Time-varying disturbance observer based on sliding-mode observer and double phases fixed-time sliding mode control for a T-S fuzzy micro-electro-mechanical system gyroscope

This paper proposes a new disturbance observer concept based on the information of the estimated and measured signals for a micro-electro-mechanical system. First, the sliding-mode observer based on the linear matrix inequality was designed to estimate the states of a micro-electro-mechanical system gyroscope. Second, a new disturbance observer was proposed for estimating perturbations of the T-S fuzzy micro-electro-mechanical system gyroscope. Third, the double phase’s fixed-time sliding-mode control was designed to control the positions and velocities of the MEMS system. The proposed disturbance observer input signals were taken into account from the measured and estimated signals. Two cases of high magnitudes and high frequencies disturbances were used to test the power of the proposed disturbance observer. Fourth, the Lyapunov condition was used to verify the corrections of the proposed controller and observer. Finally, the simulation by using MATLAB software was used to show the power of the proposed methods. The achievements of the small reaching-time, small tracking error, and stable steady-states under the vibration form outside of the system.