Terminal sliding mode control of Z-axis MEMS gyroscope with observer based rotation rate estimation

This paper presents a novel methodology for approximation of the unknown time-varying rotation rate using sliding mode observer as well as a robust control scheme for improving the performance of the MEMS gyroscope despite the coupling between vibratory gyroscope modes and inherent model uncertainties. Terminal sliding mode control (TSMC) is invoked to develop tracking control of the drive and sense modes based on the uncertain model of vibratory gyroscope and subsequently the swiftness of TSMC scheme in comparison with conventional sliding mode control (SMC) is demonstrated. The robust terms of proposed sliding mode observer are designed such that the unknown functions including Coriolis acceleration and quadrature error terms are tracked and then the unknown rotation rate and stiffness coupling are constructed. The asymptotic stability and robustness of the proposed control and observer are proved using second method of Lyapunov. Finally, effectiveness of the proposed observer based control for approximation of the unknown time-varying rotation rate is demonstrated through simulations.