Stability analysis of semi-active suspension control system based on hysteresis system theory
XU Xu1, YANG Xiaofeng2, SHEN Yujie2, LI Yue1
1. School of Science, Jiangsu University, Zhenjiang 212013, China;
2. School of Automotive and Traffic Engineering, Jiangsu University, Zhenjiang 212013, China
Abstract：In order to study effects of time delay on stability of a semi-active suspension system, a 2-DOF semi-active suspension model with time delay was established, and sufficient and necessary conditions to satisfy all delay stability of the system was derived by using the improved all delay stability algebraic criterion according to the stability theory of time delay system, and the range of controllable damping value was obtained. Aiming at semi-active suspension parameters not satisfying the all delay stability condition, the stability switching point analysis method was proposed to solve and obtain the actual stability switching point and its stability interval. The time-domain simulation showed that the generation of time delay does not lead to the deterioration of suspension performance under the all delay stability condition; under the condition of non-all delay stability, the performance of suspension drops with increase in time delay and worsens sharply when time delay exceeds the stability switching point.
徐旭1，杨晓峰2，沈钰杰2，李玥1. 基于滞后型系统理论的半主动悬架控制系统稳定性分析[J]. 振动与冲击, 2021, 40(7): 208-215.
XU Xu1, YANG Xiaofeng2, SHEN Yujie2, LI Yue1. Stability analysis of semi-active suspension control system based on hysteresis system theory. JOURNAL OF VIBRATION AND SHOCK, 2021, 40(7): 208-215.
［1］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.
［2］SAAD M,AKHTAR S,RATHORE A K,et al.Control of semi-active suspension system using PID controller［J］.IOP Conference Series: Materials Science and Engineering, 2018, 404(1):12-39.
［3］陈助碧.1/4汽车半主动悬架系统的试验方法研究［D］.杭州：浙江大学，2006.
［4］HUANG D S, ZHANG J Q, LIU Y L. The PID semi-active vibration control on nonlinear suspension system with time delay［J］. International Journal of Intelligent Transportation Systems Research, 2018, 16(7): 125-137.
［5］WANG R C, CHEN L, JIANG H B.Study of largescale system hierarchical control of semi-active suspension with time-delay［J］. China Mechanical Engineering, 2007,18(11): 1382-1385.
［6］申永军，祁玉玲，杨绍普,等.含时滞的单自由度半主动悬架系统的动力学分析［J］.振动与冲击，2012，31(24):38-40.
SHEN Yongjun,QI Yuling,YANG Shaopu,et al.Dynamic analysis of asingle degree of freedom semi-active suspension system with time delay［J］.Journal of Vibration and Shock,2012,31(24):38-40.
［7］陈长征，王刚，于慎波.含输入时滞的电动汽车悬架系统有限频域振动控制的研究［J］.振动与冲击,2016,35(11):130-137.
CHEN Changzheng, WANG Gang, YU Shenbo.Study on finite frequency domain vibration control of electric vehicle suspension system with input delay［J］. Journal of Vibration and Shock,2016,35(11):130-137.
［8］张东梅, 俞立.线性时滞系统稳定性分析综述［J］. 控制与决策,2008,23(8): 841-849.
ZHANG Dongmei, YU Li. Stability analysis of linear time-delay systems［J］. Control and Decision, 2008, 23(8): 841-849.
［9］SHEN Y J，AHMADIAN M.Nonlinear dynamical analysis on four semi-active dynamic vibration absorbers with time delay［J］.Shock and Vibration,2013,20(4):649-663.
［10］WALTON K, MARSHALL J E. Direct method for TDS stability analysis［J］. IEE Proceedings D:Control and Theory Applications,1987,134(2):101-107.
［11］ZHANG J R, KNOPSE C R, TSIOTRAS P. Stability of time-delaysystems: equivalence between Lyapunov and scaled small-gain conditions［J］. IEEE Trans on Automatic Control,2001,46(3):482-486.
［12］刘林.时滞减振机理及其在车辆中的应用［D］.淄博：山东理工大学，2012.
［13］葛超.基于改进型Lyapunov泛函的时滞系统稳定性新判据研究及应用［D］.秦皇岛：燕山大学，2014.
［14］XIANG C, WANG Q G, LU X,et al.Stabilization of second-order unstable delay processes by simple controllers［J］. Journal of Process Control, 2007, 17(8): 675-682.
［15］狄成宽.一类时滞微分方程的稳定性切换几何判据法［J］.安徽大学学报,2013,37(1):18-22.
DI Chengkuan.Stability switching geometric criterion for a class of delay differential equations［J］. Journal of Anhui University, 2013, 37(1):18-22.
［16］CEPEDA-GOMEZ R, MICHIELS W. Some special cases in the stability analysis of multi-dimensional time-delay systems using the matrix Lambert W function［J］.Automatic, 2015, 53(42): 339-345.
［17］汪若尘,陈龙,江浩斌.时滞半主动悬架模糊神经网络控制［J］. 农业机械学报, 2007, 38(7): 10-12.
WANG Ruochen, CHEN Long, JIANG Haobin. Fuzzy neural-network control of semi-active suspension with time delay［J］. Transactions of the Chinese Society of Agricultural Machinery, 2007, 38(7): 10-12.
［18］闫盖，方明霞，董天夫，等.基于状态变换法的车辆悬架 系统时滞反馈控制［J］.农业工程学报，2018，34(10):54-61.
YAN Gai, FANG Mingxia, DONG Tianfu,et al. Time-delay feedback control of vehicle suspension system based on state transformation method［J］. Transactions of the Chinese Society of Agricultural Engineering, 2018,34(10): 54-61.
［19］汪若尘，陈龙，江浩斌. 基于多项式判别理论时滞半主动悬架稳定性研究［J］. 中国机械工程，2006，17(24):28-30.
WANG Ruochen, CHEN Long, JIANG Haobin. Study on stability of delayed semi-active suspension based on discriminant theory of polynomial［J］. China Mechanical Engineering, 2006, 17(24): 28-30.
［20］陈龙，汪若尘，江浩斌，等.半主动悬架及其控制系统的 时滞研究［J］. 中国机械工程，2005，16(24): 2249-2252.
CHEN Long, WANG Ruochen, JIANG Haobin,et al. Time delay study of semi-active suspension and its control system ［J］.China Mechanical Engineering, 2005,16(24):2249-2252.［20］杨绍普，申永军.滞后非线性系统的分岔与奇异［M］.北京：科学出版社，2003.
［21］刘永清，唐功友.大型动力系统的理论与应用:滞后?稳定与控制［M］.广州：华南理工大学出版社，1992.
［23］郑远广.含时滞的奇异摄动系统的非线性动力学［D］. 南京：南京航空航天大学，2009.
［24］张作元.滞后型方程x?(t)=Ax(t)+Bx(t－τ)全时滞稳定的代数判据［J］. 科学通报, 1986, 31(23): 1768-1771.
ZHANG Zuoyuan. Algebraic criteria for fully delay stability of retarded equation x?(t)=Ax(t)+Bx(t－τ)［J］. Science Bulletin, 1986, 31(23): 1768-1771.
［25］王霄锋.汽车悬架和转向系统设计［M］. 北京：清华大学出版社，2015.
