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考虑一维地震动作用和结构参数不确定性影响,提出一种基于线性矩阵不等式(Linear Matrix Inequalities,LMI)的鲁棒非脆弱H∞控制方法。引入工程中常用的二次型最优指标,并应用线性矩阵不等式减小求解的复杂度,使得控制器的性能指标容易衡量,设计相对简单,便于工程应用。以一个三层剪切型结构模型为例进行数值分析,并与传统H∞控制方法进行对比,仿真结果初步表明:1)所提方法具有很好的控制效果和鲁棒性;2)合理地计算结构参数值,可使控制系统在具有最优反应品质的前提下,获得相对更好的鲁棒性和非脆弱性。
Considering the influence of one-dimensional ground motions and the uncertainty of structural parameters, a robust non-fragile H∞ control method based on Linear Matrix Inequalities (LMI) is proposed. The quadratic optimal index, which is commonly used in engineering, is introduced and the linear matrix inequality (LMI) is used to reduce the complexity of the solution. Therefore, the performance index of the controller is easy to measure, and the design is relatively simple and convenient for engineering application. Taking a three-layer shear structure model as an example, the numerical analysis is carried out and compared with the traditional H∞ control method. The simulation results show that: 1) The proposed method has good control effect and robustness; 2) Calculating the values of the structural parameters allows the control system to achieve relatively better robustness and non-fragility with optimal reaction quality.