Journal of Jilin University(Engineering and Technology Edition) ›› 2021, Vol. 51 ›› Issue (4): 1230-1240.doi: 10.13229/j.cnki.jdxbgxb20200642

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Linear disturbance observer suitable for sliding mode control of nonlinear active suspension

Jiang-qi LONG1(),Jin-tao XIANG1,Ping YU1(),Jun-cheng WANG2   

  1. 1.College of Mechanical and Electrical Engineering,Wenzhou University,Wenzhou 325000,China
    2.Faculty of Mechanical Engineering and Automation,Zhejiang Sci-Tech University,Hangzhou 310018,China
  • Received:2020-08-20 Online:2021-07-01 Published:2021-07-14
  • Contact: Ping YU E-mail:longjiangqi@163.com;yuping55@zju.edu.cn

Abstract:

The active suspension based on the reference sky-hook model has problems such as nonlinear force, parameters uncertainty, and actuator non-ideality. To weaken the influence of these problems on the control effect, a linear disturbance observer (LDO) was proposed for estimating the uncertainties caused by the actuator imperfections, the nonlinear and uncertain parameters in the active suspension. Combined with sliding mode control (SMC) a control system is established. The influences of the sky-hook damping coefficient and uncertain parameters on the control effect are analyzed. After that, the method for selecting the sky-hook damping coefficient is proposed and the effectiveness of the observer is proved. Finally, the performance indexes of active suspension system with LDO-SMC based on reference skyhook model (LDO-SMCRSM) and SMC based on reference sky-hook model (SMCRSM) are calculated and compared in a bump and class-C road running condition. Simulation results shows that a better suspension performance can be obtained by using the proposed LDO-SMCRSM.

Key words: vehicle engineering, active suspension, linear disturbance observer, reference skyhook model, sliding mode control

CLC Number: 

  • U461.4

Fig.1

Nonlinear two-degree-of-freedom active suspension model"

Fig.2

Improved two-degree-of-freedom skyhook model"

Fig.3

Control principle diagram of control system with disturbance observer"

Table1

Basic parameters of active suspension system"

参数数值参数数值
ms/kg2.5k1.3
mus/kg1bn-3
ks1/(N?m-1)980bp2
ks2/(N?m-3)15 000cs2/(N?s2?m-2)100
cs1/(N?s?m-1)80kst/(N?m-1)2500
cst/(N?s?m-1)10zr/m0.035
ms0/kg2c12
ks0/(N?m-1)950k120
cs0/(N?s?m-1)80α600
k01μ00

Fig.4

Displacement changes of bump road"

Fig.5

Displacement changes of C-level road"

Fig.6

Structural simulation diagram of control system with observe"

Fig.7

Peak value of active suspension performance index in control system with disturbance observer"

Fig.8

Peak value of active suspension performance index in control system without disturbance observer"

Fig.9

Suspension performance index changes with spring mass"

Fig.10

Suspension performance indicators in the presence of dead zones"

Fig.11

Control principle diagram of control system without observe"

Fig.12

Structural simulation diagram of control system without observe"

Fig.13

Performance index of active suspension excited by bump model"

Fig.14

Active suspension performance index excited by class C road model"

