Pole Placement and Stability Margine of H_∞ Robust Control Systems

Abstract

In recent years, H_∞ control design has been vigorosly studied, and some design schemes have been established. However, the solution of H_∞ control problems is, in general, not uniquely determined, and there are some freedom in the choice of the solution. Therefore, there arises a problem how to determine the free parameters to improve the closed loop properties. Especially. pole placement of closed loop system is the most important one, because it is not easy to express by H_∞ norm. In this paper, we treat this problem in the context of the robust control system, whose H_∞ norm of the complementary sensitivity function is minimized by state feedback control. At first, we consider asymptotical pole placement of a closed loop system using central solution, which is obtained by setting free parameters to zero. As a result, it is shown that some poles of this system are close to imaginary axis, when H_∞ norm of the complementary sensitivity function is minimized. Next, we investigate the design of a robust control system whose poles are located at desired places, and show that it is possible to set almost all poles of closed loop system freely, if only we make one pole close to -∞. Therefore, it is made clear that there remains much freedom in the selection of robust controller.