 2	0.001 7
	FOFITSMC	0.002 5	0.003 5
	NASTSMC	0.002 0	0.002 4
	PI	0.002 0	0.002 6
Ⅲ	FDO-FOFITSMC	0.000 8	0.001 0
	FOFITSMC	0.001 8	0.002 0
	NASTSMC	0.001 7	0.001 8
	PI	0.002 8	0.003 5

[1]	孙晓安, 栾小丽, 刘飞. 基于智能优化灰色模型的电子固废预测[J]. 系统仿真学报, 2022, 34(3): 536-542.
[2]	余伟, 梁恒辉, 罗映. 一种改进差分进化算法的分数阶系统辨识研究[J]. 系统仿真学报, 2021, 33(5): 1157-1166.
[3]	范存礼, 戴娟, 刘海涛, 苏中, 朱翠, 徐文婷. 基于神经网络与分数阶滑模的行星进入段轨迹跟踪控制[J]. 系统仿真学报, 2021, 33(11): 2697-2703.
[4]	李远禄, 李腾, 刘宝莹. 基于Haar小波运算矩阵的分数阶系统辨识方法[J]. 系统仿真学报, 2020, 32(6): 1032-1037.
[5]	张鑫, 李嘉欣. 基于分数阶微积分的机械臂滑模控制的研究[J]. 系统仿真学报, 2020, 32(5): 911-917.
[6]	董泽, 马宁. 差分量子粒子群算法的分数阶混沌系统参数估计[J]. 系统仿真学报, 2019, 31(8): 1664-1673.
[7]	刘梦, 甘朝晖, 张士英. 一种分数阶流控忆感器的幅频特性分析[J]. 系统仿真学报, 2019, 31(6): 1179-1187.
[8]	王天润, 苏中, 刘宁, 李超, 付国栋. 跌倒检测的时频特征提取方法研究[J]. 系统仿真学报, 2019, 31(12): 2600-2605.
[9]	黄宇, 谢天, 武蕊. 一类分数阶混沌系统的线性自抗扰优化控制[J]. 系统仿真学报, 2019, 31(10): 2093-2102.
[10]	甘朝晖, 张士英, 吴宇鑫. 一种带有非线性漂移函数的分数阶忆阻器模型[J]. 系统仿真学报, 2018, 30(8): 2884-2891.
[11]	赵志诚, 赵志涛, 张井岗, 赵显姣. 直流调速系统的改进型分数阶滑模控制[J]. 系统仿真学报, 2018, 30(3): 1096-1136.
[12]	栾新, 辛佳, 宋大雷, 赵维加. 分数阶微分方程组的一种高精度数值算法[J]. 系统仿真学报, 2018, 30(2): 421-426.
[13]	郑征, 马方军, 韦延方. 单相PWM整流器分数阶建模与仿真分析[J]. 系统仿真学报, 2017, 29(4): 784-790.
[14]	李杰, 王艳, 纪志成, 严大虎. 改进滑模观测器的永磁同步电机无传感器控制[J]. 系统仿真学报, 2017, 29(12): 3139-3148.
[15]	薛薇, 徐进康, 贾红艳. 一个分数阶超混沌系统同步及其保密通信研究[J]. 系统仿真学报, 2016, 28(8): 1915-1922.