网络化牵引控制系统H_∞采样控制及其应用
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摘要
基于Lyapunov-Krasovskii稳定性定理,采用采样控制方法,研究具有时滞的网络化牵引控制系统H∞控制问题。利用闭环泛函方法,构造新的包含更多采样点信息的Lyapunov-Krasovskii泛函,从而获得具有更小保守性的稳定性判据。随后,将此判据拓展到含有外部输入以及参数不确定的网络化牵引控制系统中,并给出H∞采样控制器求解方法。实例仿真结果表明:所得H∞控制器能使牵引电机模型状态趋于稳定,说明该求解方法有效的。
Based on the Lyapunov-Krasovskii stability theorem, the H_∞ control problem of networked traction control system with time delay was studied by sampled-data control approach. By constructing new Lyapunov-Krasovskii functional with loop-functional approach which contains more information of sampling points. A less conservative stability criterion was obtained. Then, the criterion was extended to the network control system with external inputs and uncertain parameter, and the H_∞ sampling controller was derived. Finally, in simulink examples, the obtained controller can make the states of networked traction control system stable, which proves that the method is feasible.
Based on the Lyapunov-Krasovskii stability theorem, the H_∞ control problem of networked traction control system with time delay was studied by sampled-data control approach. By constructing new Lyapunov-Krasovskii functional with loop-functional approach which contains more information of sampling points. A less conservative stability criterion was obtained. Then, the criterion was extended to the network control system with external inputs and uncertain parameter, and the H_∞ sampling controller was derived. Finally, in simulink examples, the obtained controller can make the states of networked traction control system stable, which proves that the method is feasible.
引文
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[2]陈刚,王信,肖伸平,等.具有混合时变时滞主从神经网络的指数采样同步控制[J].中南大学学报(自然科学版),2018,49(6):1432-1439.CHEN Gang,WANG Xin,XIAO Shenping,et al.Sampled-data exponential synchronization of master-slave neural networks with time-varying mixed delays[J].Journal of Central South University(Science and Technology),2018,49(6):1432-1439.
[3]LIU Yajuan,LEE S.H∞sampled-data control of LPV systems with time-varying delay[J].Transactions of the Korean Institute of Electrical Engineers,2015,64(1):121-127.
[4]JIANG Guoping,TANG W K,CHEN Guanrong.Astate-observer-based approach for synchronization in complex dynamical networks[J].IEEE Transactions on Circuits&Systems I:Regular Papers,2006,53(12):2739-2745.
[5]LI Xiaojian,YANG Guanghong.Adaptive fault-tolerant synchronization control of a class of complex dynamical networks with general input distribution matrices and actuator faults[J].IEEE Transactions on Neural Networks&Learning Systems,2017,28(2):559-569.
[6]YANG Xinsong,CAO Jinde,LU Jianquan.Stochastic synchronization of complex networks with nonidentical nodes via hybrid adaptive and impulsive control[J].IEEE Transactions on Circuits&Systems I:Regular Papers,2012,59(2):371-384.
[7]WU Zhengguang,SHI Peng,SU Hongye,et al.Exponential synchronization of neural networks with discrete and distributed delays under time-varying sampling[J].IEEE Transactions on Neural Networks&Learning Systems,2012,23(9):1368-1376.
[8]HESPANHA J P,NAGHSHTABRIZI P,XU Yonggang.A survey of recent results in networked control systems[J].Proceedings of the IEEE,2007,95(1):138-162.
[9]冯晓云.电力牵引交流传动及其控制系统[M].北京:高等教育出版社,2009:48-125.FENG Xiaoyun.Electric traction AC drive and its control system[M].Beijing:Higher Education Press,2009:48-125.
[10]张兴华,戴先中.基于逆系统方法的感应电机调速控制系统[J].控制与决策,2000,15(6):708-711.ZHANG Xinghua,DAI Xianzhong.Control and decision making of induction motor speed control system based on inverse system method[J].Decision and Control 2000,15(6):708-711.
[11]巫庆辉.感应电电动动机定子磁链与转矩的逆解耦及存在性[J].控制理论与应用,2009,26(9):983-987.WU Qinghui.Inverse decoupling and existence of stator flux and torque of induction motor drives[J].Control Theory and Applications,2009,26(9):983-987.
[12]李欣.基于列车通信网络的牵引控制系统建模及控制策略研究[D].兰州:兰州交通大学自动化与电气工程学院,2013:46-50.LI Xin.Research on modeling and control strategy of traction control system based on train communication network[D].Lanzhou:Lanzhou Jiaotong University.College of Automation and Electrical Engineering,2013:46-50.
[13]KWON O M,PARK M J,JU H P,et al.Stability and stabilization for discrete-time systems with time-varying delays via augmented Lyapunov-Krasovskii functional[J].Journal of the Franklin Institute,2013,350(3):521-540.
[14]KIM J H.Note on stability of linear systems with time-varying delay[J].Automatica,2011,47(9):2118-2121.
[15]TIAN Junkang,XIONG Weijun,XU Fang.Improved delay-partitioning method to stability analysis for neural networks with discrete and distributed time-varying delays[J].Applied Mathematics&Computation,2014,233(3):152-164.
[16]ZENG Hongbing,HE Yong,WU Min,et al.Complete delay-decomposing approach to asymptotic stability for neural networks with time-varying delays[J].IEEE Transactions on Neural Networks,2011,22(5):806-812.
[17]CHEN Jie,GU Keqin,KHARITONOV V L.Stability of time-delay systems[M].Birkh?user Boston,2003,5(4):213-217.
[18]SEURET A,GOUAISBAUT F.Wirtinger-based integral inequality:application to time-delay systems[J].Automatica,2013,49(9):2860-2866.
[19]ZENG Hongbing,HE Yong,WU Min,et al.Free-matrix-based integral inequality for stability analysis of systems with time-varying delay[J].IEEE Transactions on Automatic Control,2015,60(10):2768-2772.
[20]ZENG Hongbing,HE Yong,WU Min,et al.New results on stability analysis for systems with discrete distributed delay[J].Automatica,2015,60:189-192.
[21]PARK P G,LEE W I,LEE S Y.Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems[J].Journal of the Franklin Institute,2015,352(4):1378-1396.
[22]SEURET A.A novel stability analysis of linear systems under asynchronous samplings[J].Automatica,2012,48(1):177-182.
[23]KAO Chungyao.An IQC approach to robust stability of aperiodic sampled-data systems[J].IEEE Transactions on Automatic Control,2016,61(8):2219-2225.
[24]ZHANG Yijun,YUE Dong,TIAN Engang.New stability criteria of neural networks with interval time-varying delay:a piecewise delay method[J].Applied Mathematics and Computation,2009,208(1):249-259.
[25]RAKKIYAPPAN R,LATHA V P,ZHU Quanxin.Exponential synchronization of Markovian jumping chaotic neural networks with sampled-data and saturating actuators[J].Nonlinear Analysis Hybrid Systems,2017,24:28-44.
[26]ZENG Hongbing,PARK J H,SHEN Hao.Robust passivity analysis of neural networks with discrete and distributed delays[J].Neurocomputing,2015,149(PB):1092-1097.
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