地震作用下结构振动瞬时最优控制的一种改进算法
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摘要
模拟地震波输入结构的过程,在每一个时间步长建立控制目标函数,推导出了一种更为一般的瞬时最优控制算法,并用状态转移的数值方法加以实现。所获得的最优控制力表达式同时包含了当前时间步长初时刻结构响应和地震激励两部分的影响,从概念上改进了现有的瞬时最优控制算法;还导出了最优控制力系数表达式,用代数公式取代了传统的Riccati微分方程的求解,提高了计算效率。算例表明,该算法的控制效率优于现有的两种结构最优控制算法,具有更高的精度,且稳定性良好。
A generalized algorithm for instantaneous optima control of structures subjected to earthquake excitation is presented based on the way in which the earthquake is input to a structural system.The control objective function is constituted in every time step,and the calculation is realized using the numerical method of state transition.An expression of control force is obtained,which includes both the effect of initial structural response and initial external seismic excitation of this time step.The model for calculating the control force is conceptually improved compared to existing instantaneous optimal control algorithm.An expression of optimal control force coefficients is derived in replacement of the solving of traditional Riccati equation,which is a differential equation,and the efficiency of the calculation is thus improved.Simulation result shows that the proposed method is advantageous over the classical optimal control and instantaneous optimal algorithms in terms of control efficiency,and has almost the same stability with the classical optimal control algorithms.
A generalized algorithm for instantaneous optima control of structures subjected to earthquake excitation is presented based on the way in which the earthquake is input to a structural system.The control objective function is constituted in every time step,and the calculation is realized using the numerical method of state transition.An expression of control force is obtained,which includes both the effect of initial structural response and initial external seismic excitation of this time step.The model for calculating the control force is conceptually improved compared to existing instantaneous optimal control algorithm.An expression of optimal control force coefficients is derived in replacement of the solving of traditional Riccati equation,which is a differential equation,and the efficiency of the calculation is thus improved.Simulation result shows that the proposed method is advantageous over the classical optimal control and instantaneous optimal algorithms in terms of control efficiency,and has almost the same stability with the classical optimal control algorithms.
引文
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[7]杜永峰,李慧,赵国藩.地震作用下结构振动最优控制的一种一般算法[J].大连理工大学学报,2004,44(6):860~865
[8]DU Y F,LI H,Spencer JR B F.Effect of non-proportionaldamping on seismic isolation[J].J of Strut Control,2002,9(3):205~236
[2]Suhardjo J,Spencer JR B F,Sain M K.Feedback-feedforwardcontrol of structures under seismic excitation[J].StructuralSafety,1990,8:69~89
[3]周锡元,阎维明,杨润林.建筑结构的隔震、减振和振动控制[J].建筑结构学报,2002,23(2):2~12
[4]李宏男,阎石,林皋.智能结构控制发展综述[J].地震工程与工程振动,1999,19(2):29~36
[5]Soong T T.State of the art review;Active structural control incivil engineering[J].Eng Struct,1988,10:74~84
[6]YANG J N,LI Z,LIU S C.Stable controllers forinstantaneous optimal control[J].J of Eng Mech,ASCE,1992,118(8):1612~1630
[7]杜永峰,李慧,赵国藩.地震作用下结构振动最优控制的一种一般算法[J].大连理工大学学报,2004,44(6):860~865
[8]DU Y F,LI H,Spencer JR B F.Effect of non-proportionaldamping on seismic isolation[J].J of Strut Control,2002,9(3):205~236
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