Asymptotic Properties of Poles of Optimal Sliding-mode Control System

Abstract

Sliding-mode control has been introduced in many control fields because of its excellent robustness. Among various types of design methods of the hyper-plane, the optimal sliding-mode control using the feedback co-efficient of the optimal regulator is often adopted, because of the simplicity of design and the necessity for the optimal preview sliding-mode control. This paper describes asymptotic properties of the poles of the optimal sliding-mode control system. As the results, we found the following properties; (1) The asymptotic property of the poles of the optimal sliding-mode control system in γ→0 (γ designates a weight on control variable in the performance index.) inherits that of the optimal regulator and (2) In discrete time control, although the control system becomes unstable in γ→∞ for unstable plant, it becomes stable when we take γ smaller or use the design method which assigns the poles of the optimal regulator in a specified region.