This paper presents a new terminal sliding-mode control (TSMC) for the micro electro-mechanical systems (MEMS) z-axis gyroscope. However, TSMC may chatter when uncertainty values are overestimated or may exhibit a steady-state error when uncertainty values are underestimated. In this paper, an adaptive fuzzy terminal sliding-mode controller is designed to retain the advantages of the terminal sliding-mode controller and to reduce the chattering occurred with the terminal sliding-mode controller. Stability analysis of the TSMC is presented in the presence of external disturbance and model uncertainties. Moreover, an extended Kalman filter (EKF) observer is designed to estimate the angular velocity and all of the gyroscope parameters and convergence analysis of the proposed EKF algorithm is presented. Numerical simulations using the nonlinear dynamic model of an MEMS z-axis gyroscope with uncertainties demonstrate the effectiveness of the approach in fast trajectory tracking problems and robustness in estimating the gyroscope parameters and also the angular velocity.

This paper presents a novel robust adaptive control strategy for MEMS gyroscope, based on the coupling of the fuzzy logic control with sliding mode control (SMC) approach and adaptive laws. The drawbacks of the conventional SMC include chattering phenomenon and requirement of a priori knowledge of the bounds of uncertainties. In this paper, these problems are suitably attenuated by adopting an adaptive fuzzy sliding mode control (AFSMC) approach which uses two additional fuzzy self-tuning controllers as supervisory fuzzy systems to adaptively tune the output control gain, sliding gain of the AFSMC in order to speed up the convergence rates of the tracking errors and parameter estimations with a desired level of attenuation. Control system stability is proved by Lyapunov method. Numerical simulations using the MEMS gyroscope model with uncertainties demonstrate the effectiveness of this approach in high speed trajectory tracking problems and robustness in estimating the gyroscope parameters and the angular velocity. Numerical simulations show that the chattering is effectively attenuated by this method. Convergence rate of tracking errors and the gyroscope parameters is better than convergence rates in the literature.

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This paper investigates a passivity-based hierarchical SM control (PBHSMC) approach to solve the trajectory tracking issue of a special class of UMSs using unmeasured states and in presence of both unmatched and matched perturbations. First, a passivity-based SM observer (PBSMO) is designed for quick estimation of states in the UMS. Then, we develop a nonlinear two-layer switching surface using feedback passivation. The passivation-based approach ensures global asymptotical convergence of tracking error on the switching surface with the discontinuous term. Moreover, we develop an SMC law that can satisfy reaching mode and sliding mode conditions. Finally, to illustrate the performance of theoretical results, the developed control scheme is assessed by numerical simulation of two case studies including flexible-joint manipulator (FJM) and underactuated surface vessel (USV) systems. The simulation results indicate the superiority of the PBSMO-based PBHSMC scheme over the conventional SMO-based HSMC in suppressing unwanted oscillations of link, low tracking error and overshoot, short settling time, smooth and small control efforts, and also more accurate estimation of state variables with less chattering.