Strong Stabilization Robust H_∞ Controller Design

The parimary purpose of this thesis is strong stabilizality H∞robust controller design.For pratical reasons, the controller of the closed-loop control system is always required stable. H∞Control theory can guarantee the robust stability of the closed-loop system does not guarantee the stability of the controller K ( s ). Therefore, people raised the issue of stability control, strong stabilization problem is known as the design of a stable feedback controller K ( s ) which stabilizes the given plant and the Closed-loop control system meet a certain performance indicator.In the first part of this paper introduces the basis theory of robust H∞control and the standard of robust H∞control problem, describes the basis theory of strong stabilizality control, including a necessary and sufficient condition that Youla and others raised for the existence of a stable stabilizing controller for a given plant is the so-called parity interlacing property. Followed by an in-depth study of several design procedures for strongly stabilizing controllers, including coprime decomposition algorithm, M. Zeren's algorithm, A. A. Saif's algorithm, the algorithm based on coprime decomposition and Youla parameterization, and the algorithm based on linear matrix inequalities. The order of controller got from A. A. Saif's algorithm is the same as plant G ( s ), but get generally robust performance, the M. Zeren's algorithm and the algorithm based on coprime decomposition and Youla parameterization can get a"good"robust performance, However, the order of stable controller is twice as the target plant G ( s ). Improve some of these methods and achieve the performance indicators to meet some requirements. Simulate with MATLAB and produce satisfactory results.Secondly, based on the thorough study of the past algorithms, a linear matrix inequalities based design method is given to find strongly stabilizing controllers. A sufficient condcition is derived for the existence of suboptimal H∞controller and the controller order is the same as that of the plant, the robust performance of the closed-loop system is relatively good. Finally, analysis all the algorithms in this paper, and simulation studies.