结构振动的时滞输出反馈控制器设计
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摘要
研究结构振动的时滞输出反馈控制,通过部分可测输出量实现整个系统的主动振动控制.首先将系统的运动微分方程改写成状态空间模型,其控制输入中存在时滞.再利用一个线性项加积分项的变换将原时滞输入系统转化成无时滞的形式.在此基础上,应用输出反馈原理和合理的性能指标设计出系统的控制律.最后以一个三层建筑结构为例,研究系统在地震载荷下的动态响应.在数值计算中,时滞量取为采样周期的整数倍,积分步长取为采样周期.仿真结果表明,本文提出的时滞输出反馈控制律是有效且实用的.
Time delay control of structural vibration was investigated in terms of output feedback,i.e.,utilizing the measurable output to realize an active vibration control of the entire system.The differential equation of motion of the system was first transformed to a state-space model with time-delay control input.Then,a transformation with a linear term and an integral term was employed to transform the original time-delay system into a form without time-delays.Accordingly,the principle of output feedback was used to design a control law for the system in terms of a reasonable performance index.Finally,as an example,the dynamical responses of a three-story model under earthquake loadings was investigated by numerical calculation,where the value of the time delay is integer times the sampling period and the integration time step is chosen to be identical to the sampling period.The numerical results show that the time delay control algorithm by output feedback proposed is valid and practically applicable.
Time delay control of structural vibration was investigated in terms of output feedback,i.e.,utilizing the measurable output to realize an active vibration control of the entire system.The differential equation of motion of the system was first transformed to a state-space model with time-delay control input.Then,a transformation with a linear term and an integral term was employed to transform the original time-delay system into a form without time-delays.Accordingly,the principle of output feedback was used to design a control law for the system in terms of a reasonable performance index.Finally,as an example,the dynamical responses of a three-story model under earthquake loadings was investigated by numerical calculation,where the value of the time delay is integer times the sampling period and the integration time step is chosen to be identical to the sampling period.The numerical results show that the time delay control algorithm by output feedback proposed is valid and practically applicable.
引文
1孙国春,史文库,田彦涛.振动主动控制技术的研究与发展.机床与液压,2004,(13):1~6(Sun Guochun,ShiWenku,Tian Yantao.Research and development in activevibration control technology.Machine Tool&Hydraulics,2004,(13):1~6(in Chinese))
2陈丽萍.振动主动控制技术的研究进展.现代机械,2005,(2):52~55(Chen Liping.Research status and developingtrend of active vibration control.Modern Machinery,2005,(2):52~55(in Chinese))
3严艳,杨玉华,魏晓燕,卢占会.带有时滞的区间动力系统的鲁棒稳定性研究.动力学与控制学报,2008,9:1~4(Yan Yan,Yang Yuhua,Wei Xiaoyan,Lu Zhanhui.Studyon robust stability of interval system with time-delay.Jour-nal ofDynamics and Control,2008,9:1~4(in Chinese))
4王京祥,王在华.时滞状态反馈控制系统的稳定性增益区域.动力学与控制学报,2008,6(4):301~306(WangJingxiang,Wang Zaihua.Stable region of the feedback gainsin a controlled system with delay feedback.Journal ofDy-namics and Control,2008,6(4):301~306(in Chinese))
5潘颖,王超,蔡国平.线性时滞系统的离散最优控制.计算力学学报,2004,21(2):177~184(Pan Ying,WangChao,Cai Guoping.Discrete-time optimal control method forlinear time-delay systems.Chinese Journal ofComputationalMechanics,2004,21(2):177~184(in Chinese))
6蔡国平,黄金枝.时滞线性系统振动主动控制的最优化方法.上海交通大学学报,2002,36(11):1596~1599(Cai Guoping,Huang Jinzhi.Optimal control method forlinear vibration systems with time delay in control.JournalofShanghai Jiaotong University,2002,36(11):1596~1599(in Chinese))
7 G P Cai,J Z Huang,S X Yang.An optimal control methodfor linear systems with time delay.Computers and Struc-tures,2003,81:1539~1546
8 G P Cai,J Z Huang.Optimal control method for seismicallyexcited building structures with time-delay in control.Jour-nal ofEngineering Mechanics,2002,128(6):602~612
9 G P Cai,J Z Huang.Instantaneous optimal method for vi-bration control of linear sampled-data systems with time de-lay in control.Journal ofSound and Vibration,2003,262:1057~1071
10 G P Cai,F Sun.Sub-optimal control of structures.Earth-quake Engineering and Structures,2003,32:127~2142
