毗邻建筑非平稳随机地震响应LQG控制问题的闭合解

CLOSED FORM SOLUTION OF LQG CONTROL PROBLEM FOR NON-STATIONARY STOCHASTIC SEISMIC RESPONSE OF ADJACENT BUILDINGS

研究了毗邻建筑在非平稳随机地震激励下的 LQG 控制问题．首先建立了主动液压传动装置连接的 毗邻建筑在地震激励下的动力方程，然后采用复模态分析得到系统的动力特性，包括模态频率和模态阻尼 比；通过引入成形滤波器来描述地震功率谱密度函数，最终利用虚拟激励法和留数定理推导出 LQG 控制问 题的闭合解．算例结果表明：只要适当选择 LQG 控制器参数，LQG 控制可有效地减小两栋建筑的地震响应， 并且其响应达到稳态的速度比无控时要快得多．

The linear quadratic Gaussian （LQG） control problem for non - stationary stochastic seismic response of adjacent buildings was studied. The motion equations of adjacent buildings connected by hydraulic actuators against earthquake were established. The complex modal superposition method was then used to determine the dynamic characteristics, including modal frequencies and modal damping ratios. The shaping filter was introduced to deal with the power spectral density function of earthquake excitations, and then a closed form solution was derived by combining the pseudo- excitation method and the residue theorem. The results from a numerical example show that, if the parameters of LQG controllers are selected appropriately, the seismic responses of both buildings can be considerably reduced when LQG controllers are used. Moreover, the steady states of seismic response of controlled buildings can be achieved much quickly than the uncontrolled buildings.