抗震结构振动混合最优控制

An Active Passive Hybrid Optimal Control of Seismic Structure

利用“瞬态最优控制”理论、泛函极值理论和梯形积分公式 ,导出了状态空间内的混合控制结构的最优控制算法 ,随后以结构在某瞬时的能量以及外界输入能量之和为性能指标函数 ,在构型空间内直接从结构运动微分方程导出基于 Newmark直接积分法的瞬态最优闭环控制算法 ;对于带主动控制机构的混合控制 ,给出了求最优控制力时用到的权阵 Q的选择 ;在数值模拟分析的基础上 。

We derived an instantaneous optimal closed loop control algorithm in structural space, using the Newmark Scheme. To guarantee the control stability, we worked out several options for the weighting matrix Q on the basis of the Lyapunov direct method. These options were expressed as Q 1=α 1k e, Q 2=α 2k e, Q 3=α 3k e , where α 1, α 2, α 3 were adjustable and so selected as to make control forces suitable for reducing earthquake damage as much as possible. We took the 20 story existing structure in Ref.[3], and assumed the environment to be an EL Centro earthquake wave (1940, N S direction) with a peak acceleration of 3.41 m/s 2. We calculated the acceleration ( A a ) and displacement ( X ) responses of the top story. Figs.1 and 2 give respectively the responses for no control and passive control. Figs.3 and 4 give respectively the response for “LRB+TMD(base)” hybrid active passive control and that for “LRB+AMD(top)” hybrid active passive control. Comparison of Figs.1 through 4 shows preliminarily that our active passive hybrid optimal control method is effective and feasible.