H∞/μ control-based frequency-shaped sliding mode control for flexible structures

Abstract

In this paper we propose a new sliding mode control method using H∞/μ synthesis theory. This concept is based on the frequency-shaped approach. A conventional hyperplane consists of a desired reference model without dynamics. Therefore, the sliding mode control system often becomes unstable based on spillover phenomena in a high-frequency region. On the other hand, the proposed design method can completely suppress such spillover phenomena because of the frequency-shaped hyperplane. Also, the controller designed by the proposed method has not only stability robustness but also robust performance in cases of parameter variations in the hyperplane to minimize the maximum singular value and structured singular value from some noise to the controlled variables. We have applied this new method to a flexible structure of a miniature test rig with four stories. We have verified from simulations that the new sliding mode control method proposed by us exhibits good performance and is very useful for suppressing the spillover in a high-frequency region.