基于LMI的降阶鲁棒控制器设计

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_∞性能与控制器期望阶次的折中设计提供了一条可行途径.

Robust Reduced-Order Controller Design Based on LMI

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.