Chattering-Free Adaptive Finite-Time Sliding Mode Control for Trajectory Tracking of MEMS Gyroscope

Abstract

One of the inevitable problems with real-time control systems is the presence of the uncertainties and external disturbances. The existence of these uncertainties in the fabrication processes of the MEMS Gyroscope devices can deeply impact the performance of the devices. In this paper, five adaptive finite time robust control methods are employed based on SMC method for a Micro-Electro-Mechanical System (MEMS) Gyroscope with mismatched uncertainties and external disturbances to achieve trajectory tracking goal. A new Stepping SMC method is proposed in this study to improve some deficiencies of conventional and existing methods including Simple SMC, Classical SMC, Cubic SMC, and Hexagonal SMC. The upper bound of mismatched uncertainties is estimated in finite time and their estimation is utilized in the control inputs for all five control methods. The elimination of chattering phenomenon is considered in this paper. The system finite time stability proof is obtained using Lyapunov stability theory. The numerical simulation is performed in Simulink/MATLAB for the MEMS gyroscope system to demonstrate the effectiveness of our proposed control method, Stepping SMC, compared with four other methods. To make an extensive comparison among results, the performance criterion, Integral of the square value (ISV), is used.