Adaptive terminal sliding mode control with an improved reaching law for MEMS gyroscope based on disturbance observer

To address the fundamental trade-off between convergence speed and chattering suppression in MEMS gyroscope control, this work proposes a novel robust adaptive terminal sliding mode control framework that uniquely integrates an improved reaching law with a nonlinear disturbance observer, thereby simultaneously ensuring finite-time convergence, chattering mitigation, and strong robustness against compound uncertainties. Specifically, the proposed reaching law incorporates time-varying terminal and exponential terms alongside a stabilising linear component, guaranteeing that system states not only reach the sliding surface in finite time but also remain there asymptotically. To cope with the inherent parameter uncertainties and unmodeled environmental disturbances in MEMS gyroscopes, (i) an online adaptive rule for real-time estimation of unknown model parameters is designed, and (ii) a high-gain nonlinear disturbance observer for continuous, decoupled estimation of disturbances is developed. Furthermore, this paper precisely derives the upper bound of the convergence time and completes the stability analysis, confirming that this closed-loop system possesses global asymptotic stability under the conditions of bounded disturbances and parameter perturbations. Compared with traditional sliding mode control and adaptive sliding mode control methods, this method has better trajectory tracking accuracy, faster dynamic response speed, and can significantly reduce the chattering phenomenon.