建筑结构振动系统的多重叠分散静态输出反馈 H∞控制方法

摘要

A decentralized control scheme can effectively solve the control problem of large scale civil engineering structure vibration under earthquake.In this paper,combining the static output feedback, overlapping decentralized control method,linear matrix inequality and H ∞ norm control algorithm,the multi-overlapping decentralized static output feedback H ∞ control method has been established.The small perturbation matrix was added to the state matrix in order to overcome the computational difficul-ties encountered in solving the linear matrix inequality (LMI).The vibration control of a twenty layers Benchmark structure model was analyzed with the numerical method.The results show that the part feedback control,the overlapping static output feedback control and the multiple overlapping static out-put feedback control is similar to the whole state centralized control.The computational cost and com-plexity of controller design have been reduced.%采用分散控制方案能有效解决大尺度土木结构在地震作用下的结构振动控制问题。本文将静态输出反馈、重叠分散控制方法、线性矩阵不等式方法和 H ∞范数控制算法相结合，提出了多重叠分散静态输出反馈 H ∞控制方法。通过对状态矩阵添加一个微小的扰动，解决了在求解相应的线性矩阵不等式(LMI)时所遇到的计算困难问题。文中对20层 Benchmark 建筑结构模型进行数值模拟与计算。结果表明，部分输出反馈控制、重叠静态输出反馈控制和多重叠静态输出反馈控制均获得了与全状态集中控制相近的控制效果，减少了计算成本和控制器设计的复杂性。