广义线性系统基于PI观测器鲁棒极点配置分离原理

Separation Principle for Robust Pole Assignment Based on PI Observers in Descriptor Linear Systems

对广义线性系统提出了基于全维比例-积分观测器的控制系统设计的鲁棒极点配置分离原理.基于矩阵灵敏度理论证明了如下事实:与状态反馈系统相同的闭环系统极点具有和状态反馈系统极点相同的极点灵敏度,与观测器系统相同的闭环系统极点具有和观测器系统极点相同的极点灵敏度.于是基于全维PI观测器的状态反馈控制器的具有最小灵敏度的鲁棒极点配置可以通过求解两个分开的鲁棒状态反馈极点配置问题实现.

A separation principle for robust pole assignment in the full-order proportionalintegral （PI） observer-based control system designs is proposed for descriptor linear systems. It reveals that the two facts：the closed-loop poles which are identical with those in the state feedback control system have the same sensitivities with respect to the perturbation parameters in the open-loop system coefficient matrices as those in the state feedback control system;the closed-loop poles which are identical with those in the observer system have the same sensitivities with respect to the perturbation parameters in the open-loop system coefficient matrices as those in the observer system. Thus, pole assignment with minimum sensitivities in a descriptor linear system using a full-order PI observer-based state feedback controller can be easily realized by solving two separate state feedback robust pole assignment problems.