Fractional Order Fuzzy Dynamic Backstepping Sliding Mode Controller Design for Triaxial MEMS Gyroscope Based on High-gain and Disturbance Observers

Abstract

In this paper, a dynamic backstepping sliding mode controller with a fractional order sliding surface, which has a fuzzy boundary layer, is designed based on high-gain and disturbance observers for controlling the performance of a micro-electro-mechanical triaxial gyroscope. To compensate uncertainties of a system, a combination of sliding mode and robust nonlinear backstepping controller is used. In this design, in order to increase the degree of freedom of the controller, the sliding surface is selected to be of fractional order. in this paper, in order to significantly reduce the chattering phenomenon in the control signal, a new dynamic sliding surface in addition to the initial sliding surface and also fuzzy control theory to controllig the boundary layer are used. In addition, a high-gain observer and a disturbance observer are used to estimate the system states and incoming disturbances to the system. The asymptotic stability of the closed-loop system is proven by Lyapunov stability theorem. In order to evaluate the performance of the designed controller, this controller is compared with other sliding mode controllers. Simulation results show that the proposed controller has much less chattering phenomenon in control signal, increasing system stability, reducing the rise time and better tracking.