离散系统降阶H_∞控制器的设计

Design of reduced-order H_∞ controller for discrete system

针对离散控制系统,研究其降阶H∞控制器设计方法。首先,采用线性矩阵不等式方法,给出离散系统状态反馈H∞控制器存在的条件;利用离散系统H∞控制器可解的条件,研究离散系统的降维观测器设计方法;通过设计系统的降维观测器,使降维观测器的观测输出和系统的状态反馈输入误差趋于零,以降阶观测器的输出作为系统的控制输入,使闭环控制系统满足H∞控制条件;最后给出基于Sylvester方程和降阶观测器存在条件的降阶H∞控制器设计方法。仿真结果说明了设计方法的有效性。

A reduced-order H∞controller for a discrete system was studied for discrete system.First,the existent condition of the state feedback H∞controller was proposed for the discrete system.A reduced-order observer was designed to make the error between the output of the controller and the input of the state feedback to zero by the existent condition of the controller.The system was controlled to satisfy the H∞ condition by the output of the reduce-order observer.Finally,the approach to design the H∞ controller for discrete system was presented by Sylvester equation and the condition of the H∞ controller,and a numerical example was given to show the feasibility of the proposed design approach.