1 Pang H, Zhang X, Xu Z. Adaptive backstepping-based tracking control design for nonlinear active suspension system with parameter uncertainties and safety constraints[J]. Isa Transactions, 2019, 88: 23-36.
2 Ma X, Wong P K, Zhao J. Practical multi-objective control for automotive semi-active suspension system with nonlinear hydraulic adjustable damper[J]. Mechanical Systems and Signal Processing, 2019, 117: 667-688.
3 Jing H, Wang R, Li C, et al. Robust finite-frequency H control of full-car active suspension[J]. Journal of Sound and Vibration, 2019, 441: 221-239.
4 Pusadkar U S, Chaudhari S, Shendge P D, et al. Linear disturbance observer based sliding mode control for active suspension systems with non-ideal actuator[J]. Journal of Sound and Vibration, 2019, 442: 428-444.
5 Pan H, Sun W, Jing X, et al. Adaptive tracking control for active suspension systems with non-ideal actuators[J]. Journal of Sound and Vibration, 2017, 399: 2-20.
6 Pang H, Zhang X, Yang J, et al. Adaptive backstepping-based control design for uncertain nonlinear active suspension system with input delay[J]. International Journal of Robust and Nonlinear Control, 2019, 29(16): 5781-5800.
7 于树友,曹瑞丽,刘清宇,等.具有双层控制结构的馈能悬架输出反馈控制策略[J].吉林大学学报:工学版,2020, 50(4): 1191-1200.
Yu Shu-you, Cao Rui-li, Liu Qing-yu, et al. Two-layered output feedback control of energy-regenerative suspensions[J]. Journal of Jilin University (Engineering and Technology Edition),2020, 50(4): 1191- 1200.
8 Zhang J, Ding F, Zhang N, et al. A new SSUKF observer for sliding mode force tracking H control of electrohydraulic active suspension[J]. Asian Journal of Control, 2020, 22(2): 761-778.
9 Li W, Xie Z, Zhao J, et al. Fuzzy finite-frequency output feedback control for nonlinear active suspension systems with time delay and output constraints[J]. Mechanical Systems and Signal Processing, 2019, 132: 315-334.
10 Liu Y J, Zeng Q, Liu L, et al. An adaptive neural network controller for active suspension systems with hydraulic actuator[J]. IEEE Transactions on Systems, Man, and Cybernetics, 2018, 50(12): 5351-5360.
11 Sun H, Li Y M, Tong S C. A fuzzy adaptive control strategy for active suspension systems with unknown dynamics[C]∥International Conference on Security, Pattern Analysis, and Cybernetics, Jinan, China,2018:No. 8965615.
12 陈潇凯,王晨宇,施国标. 车辆主动悬架与电动助力转向系统协同优化[J].吉林大学学报:工学版,2020, 50(4): 1153-1159.
Chen Xiao-kai, Wang Chen-yu, Shi Guo-biao. Collaborative optimization of vehicle active suspension and electric power steering system[J]. Journal of Jilin University (Engineering and Technology Edition),2020, 50(4):1153-1159.
13 姚嘉凌,郑加强,蔡伟义.车辆半主动悬架模型参考滑模控制[J].农业机械学报,2008, 39(4):5-8, 38.
Yao Jia-ling, Zheng Jia-qiang, Cai Wei-yi. Sliding mode model-following control of automobile semi-active suspension system[J]. Transactions of the Chinese Society for Agricultural Machinery,2008, 39(4):5-8, 38.
14 侯力文.汽车悬架系统运动特性与半主动控制研究[D].济南:山东大学机械工程学院,2019.
Hou Li-wen. Research on motion characteristics and semi-active control of automobile suspension system[D]. Jinan: School of Mechanical Engineering, Shandong University,2019.
15 黄喆.基于状态观测器的主动悬架滑模控制研究[D]. 西安:长安大学汽车学院, 2019.
Huang Zhe. Research on active suspension sliding mode control based on state observer[D]. Xi'an:College of Automobile, Chang'an University, 2019.
16 Xiao L. Uncertainty and disturbance estimator based control of active suspensions with a hydraulic actuator[J]. International Test Conference, 2016, 45(4): 376-383.
17 秦武,上官文斌,吕辉.非线性二自由度主动悬架滑模控制方法的研究[J]. 机械工程学报,2020, 56(1): 58-68.
Qin Wu, Shangguan Wen-bin, Lv Hui. Research on sliding mode control for nonlinear active suspension with two degrees of freedom [J]. Chinese Journal of Mechanical Engineering,2020, 56(1): 58-68.
18 秦武,康英姿,上官文斌,等.基于天棚模型和扰动观测器的主动悬架滑模控制研究[J].华南理工大学学:自然科学版,2020, 48(6): 16-24, 33.
Qin Wu, Kang Ying-zi, Shangguan Wen-bin, et al. Study on sliding mode control with disturbance observer integrating skyhook model for active suspension[J]. Journal of South China University of Technology (Natural Science Edition), 2020, 48(6): 16-24, 33.
19 Corina Sandu, Andersen Erik R, Steve Southward, et al. Multibody dynamics modelling and system identification of a quarter-car test rig with McPherson strut suspension[J]. Vehicle System Dynamics, 2011, 49(1/2): 153-179.
20 Zhou J. Brief paper: decentralized adaptive control for large-scale time-delay systems with dead-zone input[J]. Automatica, 2008, 44(7): 1790-1799.
21 Corless M, Leitmann G. Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems[J]. IEEE Transactions on Automatic Control, 1981, 26(5): 1139-1144.
22 Sun W, Zhao Z, Gao H, et al. Saturated adaptive robust control for active suspension systems[J]. IEEE Transactions on Industrial Electronics, 2013, 60(9): 3889-3896.
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