一种LMI建筑结构振动控制算法

An LMI Vibration Control Algorithm for Building Structures

摘要: 由于H_∞控制器中Riccati方程较难求解，本文通过利用李雅普诺夫稳定性理论及Matlab的LMI工具箱推导了一种LMI控制算法，并建立了一栋20层结构LMI最优主动控制的分析模型，并利用Matlab语言编制了求解软件，通过对El-Centro波下结构动力反应进行数值模拟，从楼层位移、速度、加速度，层间位移，AMD作动器控制力输出方面对LMI控制算法效果进行分析。计算结果表明：LMI控制能有效降低建筑结构楼层位移、速度、加速度、层间位移响应，但需要付出一定的控制成本。可以通过调整权重参数达到目标减振效果，权重越大，控制效果越好，控制成本越高。顶层控制力最大，当时减振效果较好，顶层控制力幅值为楼面重力荷载27.8%。

Abstract: Because Riccati equation in H_∞ controller is more difficult to solve, in this paper, by using Lyapunov stability theory and LMI toolbox of Matlab, an LMI control algorithm was deduced, an analysis model of LMI optimal active control for a 20-story structure was established, and Matlab language was used to compile the solution software. The structural dynamic response under El-Centro wave was numerically simulated, and the effect of LMI control algorithm was analyzed from floor displacement, velocity, acceleration, inter-floor displacement and AMD actuator control output side. The calculation results show that the LMI control can effectively reduce the floor displacement, velocity, acceleration and inter-floor displacement response of the building structure, but it needs to pay a certain control cost. The target damping effect can be achieved by adjusting the weight parameters. The greater the weight is, the better the control effect is and the higher the control cost is. The top floor control force is the largest, and the damping effect is better when ; the amplitude of the top floor control force is 27.8% of the floor gravity load.