以随机地震动作用下具有Bouc-Wen滞回特性的非线性结构系统为受控对象，开展了最优多项式控制算法研究：包括系统矩阵中Maclaurin展开取初始零值衍生的具有时不变增益矩阵的控制律，和系统矩阵中Maclaurin一阶展开衍生的具有时变增益矩阵的控制律。研究表明，受控结构层间位移响应的变异性明显降低，结构的安全性显著提高。同时，基于时不变增益矩阵的控制律的控制效果在一定程度上受制于控制力施加的大小与系统稳定性之间的平衡关系，而考虑了每一个时间步位移和速度对增益矩阵影响、基于时变增益矩阵的控制律则能以较小的控制出力获得较好的控制效果。
Abstract
The physically-motivated stochastic optimal control has been proved to be efficient in performance improvement and risk mitigation of engineering structures. In this paper, the polynomial control method in context of the physical scheme ruling nonlinear stochastic systems is re-visited, of which time-variant gain parameters are considered. It is typically different from the previous investigation on the control policy with time-invariant gain parameters. The exceedance probability of structural states and control force serves as the critical argument of probabilistic criterion, whereby the parameter optimization of control policy can be readily achieved. A randomly base-excited shear frame structure with Bouc-Wen behaviors is used as the objective for control test. Numerical result indicates the efficiency of the proposed stochastic optimal control schemes that the variation of inter-storey drift of the structure reduces significantly, and the structural safety is enhanced sufficiently. The benefit of optimal polynomial control with time-invariant gain parameters limits in system stability hinging on the control force; while the optimal control with time-variant gain parameters involves the contribution of structural velocity and displacement to the gain matrix at each time step, which results in a better structural performance with a lower control effort.
关键词
多项式控制 /
增益矩阵 /
超越概率 /
非线性结构 /
时变
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Key words
polynomial control /
gain matrix /
exceedance probability /
nonlinear structures /
time-variant
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参考文献
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