Dynamical analysis and accelerated adaptive prescribed performance control of a small coupling network of MEMS gyros

This paper delves into dynamic analysis, electronic circuit design, and accelerated adaptive prescribed performance control of a small coupling network of micro-electro-mechanical-system (MEMS) gyros. Initially, to compensate for the low sensitivity and bandwidth in single-/dual-mass gyro, we propose a small coupling network structure of MEMS gyros with mutual coupling, and further build its mathematical model via the Newton's laws and vibration dynamics theory. The subsequent dynamical analysis reveals abundant dynamic characteristics of such a coupling network using tools like Lyapunov exponents. Subsequently, to understand the dynamics of this coupling network at the hardware level and facilitate the subsequent die production of electronic components, we design an equivalent analog circuit based on energy flow theory, and its simulated results closely match those of the dynamical analysis above. To mitigate the harmful oscillations and address the state constraints, we propose an accelerated adaptive prescribed performance control scheme. In this scheme, a speed function is incorporated to accelerate error convergence rate, and a hyperbolic tangent tracking differentiator (HTTD) is designed to approximate the derivatives of the virtual control inputs to reduce computational complexity and effectively avoiding “complexity explosion”. Additionally, nonlinear unknown function of the system is approximated using a type-2 fuzzy wavelet neural network (T2FWNN), and tracking errors are constrained within a given boundary by prescribed performance functions. Finally, extensive simulations and comparison results provide compelling evidence of the feasibility and efficacy of our scheme.