输出时滞控制系统稳定性分析及控制器设计
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摘要
考虑滤波器时滞对受控系统的影响,研究受控输出时滞系统的稳定性能。根据稳定性切换理论,确定多自由度受控系统的稳定时滞区域。经过分析获得受控系统脉冲响应衰减时间接近最短时的时滞量,在此基础上采用时滞引入法和滤波器设计法进行控制器设计。结合悬臂梁模型进行数值分析,结果表明:根据时滞系统稳定性分析设计的控制器能够使受控系统脉冲响应衰减速度提高80%以上,有效改善系统的控制效果和稳定性能。
The stability of a class of controlled systems with output time delay is analyzed in this paper.The range of time delay,in which the controlled system is stable,is confirmed by the stability switch theory.The time delay,which corresponds to the shortest decay time for step responses of the controlled system,is obtained analytically.According to time delay and filter design method,an effective controller is designed.And numerical simulations are performed on a cantilever beam to validate the proposed method.The results show that the decay rate of the system response is improved up to 80% after control,which ehhances control performence and stability of the system effectively.
The stability of a class of controlled systems with output time delay is analyzed in this paper.The range of time delay,in which the controlled system is stable,is confirmed by the stability switch theory.The time delay,which corresponds to the shortest decay time for step responses of the controlled system,is obtained analytically.According to time delay and filter design method,an effective controller is designed.And numerical simulations are performed on a cantilever beam to validate the proposed method.The results show that the decay rate of the system response is improved up to 80% after control,which ehhances control performence and stability of the system effectively.
引文
[1]Ali M S,Hou Z K,Noori M N.Stability and perfor-mance of feedback control systems with time delays[J].Computer&Structures,1998,66(2-3):241—248.
[2]胡海岩.振动主动控制中的时滞动力学问题[J].振动工程学报,1997,10(3):273—279.Hu Haiyan.On dynamics in vibration control withtime delay[J].Journal of Vibration Engeering,1997,10(3):273—279.
[3]陈龙祥,蔡国平.地震作用下建筑结构的多时滞最优控制[J].振动与冲击,2008,27(4):63—66.Chen Longxiang,Cai Guoping.Optimal controlmethod for seismically excited structures with multi-ple time delay in control[J].Journal of Vibration andShock,2008,27(4):63—66.
[4]Mohamed A R.Time-delay effects on active dampedstructures[J].Journal of Engineering Mechanics,1987,113(11):1 709—1 719.
[5]Mc Greery S,Soong T T,Reinhorn A M.An experi-ments study of time delay compensation in activestructural control[A].Proceedings of Sixth Interna-tional Modal Analysis Conference[C].Orlando,FL,USA,1988:1 733—1 739.
[6]李卫,孙增圻.包含延时的采样系统的最优控制[J].控制理论与应用,1987,4(2):10—18.Li Wei,Sun Zengqi.The linear quadratic optimal con-trol for sampled-data systems with delay in control[J].Control Theory&Applications,1987,4(2):10—18.
[7]Cai G P,Huang J.Optimal control method with timedelay in control[J].Journal of Sound and Vibration,2002,251(3):383—394.
[8]Chen L X,Cai G P.Design method of multiple time-delay controller for active structural vibration control[J].Applied Mathematics and Mechanics,2009,30(11):1 405—1 411.
[9]Haraguchi M,Hu H Y.Using a new discretization ap-proach to design delayed LQG controller[J].Journalof Sound and Vibration,2008,314(3-5):558—570.
[10]Sipahi R,Olgac N.Degenerate cases in using the di-rect method[J].Journal of Dynamic Systems,Mea-surement and Control,2003,125(2):194—201.
[11]Sipahi R,Olgac N.Direct method implementation forthe stability analysis of multiple time delayed systems[A].Proceedings of 2003 IEEE Conference on Con-trol Applications[C].Istanbul,Turkey,2003,2:943—948.
[12]Udwadia F E,von Bremen H F,Kumar R,et al.Time delayed control of structural systems[J].Earthquake Engineering and Structural Dynamics,2003,32(4):495—535.
[13]Wang Z H,Hu H Y.Stability switches of time-de-layed dynamic systems with unknown parameters[J].Journal of Sound and Vibration,2000,233(2):215—233.
[14]刘博,胡海岩.群时延引起的受控小车二级摆失稳及其抑制[J].振动工程学报,2009,22(5):443—448.Liu Bo,Hu Haiyan.Group delay induced instabilityand its suppression for a controlled-double pendulum[J].Journal of Vibration Engineering,2009,22(5):443—448.
[2]胡海岩.振动主动控制中的时滞动力学问题[J].振动工程学报,1997,10(3):273—279.Hu Haiyan.On dynamics in vibration control withtime delay[J].Journal of Vibration Engeering,1997,10(3):273—279.
[3]陈龙祥,蔡国平.地震作用下建筑结构的多时滞最优控制[J].振动与冲击,2008,27(4):63—66.Chen Longxiang,Cai Guoping.Optimal controlmethod for seismically excited structures with multi-ple time delay in control[J].Journal of Vibration andShock,2008,27(4):63—66.
[4]Mohamed A R.Time-delay effects on active dampedstructures[J].Journal of Engineering Mechanics,1987,113(11):1 709—1 719.
[5]Mc Greery S,Soong T T,Reinhorn A M.An experi-ments study of time delay compensation in activestructural control[A].Proceedings of Sixth Interna-tional Modal Analysis Conference[C].Orlando,FL,USA,1988:1 733—1 739.
[6]李卫,孙增圻.包含延时的采样系统的最优控制[J].控制理论与应用,1987,4(2):10—18.Li Wei,Sun Zengqi.The linear quadratic optimal con-trol for sampled-data systems with delay in control[J].Control Theory&Applications,1987,4(2):10—18.
[7]Cai G P,Huang J.Optimal control method with timedelay in control[J].Journal of Sound and Vibration,2002,251(3):383—394.
[8]Chen L X,Cai G P.Design method of multiple time-delay controller for active structural vibration control[J].Applied Mathematics and Mechanics,2009,30(11):1 405—1 411.
[9]Haraguchi M,Hu H Y.Using a new discretization ap-proach to design delayed LQG controller[J].Journalof Sound and Vibration,2008,314(3-5):558—570.
[10]Sipahi R,Olgac N.Degenerate cases in using the di-rect method[J].Journal of Dynamic Systems,Mea-surement and Control,2003,125(2):194—201.
[11]Sipahi R,Olgac N.Direct method implementation forthe stability analysis of multiple time delayed systems[A].Proceedings of 2003 IEEE Conference on Con-trol Applications[C].Istanbul,Turkey,2003,2:943—948.
[12]Udwadia F E,von Bremen H F,Kumar R,et al.Time delayed control of structural systems[J].Earthquake Engineering and Structural Dynamics,2003,32(4):495—535.
[13]Wang Z H,Hu H Y.Stability switches of time-de-layed dynamic systems with unknown parameters[J].Journal of Sound and Vibration,2000,233(2):215—233.
[14]刘博,胡海岩.群时延引起的受控小车二级摆失稳及其抑制[J].振动工程学报,2009,22(5):443—448.Liu Bo,Hu Haiyan.Group delay induced instabilityand its suppression for a controlled-double pendulum[J].Journal of Vibration Engineering,2009,22(5):443—448.
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