Frequency-shaped sliding mode control using H∞ control and μ synthesis theory

This paper proposes a new sliding mode control method using H_∞/μ control theory and shows its applications. 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 higher frequency region. On the other hand, the proposed design method can completely suppress such spillover phenomena because of the frequency-shaped hyperplane. Also, it has good robustness and robust performance in cases of parameter variations on 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 the flexible structure of the miniature test rig with four stories like high rise building and the positioning control system with the flexible arm. We have verified from simulations and experiments that the new sliding mode control method proposed in previous paper has good performances and it is very useful to suppress the spillover in a higher frequency region