基于LMI的降阶鲁棒控制器设计

Robust Reduced-Order Controller Design Based on LMI

基于线性矩阵不等式 (LMI)的H∞ 设计方法给出了所有全阶和降阶控制器的参数化结果 ,其中降阶控制器的求解需要满足一个秩条件 ,这个秩条件是非凸的 .为了避开非凸问题的求解 ,提出了一种新的设计降阶控制器的凸优化方法 ,从而得到了保证H∞ 性能指标的降阶控制器 .为了减少保守性 ,进而基于投影原理提出了一种设计更低阶次鲁棒控制器的新方法 .该方法为系统的H∞

A non convex problem has to be solved in the designing of reduced order H ∞ controller based on linear matrix inequality(LMI), which is so far an open problem. In this paper, a new method is presented to design reduced order H ∞ contrller with convex optimization. It guarantees H ∞ performance, but some conservation may be introduced. In order to decrease the conservation, the projection principle is used. Thus, a lower order robust controller can be obtained but the H ∞ performance may not be guaranteed. It is a trade off between the order of controller and the H ∞ performance in practice. Generally, if the projection error is small enough, the design result could be satisfied. The simulation results illustrate the advantages of this method.