基于观测器的 LMI 振动控制算法

摘要

针对基于观测器的 LMI 控制器设计中一个线性矩阵不等式中出现双变量的问题，提出一种赋初值迭代求解方法。考虑到双变量中一个为正定矩阵变量、一个为标量的特点，为了保证迭代收敛性和满足矩阵正定的要求，把正定矩阵变量作为初值赋予对象。仿真分析发现所设计的控制器仅能保证控制趋势，达不到预期控制效果，为此提出了调节因子的概念。最后，以3层基准建筑物为例进行仿真分析，结果表明该方法是可行的。%In the design of an observer-based LMI (linear matrix inequality) controller, bivariate values appear in one linear matrix inequality. To solve this problem, we propose an initial value-iteration method in this paper. Of the bivariate values, one is a positive definite matrix variable and the other is a scalar. Considering these two characteristics, we take the positive definite matrix variable as the initial value, in order to ensure the astringency of the iteration and to meet the requirements of positive definite matrices. Simulation analysis shows that the designed controller can guarantee the control trend, which was far from the expected control result. We subsequently put forward the concept of a regulatory factor. As a case study, the simulation analysis of a three-storey benchmark building shows that the proposed method is feasible.