11唐功友,赵翀,雷靖.含有时滞控制系统的输出反馈扰动抑制.中国海洋大学学报,2007,37(4):667~-670(Tang Gongyou,Zhao Chong,Lei Jing.Disturbance rejec-tion for linear systems with control delay via output feed-back.Periodical of Ocean University of China,2007,37(4):667~670(in Chinese))
12应祖光,洪沁.一种基于随机平均的最优时滞控制方法.动力学与控制学报,2008,6(3):260~263(Ying zu-guang,Hong Qin.An optimal time-delay control methodbased on the stochastic averaging.Journal ofDynamics andControl,2008,6(3):260~263(in Chinese))
13刘豹.现代控制理论(第二版).北京:机械工业出版社,2004(Liu Bao.Modern Control Theory(2nd edition).Beijing:China Machine Press,2004(in Chinese))
14 W H Kwon,K E Pearson.Feedback stabilization of linearsystems with delayed control.IEEE Transactions on Auto-matic Control,1980,25(2):266~269
15顾仲权,马扣根,陈卫东.振动主动控制.北京:国防工业出版社(第1版),1997,31-94(Gu Zhongquan,MaKougen,Chen Weidong.Active vibration control.Beijing:National defense industry Press(1st edition),1997(inChinses))
16 J N Yang.Application of optimal control theory to civil en-gineering structures.Journal of Engineering Mechanics,1975,10l:818~838
17蔡国平,黄金枝.控制存在延时的建筑结构地震作用下的最优控制方法.应用力学学报,2001,18(4):42~49(Cai Guoping,Huang Jinzhi.Optimal control method forseismic-excited building structures with time delay in con-trol.Chinese Journal ofApplication Mechanics,2001,18(4):42~49(in Chinese))
2陈丽萍.振动主动控制技术的研究进展.现代机械,2005,(2):52~55(Chen Liping.Research status and developingtrend of active vibration control.Modern Machinery,2005,(2):52~55(in Chinese))
3严艳,杨玉华,魏晓燕,卢占会.带有时滞的区间动力系统的鲁棒稳定性研究.动力学与控制学报,2008,9:1~4(Yan Yan,Yang Yuhua,Wei Xiaoyan,Lu Zhanhui.Studyon robust stability of interval system with time-delay.Jour-nal ofDynamics and Control,2008,9:1~4(in Chinese))
4王京祥,王在华.时滞状态反馈控制系统的稳定性增益区域.动力学与控制学报,2008,6(4):301~306(WangJingxiang,Wang Zaihua.Stable region of the feedback gainsin a controlled system with delay feedback.Journal ofDy-namics and Control,2008,6(4):301~306(in Chinese))
5潘颖,王超,蔡国平.线性时滞系统的离散最优控制.计算力学学报,2004,21(2):177~184(Pan Ying,WangChao,Cai Guoping.Discrete-time optimal control method forlinear time-delay systems.Chinese Journal ofComputationalMechanics,2004,21(2):177~184(in Chinese))
6蔡国平,黄金枝.时滞线性系统振动主动控制的最优化方法.上海交通大学学报,2002,36(11):1596~1599(Cai Guoping,Huang Jinzhi.Optimal control method forlinear vibration systems with time delay in control.JournalofShanghai Jiaotong University,2002,36(11):1596~1599(in Chinese))
7 G P Cai,J Z Huang,S X Yang.An optimal control methodfor linear systems with time delay.Computers and Struc-tures,2003,81:1539~1546
8 G P Cai,J Z Huang.Optimal control method for seismicallyexcited building structures with time-delay in control.Jour-nal ofEngineering Mechanics,2002,128(6):602~612
9 G P Cai,J Z Huang.Instantaneous optimal method for vi-bration control of linear sampled-data systems with time de-lay in control.Journal ofSound and Vibration,2003,262:1057~1071
10 G P Cai,F Sun.Sub-optimal control of structures.Earth-quake Engineering and Structures,2003,32:127~2142
11唐功友,赵翀,雷靖.含有时滞控制系统的输出反馈扰动抑制.中国海洋大学学报,2007,37(4):667~-670(Tang Gongyou,Zhao Chong,Lei Jing.Disturbance rejec-tion for linear systems with control delay via output feed-back.Periodical of Ocean University of China,2007,37(4):667~670(in Chinese))
12应祖光,洪沁.一种基于随机平均的最优时滞控制方法.动力学与控制学报,2008,6(3):260~263(Ying zu-guang,Hong Qin.An optimal time-delay control methodbased on the stochastic averaging.Journal ofDynamics andControl,2008,6(3):260~263(in Chinese))
13刘豹.现代控制理论(第二版).北京:机械工业出版社,2004(Liu Bao.Modern Control Theory(2nd edition).Beijing:China Machine Press,2004(in Chinese))
14 W H Kwon,K E Pearson.Feedback stabilization of linearsystems with delayed control.IEEE Transactions on Auto-matic Control,1980,25(2):266~269
15顾仲权,马扣根,陈卫东.振动主动控制.北京:国防工业出版社(第1版),1997,31-94(Gu Zhongquan,MaKougen,Chen Weidong.Active vibration control.Beijing:National defense industry Press(1st edition),1997(inChinses))
16 J N Yang.Application of optimal control theory to civil en-gineering structures.Journal of Engineering Mechanics,1975,10l:818~838
17蔡国平,黄金枝.控制存在延时的建筑结构地震作用下的最优控制方法.应用力学学报,2001,18(4):42~49(Cai Guoping,Huang Jinzhi.Optimal control method forseismic-excited building structures with time delay in con-trol.Chinese Journal ofApplication Mechanics,2001,18(4):42~49(in Chinese))
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