Sliding mode type-2 fuzzy control of robotic arm using ellipsoidal membership functions

Abstract

Several papers claim that the performance of the type-2 fuzzy logic systems is superior over their type-1 counterparts, especially under noisy conditions. In order to show the effectiveness of the noise reduction capabilities of the type-2 fuzzy logic systems, a novel type-2 fuzzy membership function, ellipsoidal membership function, has recently been proposed. The novel membership function has certain values on both ends of the support and the kernel, and some uncertain values on the other values of the support. The parameters responsible for the width of uncertainty are decoupled from the parameters responsible for the center and the support of the membership function. In this study, a sliding mode control theory based learning algorithm has been proposed to tune the consequent part parameters tuning of the ellipsoidal type-2 fuzzy membership functions. The applicability of the novel membership function with the proposed novel parameter update rules has been shown on the control of a 2DOF robotic arm. The simulation results show that the type-2 fuzzy neural networks working in parallel with conventional PD controllers have the ability of controlling the robotic arm with a high accuracy especially under noisy conditions.