This paper presents a novel algorithm for the design and analysis of an adaptive backstepping controller (ABC) for a microgyroscope. Firstly, Lagrange–Maxwell electromechanical equations are established to derive the dynamic model of a z-axis microgyroscope. Secondly, a nonlinear controller as a backstepping design approach is introduced and deployed in order to drive the trajectory tracking errors to converge to zero with asymptotic stability. Meanwhile, an adaptive estimator is developed and implemented with the backstepping controller to update the value of the parameter estimates in the Lyapunov framework in real-time. In addition, the unknown system parameters including the angular velocity may be estimated online if the persistent excitation (PE) requirement is met. A robust compensator is incorporated in the adaptive backstepping algorithm to suppress the parameter variations and external disturbances. Finally, simulation studies are conducted to prove the validity of the proposed ABC scheme with guaranteed asymptotic stability and excellent tracking performance, as well as consistent parameter estimates in the presence of model uncertainties and disturbances.

An adaptive nonsingular terminal sliding mode (NTSM) tracking control scheme based on backstepping design is presented for micro-electro-mechanical systems (MEMS) vibratory gyroscopes in this paper. The NTSM controller is designed based on backstepping strategy to eliminate the singularity, while ensuring the control system to reach the sliding surface and converge to equilibrium point in a finite period of time from any initial state. In addition, the proposed approach develops an online identifier scheme, which can real-time estimate the angular velocity and the damping and stiffness coefficients. All adaptive laws in the control system are derived in the same Lyapunov framework, which can guarantee the globally asymptotical stability of the closed-loop system. Numerical simulations for a MEMS gyroscope are investigated to demonstrate the validity of the proposed control approaches.

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