结构振动主动控制的多时滞控制律的设计方法
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摘要
对遭受地震激励的建筑结构主动控制中的多时滞问题进行研究.通过一种特殊的系统状态变量增广,将包含有多时滞项的系统状态方程转化为形式上不包含时滞的标准离散形式,然后采用离散最优控制方法设计时滞控制律.最后通过数值仿真验证了多时滞控制律的有效性.仿真结果显示,若对时滞不进行处理,控制系统会在很小时滞量的情况下出现发散,而该文中的时滞问题处理方法能够取得良好的控制效果,而且该方法不但能处理小时滞量问题,也能处理大时滞量问题.
Optimal control method for seismically excited building structures with multiple time delays is investigated. Firstly the system state equation with multiple time delays is discretized and transformed into a standard discrete form without any explicit time delay by a particular augmenting for state variables. Then a time-delay controller is designed based on this standard equation using the discrete optimal control method. Finally the effectiveness of the proposed controller is demonstrated by numerical simulations. Simulation results indicate that a very small time delay may result in instability of the control system if it is not compensated in control design. Time delay may be compensated effectively by the proposed controller and good control effectiveness may be obtained simultaneously. Moreover,the proposed controller is available for both small and large time delay.
Optimal control method for seismically excited building structures with multiple time delays is investigated. Firstly the system state equation with multiple time delays is discretized and transformed into a standard discrete form without any explicit time delay by a particular augmenting for state variables. Then a time-delay controller is designed based on this standard equation using the discrete optimal control method. Finally the effectiveness of the proposed controller is demonstrated by numerical simulations. Simulation results indicate that a very small time delay may result in instability of the control system if it is not compensated in control design. Time delay may be compensated effectively by the proposed controller and good control effectiveness may be obtained simultaneously. Moreover,the proposed controller is available for both small and large time delay.
引文
[1]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.
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[4]Mc Greery S,Soong T T,Reinhorn A M.An experiments study of time delay compensation in active structural control[C].In:Proc of6th Int Modal Analysis Conference,SEM,1988,1733-1739.
[5]CAI Guo-ping,HUANG Jin-zhi.Optimal control method for seismically excited building struc-tures with time-delay in control[J].Journal of Engineering Mechanics,ASCE,2002,128(6):602-612.
[6]Xu J,Chung K W.Effects of time delayed position feedback on a van der Pol-Duffing oscillator[J].Physica D,2003,18(1/2):17-39.
[7]Hosek M,Olgac N.A single-step automatic tuning algorithm for the delayed resonator vibra-tion absorber[J].IEEE/ASME Transactions on Mechatronics,2002,7(2):245-255.
[8]陈龙祥.结构振动的时滞反馈控制及其实验研究[D].博士学位论文.上海:上海交通大学,2008.
[9]CAI Guo-ping,Lim C W.Optimal tracking control of flexible hub-beam system with time delay[J].Multibody System Dynamics,2006,16(4):331-350.
[10]Wang Z H,Hu H Y.Stabilization of vibration systems via delayed state difference feedback[J].Journal of Sound and Vibration,2006,296(1/2):117-129.
[11]孙增祈.计算机控制理论及应用[M].北京:清华大学出版社,1989.
[12]Yang J N,Wu J C,Reinhorn A M,et al.Control of sliding-isolated buildings using sliding-mode control[J].Journal of Structural Engineering,1996,122(2):179-186.
[2]Abdel-Rohman M.Time-delay effects on active damped structures[J].Journal of Engineering Mechanics,ASCE,1987,113(11):1709-1719.
[3]Chung L L,Reinhorn A M,Soong T T.Experiments on active control of seismic structures[J].Journal of Engineering Mechanics,ASCE,1988,114(2),241-256.
[4]Mc Greery S,Soong T T,Reinhorn A M.An experiments study of time delay compensation in active structural control[C].In:Proc of6th Int Modal Analysis Conference,SEM,1988,1733-1739.
[5]CAI Guo-ping,HUANG Jin-zhi.Optimal control method for seismically excited building struc-tures with time-delay in control[J].Journal of Engineering Mechanics,ASCE,2002,128(6):602-612.
[6]Xu J,Chung K W.Effects of time delayed position feedback on a van der Pol-Duffing oscillator[J].Physica D,2003,18(1/2):17-39.
[7]Hosek M,Olgac N.A single-step automatic tuning algorithm for the delayed resonator vibra-tion absorber[J].IEEE/ASME Transactions on Mechatronics,2002,7(2):245-255.
[8]陈龙祥.结构振动的时滞反馈控制及其实验研究[D].博士学位论文.上海:上海交通大学,2008.
[9]CAI Guo-ping,Lim C W.Optimal tracking control of flexible hub-beam system with time delay[J].Multibody System Dynamics,2006,16(4):331-350.
[10]Wang Z H,Hu H Y.Stabilization of vibration systems via delayed state difference feedback[J].Journal of Sound and Vibration,2006,296(1/2):117-129.
[11]孙增祈.计算机控制理论及应用[M].北京:清华大学出版社,1989.
[12]Yang J N,Wu J C,Reinhorn A M,et al.Control of sliding-isolated buildings using sliding-mode control[J].Journal of Structural Engineering,1996,122(2):179-186.
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