基于能量-峰值控制算法的建筑结构重叠分散控制研究

Study on the building structural overlapping decentralized control based on energy-to-peak control algorithm

分散控制策略为解决大型土木结构的振动控制问题提供了新的途径。本文将重叠分散控制方法、线性矩阵不等式方法、静态输出反馈法、能量-峰值控制算法相结合,提出了重叠分散静态反馈能量-峰值控制方法。依据建筑结构的链型拓扑结构特点,建立了建筑结构地震振动响应的简化动力学模型。在求解每个重叠子系统的控制增益矩阵时,通过对状态矩阵添加一个微小的扰动矩阵,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。文中对美国加利福尼亚州规范(SAC)设计的20层Benchmark钢结构模型进行了数值模拟与计算。结果表明:全状态集中控制、速度反馈集中控制、重叠分散速度反馈控制、多重叠分散速度反馈控制的平均控制率分别达到了66.8%、61.8%、44.9%、31.8%,采用这些控制方法都获得了较好的控制效果;重叠分散控制策略增加了控制器设计的灵活性。

Decentralized control strategy is used as a new way to solve the control problem of large scale civil engineering structure vibration. Present study gives a birth to the overlapping decentralized static output feedback energy-to-peak control method by combining the overlapping decentralized control method, linear matrix inequality method, static output feedback and energy-to-peak control algorithm. According to the characteristics of longitudinal topology structure of building structure, a simplified dynamic model of the seismic vibration response of building structure is established. During the procedure of solving the control gain matrix of each overlapping subsystem, a small perturbation matrix is added to the state matrix in order to overcome the computational difficulties encountered in solving the corresponding linear matrix inequality(LMI). The vibration control of a twenty layers Benchmark structure model designed by California standard(SAC) is analyzed by the developed method. Results obtained show that the average control rate of the centralized full state control is 66.8%. The centralized velocity feedback control, the overlapping decentralized velocity feedback control and the multiple overlapping decentralized velocity feedback control can respectively obtain 61.8%, 44.9% and 31.8% control rate on average. These methods all achieve good control effects. The overlapping decentralized control strategy provides the flexibility of the controller in design process.