Backstepping-Based Recurrent Type-2 Fuzzy Sliding Mode Control for MIMO Systems (MEMS Triaxial Gyroscope Case Study)

Abstract

This paper presents a novel type-2 fuzzy sliding mode control with nonlinear consequent part in fuzzy rules for control of Micro-Electro-Mechanical Systems (MEMS) gyroscope. The MEMS gyroscope consists of the basic mechanical structure, an electronic transducer to excite the system as well as an electronic sensor to detect the change in the mechanical structures modal shape. A nonlinear consequent part recurrent type-2 fuzzy system is used to approximate the conventional sliding mode control (SMC) law. A supervisory compensator is introduced to eliminate the effect of the approximation error. The adaptive adjustment algorithms for type-2 fuzzy parameters are derived in the sense of projection algorithm and Lyapunov stability theorem. The proposed type-2 fuzzy system has simple structure with six layers. Recurrent feedbacks at the fifth layer uses delayed outputs for improve the performance of type-2 fuzzy system. Finally the proposed type-2 fuzzy sliding mode control system is used to tracking control design with regard to uncertainty in MEMS gyroscope system. Combination of backstepping method and sliding mode control helps to compensate the control signal and get a better performance. The backstepping method is used to improve the global ultimate asymptotic stability and applying the sliding mode control to obtain high response and invariability to uncertainties. Simulation results show the proposed type-2 fuzzy system has better performance than ANFIS-based sliding mode control.