Adaptive fuzzy terminal sliding-mode control of MEMS z-axis gyroscope with extended Kalman filter observer

This paper presents a new terminal sliding-mode control (TSMC) for the micro electro-mechanical systems (MEMS) z-axis gyroscope. However, TSMC may chatter when uncertainty values are overestimated or may exhibit a steady-state error when uncertainty values are underestimated. In this paper, an adaptive fuzzy terminal sliding-mode controller is designed to retain the advantages of the terminal sliding-mode controller and to reduce the chattering occurred with the terminal sliding-mode controller. Stability analysis of the TSMC is presented in the presence of external disturbance and model uncertainties. Moreover, an extended Kalman filter (EKF) observer is designed to estimate the angular velocity and all of the gyroscope parameters and convergence analysis of the proposed EKF algorithm is presented. Numerical simulations using the nonlinear dynamic model of an MEMS z-axis gyroscope with uncertainties demonstrate the effectiveness of the approach in fast trajectory tracking problems and robustness in estimating the gyroscope parameters and also the angular velocity.