Logarithmic global sliding mode control with adaptive disturbance observer for micro gyroscope

Abstract A micro gyroscope exhibits nonlinearity due to the strong coupling between multiple variables and is also susceptible to parameter uncertainties, electromechanical perturbations, and external disturbances. In this study, to track the desired signals along the ‐ and ‐axes of the micro gyroscope, a sliding mode control based on a new logarithmic global attractor is introduced, which ensures fast and smooth convergence into a small equilibrium neighborhood without a reaching phase and subsequently converges asymptotically to the origin. Additionally, to approximate time‐varying lumped disturbances, a proportional–integral type adaptive disturbance observer is developed, which dynamically adjusts its gains using only observation error information. The observer enhances estimation accuracy, especially when combined with a switching (tanh) function, leading to faster convergence. The stability of the proposed logarithmic global sliding mode control is verified through Lyapunov theory, and then a comparison with global sliding mode control and proportional integral derivative global sliding mode control is accomplished in the presence of identical global nonlinear term and switching protocol. To further evaluate the effectiveness of the proposed approach, a quantitative analysis is conducted, focusing on root mean square error, integral absolute error, integral time absolute error, and convergence time in the sinusoidal tracking scenario. Additionally, in the hybrid tracking scenario, the analysis incorporates stabilization time along with the previously mentioned criteria. This proposed approach improves disturbance rejection, tracking precision, and stabilization performance, as verified by simulation and quantitative results.