线性系统极点正规配置问题

Pole Normal Assignment for Linear Control Systems

基于正规矩阵特征值对其元素变化的不敏感性,讨论线性系统极点的正规配置问题,即设计状态反馈控制律,将闭环控制系统极点配置到期望位置的同时使闭环状态矩阵为正规矩阵,从而达到增强控制系统的鲁棒性的目的。对于线性时不变系统,给出期望极点集可正规配置的充分必要条件及反馈控制律的一般表达式,并结合示例给出算法。

The eigenvalues of a normal matrix are not sensitive to its elements perturbation. Based on the fact, the pole normal assignment problem for linear control systems is discussed. The aim is to find a state feedback control law. When the closed-loop system has desired poles and the closed-loop system matrix is a normal matrix, the robustness of the control system is enhanced. For linear constant systems, a necessary and sufficient condition is given to normal assignment of the desired poles. When the condition holds, a unified expression of the state feedback control laws is showed. An example is given for illustration of the proposed algorithm.