柔性板的时滞H_∞控制的理论与实验研究
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摘要
以柔性板为对象,开展时滞H_∞控制的理论与实验研究.首先给出柔性板的时滞动力学方程;然后利用Lyapunov-Krasovskii泛函和自由权矩阵法,推导了闭环时滞系统渐近稳定的矩阵不等式;进而根据该矩阵不等式采用参数调节法及遗传算法,研究了如下两类控制设计问题:已知控制律求解最大稳定时滞量,已知最大稳定时滞量求解H_∞控制律;最后对理论研究成果进行了数值仿真和实验验证.结果显示,获得的H_∞控制律能够有效地抑制板的弹性振动,所确定出的保证系统稳定性的时滞区间更接近实际情况.
This paper presents theoretical and experimental studies of H_∞control for a flexible plate with time delay.Firstly,the time-delay dynamic equation of the plate is established.Secondly,a matrix inequality for system asymptotic stability is derived by using the Lyapunov-Krasovskii functional and free-weighting matrix method.Based on the matrix inequality,two control design problems are solved by using the parameter adjustment method and genetic algorithm:(1)H_∞controller design with known maximum time delay of the system;(2)determination of maximum time delay with known controller.Finally,simulation and experiments are carried out to verify the theoretical results.Simulation and experimental results demonstrate that the designed H_∞controller is effective in reducing the plate vibration and the determined maximum time delay guaranteeing the system stability is close to the real time delay of the system.
This paper presents theoretical and experimental studies of H_∞control for a flexible plate with time delay.Firstly,the time-delay dynamic equation of the plate is established.Secondly,a matrix inequality for system asymptotic stability is derived by using the Lyapunov-Krasovskii functional and free-weighting matrix method.Based on the matrix inequality,two control design problems are solved by using the parameter adjustment method and genetic algorithm:(1)H_∞controller design with known maximum time delay of the system;(2)determination of maximum time delay with known controller.Finally,simulation and experiments are carried out to verify the theoretical results.Simulation and experimental results demonstrate that the designed H_∞controller is effective in reducing the plate vibration and the determined maximum time delay guaranteeing the system stability is close to the real time delay of the system.
引文
1吴敏,何勇.时滞系统鲁棒控制-自由权矩阵法.北京:科学出版社,2008(Wu Min,He Yong.Robust Control for Time Delay System-Free-Weighting Matrices.Beijing:Science Press,2008(in Chinese))
2贾英民鲁棒H_∞控制.北京.科学出版社,2007(Jia Yingmin. Robust Hoo Control.Beijing:Science Press,2007(in Chinese))
3 Jamshidi M.Robust Control Systems with Genetic Algorithms. CRC Press,2003
4 Abdel-Rohman M.Time-delay effects on actively damped structures.Journal of Engineering Mechanics,ASCE, 1987,113(11):1709-1719
5 Chung LL,Reinhorn AM,Soong TT.Experiments on active control of seismic structures.Journal of Engineering Mechanics,ASCE,1988,114(2):241-256
6 Greery SM,Soong TT,Reinhorn AM.An experimental study of time delay compensation in active structural control. Proceedings of the sixth International Modal Analysis Conference,SEM,Orlando,USA,1988,1:733-739
7 Cai GP,Huang JZ.Optimal control method for seismically excited building structures with time delay in control. Journal of Engineering Mechanics,ASCE,2002,128(6): 602-612
8 Cai GP,Huang JZ,Yang SX.An optimal control method for linear systems with time delay.Computers and Structures, 2003,81(15):1539-1546
9 Chen LX,Cai GP,Pan J.Experimental study of delayed feedback control for a flexible plate.Journal of Sound and Vibration,2009,322(4-5):629-651
10陈龙祥.结构振动的时滞反馈控制及其实验研究.[博士论文].上海:上海交通大学,2009(Chen Long-Xiang,Delayed feedback control and experiment study of flexible structures. [PhD Thesis].Shanghai:Shanghai Jiaotong University, 2009(in Chinese))
11 Cai GP,Chen LX.Delayed feedback control experiments on some flexible structures.Acta Mechanica Sinica,2010, 26(6):951-965
12 Liu B,Masakazu H,Hu HY.A new reduction-based LQ control for dynamic systems with a slowly time-varying delay. Acta Mechanica Sinica,2009,25(4):529-537
13 Masakazu H,Hu HY.Using a new discretization approach to design a delayed LQG controller.Journal of Sound and Vibration,2008,314(3-5):558-570
14 Du HP,Zhang N.H_∞control for buildings with time delay in control via linear matrix inequalities and genetic algorithms. Engineering Structures,2008,30(1):81-92
