基于扇形区域极点配置状态反馈H_∞控制

State Feedback H_∞ Control Based on Sector Region Pole Assignment

本文针对线性定常系统,在执行器无故障的前提下,研究了扇形区域极点配置的状态反馈H∞控制问题,以解决外部的扰动和限定闭环极点的区域位置对被控输出的影响问题。利用求解线性矩阵不等式的方法,将两类指标约束的状态反馈控制器设计问题转化成一组LMI的可行解问题,借助MATLAB-LMI工具箱进行有效求解,完成了状态反馈控制器的设计。所得结论不仅使极点配置在扇形区域内,而且能够使闭环系统保持稳定性且达到给定的H∞性能指标,保证了系统的性能,实现了期望的闭环极点。最后的数值仿真验证了本文结果的有效性和可行性。

In this paper,the state feedback H∞control problem of the sector region pole assignment is studied for the linear time-invariant system under the premise that the actuator is trouble-free.By using the method of solving linear matrix inequality,the state feedback controller design problem with two kinds of index constraints is transformed into a set of LMI feasible solution problems.The results not only make the pole assignment in the sector region,but also keep the stability of the closed-loop system and reach the given H∞performance index,so as to ensure the performance of the system and realize the desired closed-loop pole assignment.The validity and feasibility of the results are verified by numerical simulation.