Dynamical analysis and accelerated adaptive backstepping control of MEMS triaxial gyroscope with output constraints

This paper proposes an accelerated adaptive backstepping control scheme for a micro-electro-mechanical systems (MEMS) triaxial gyroscope, which has complicated nonlinear behaviors. The mathematical model of the gyroscope with output constraints is established. Its dynamical evolution laws are analyzed through phase diagrams, time histories and Lyapunov exponents. In designing the controller, a type-2 fuzzy wavelet neural network (T2FWNN) is utilized to approximate the nonlinear unknown functions of the system. Then, in backstepping, a speed function is employed to realize the accelerated convergence with less fluctuations and after that, a time-varying barrier Lyapunov function (BLF) is constructed to restrict state variables into the prescribed ranges. Meanwhile, a hyperbolic tangent tracking differentiator (HTTD) is employed to approximate the virtual control inputs with high precision thus reducing the computation complexity in the backstepping framework. The whole controller fuses the T2FWNN, the speed function, the time-varying BLF, the HTTD and the adaptive law into the backstepping scheme. Besides, stability analysis proves that all signals in the closed-loop system are ultimately bounded. Finally, the majority of the simulated results prove that the designed controller not only satisfies the constraints of state variables, but also suppresses any chaotic oscillations with good tracking performance.