基于扇形区域极点配置的静态输出反馈H_∞控制

State output feedback H_∞ control based on sector region pole assignment

针对线性定常系统,研究了扇形区域内极点配置的静态输出反馈H∞控制问题。设计能够达到H∞性能指标且符合区域极点配置要求的静态输出反馈控制器,以解决外部的扰动和区域对极点的限定问题;利用求解线性矩阵不等式组的方法,将具有H∞指标约束和区域极点配置要求的静态输出反馈控制器设计问题转化成求一组线性矩阵不等式的可行解问题,借助MATLAB-LMI工具箱进行有效求解,得到了符合要求的可靠控制率,完成了扇形区域内H∞静态输出反馈控制器的设计(其中的H∞控制器为次优H∞控制器)。所得结论不仅能使极点配置在给定的扇形区域内,也能够使闭环系统保持稳定性且达到给定的H∞性能指标,从而保证了系统的性能,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。

For linear time-invariant systems, the static output feedback H ∞ control problem of pole placement in sector region is studied.The main contents are as follows: To design a static output feedback controller which can meet the H ∞ performance index and meet the requirements of regional pole placement, so as to solve the external disturbance and the limitation of poles in the region.By solving linear matrix inequalities, the design of static out-put feedback controllers with H ∞ index constraints and regional pole assignment requirements is transformed into a feasible solution of a set of linear matrix inequalities.With the help of MATLAB-LMI toolbox, a reliable con-trol rate is obtained, and the design of H ∞ static output feedback controllers in sector region is completed(The H ∞ controller is a suboptimal H ∞ controller).The H ∞ controller is a suboptimal H ∞ controller.The conclusion can not only configure the poles in a given sector area, but also keep the closed-loop system stable and achieve the given H ∞ performance index, thus ensuring the system performance and achieving the desired closed-loop poles.Finally, numerical simulation verifies the validity and feasibility of the results.