Fuzzy sliding mode control design based on stability margins

Abstract

Fuzzy Sliding Mode Control (FSMC) algorithms have been widely studied and implemented to combine the robustness of the classical sliding mode control with lower chattering levels, but industrial implementation requires a robustness measurement such as the stability margins. Due to the significance of stability margins in control systems, the computation of the phase Margin (PM) and gain margin (GM) in FSMC has already been proposed with the self-sustained oscillations considered as an unstable behavior. However, a procedure to obtain the desired PM and GM from the FSMC design itself has not been developed yet. Hence, in this study, a method to design FSMC algorithms with desired PM and GM is presented. The describing function (DF) and harmonic balance (HB) techniques were used to identify the limit cycles; then, a step-by-step process to tune the FSMC parameters was provided. Examples and simulations are presented to validate the proposed method.