Design Principle of Frequency Shaped Non-Switching Integral Sliding Mode Controller

Abstract

This paper proposes the frequency shaped non-switching integral sliding mode controller (FS-NS-ISMC). Non-switching integral sliding mode controller (NS-ISMC) was proposed as the first sliding mode controller guaranteeing robust stability and performance. The NS-ISMC was basically allowed to control the only matched channels like a conventional sliding mode controller. It means that NS-ISMC cannot suppress unmatched perturbation which is sensitive against control input while making the matched channel behaves as a sliding mode. However, if the robust vector gain, which is a parameter of NS-ISMC, could be designed in frequency to avoid to input in the range where the unmatched perturbation is sensitive while guaranteeing the stability of the error between the matched channel and integral sliding mode, unmatched perturbations could have been suppressed at the same time. In this paper, the design method of FS-NS-ISMC by D-K iteration $\boldsymbol{\mu}$-synthesis to suppress unmatched perturbation is introduced. A flexible manipulator is chosen as the system example. Design process against the manipulator is described and its effectiveness is shown in the numerical simulation.