15于骁,谭述君,林家浩.地震作用下建筑结构基于平衡降阶的时滞离散H_∞控制.工程力学,2008,25(2):148-153(Yu Yao,Tan Shujun,Lin Jiahao.Balanced-reduction control for vibration attenuation of seismic-excited buildings with controller delays.Engineering Mechanics,2008,25(2):148-153(in Chinese))
16 Chen P,Tian YC.Delay-dependent robust H_∞control for uncertain systems with time-varting delay.Information Science,2009,179(18):3187-3197
17 Cavallo A,Maria GD,Natale C,et al.Robust control of flexible structures with stable bandpass controllers.Automatica, 2008,44(5):1251-1260
18 Qiu ZC,Zhang XM,Wu HX,et al.Optimal placement and active vibration control for piezoelectric smart flexible cantilever plate.Journal of Sound and Vibration,2007, 301(3-5):521-543
19 Boyd S,Ghaoui LE,Feron E,et al.Linear Matrix Inequality in System and Control Theory.Volume 15 of Studies in Applied Mathematics,Society for Industrial and Applied Mathematics(SIAM),Philadelphia,1994,ISBN o-89871- 334-X
20 Gu KQ.A further refinement of discretized Lyapunov functional method for the stability of time-delay systems.International Journal of Control,2001,74(10):967-976
21苏育才,姜翠波,张跃辉.矩阵理论.北京,科学出版社,2006 (Su Yucai,Jiang Cuibo,Zhang Yaohui.Matrix Theory. Beijing:Science Press,2006(in Chinese))
2贾英民鲁棒H_∞控制.北京.科学出版社,2007(Jia Yingmin. Robust Hoo Control.Beijing:Science Press,2007(in Chinese))
3 Jamshidi M.Robust Control Systems with Genetic Algorithms. CRC Press,2003
4 Abdel-Rohman M.Time-delay effects on actively damped structures.Journal of Engineering Mechanics,ASCE, 1987,113(11):1709-1719
5 Chung LL,Reinhorn AM,Soong TT.Experiments on active control of seismic structures.Journal of Engineering Mechanics,ASCE,1988,114(2):241-256
6 Greery SM,Soong TT,Reinhorn AM.An experimental study of time delay compensation in active structural control. Proceedings of the sixth International Modal Analysis Conference,SEM,Orlando,USA,1988,1:733-739
7 Cai GP,Huang JZ.Optimal control method for seismically excited building structures with time delay in control. Journal of Engineering Mechanics,ASCE,2002,128(6): 602-612
8 Cai GP,Huang JZ,Yang SX.An optimal control method for linear systems with time delay.Computers and Structures, 2003,81(15):1539-1546
9 Chen LX,Cai GP,Pan J.Experimental study of delayed feedback control for a flexible plate.Journal of Sound and Vibration,2009,322(4-5):629-651
10陈龙祥.结构振动的时滞反馈控制及其实验研究.[博士论文].上海:上海交通大学,2009(Chen Long-Xiang,Delayed feedback control and experiment study of flexible structures. [PhD Thesis].Shanghai:Shanghai Jiaotong University, 2009(in Chinese))
11 Cai GP,Chen LX.Delayed feedback control experiments on some flexible structures.Acta Mechanica Sinica,2010, 26(6):951-965
12 Liu B,Masakazu H,Hu HY.A new reduction-based LQ control for dynamic systems with a slowly time-varying delay. Acta Mechanica Sinica,2009,25(4):529-537
13 Masakazu H,Hu HY.Using a new discretization approach to design a delayed LQG controller.Journal of Sound and Vibration,2008,314(3-5):558-570
14 Du HP,Zhang N.H_∞control for buildings with time delay in control via linear matrix inequalities and genetic algorithms. Engineering Structures,2008,30(1):81-92
15于骁,谭述君,林家浩.地震作用下建筑结构基于平衡降阶的时滞离散H_∞控制.工程力学,2008,25(2):148-153(Yu Yao,Tan Shujun,Lin Jiahao.Balanced-reduction control for vibration attenuation of seismic-excited buildings with controller delays.Engineering Mechanics,2008,25(2):148-153(in Chinese))
16 Chen P,Tian YC.Delay-dependent robust H_∞control for uncertain systems with time-varting delay.Information Science,2009,179(18):3187-3197
17 Cavallo A,Maria GD,Natale C,et al.Robust control of flexible structures with stable bandpass controllers.Automatica, 2008,44(5):1251-1260
18 Qiu ZC,Zhang XM,Wu HX,et al.Optimal placement and active vibration control for piezoelectric smart flexible cantilever plate.Journal of Sound and Vibration,2007, 301(3-5):521-543
19 Boyd S,Ghaoui LE,Feron E,et al.Linear Matrix Inequality in System and Control Theory.Volume 15 of Studies in Applied Mathematics,Society for Industrial and Applied Mathematics(SIAM),Philadelphia,1994,ISBN o-89871- 334-X
20 Gu KQ.A further refinement of discretized Lyapunov functional method for the stability of time-delay systems.International Journal of Control,2001,74(10):967-976
21苏育才,姜翠波,张跃辉.矩阵理论.北京,科学出版社,2006 (Su Yucai,Jiang Cuibo,Zhang Yaohui.Matrix Theory. Beijing:Science Press,2006(in Chinese))
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