Dynamical analysis and event-triggered neural backstepping control of two Duffing-type MEMS gyros with state constraints

The DSP (Digital Signal Processing) implementation of two Duffing-type micro-electro-mechanical systems (MEMS) gyros and their event-triggered neural backstepping control with state constraints are investigated in this paper. Initially, we design the two Duffing-type MEMS gyros with a fully decoupled structure and establish a mathematical model based on the Newton's Second Law and the Lagrange equation. Due to the significant differences in the integrated circuit design and engineering application between embedded platforms and computer simulations, we selected the DSP platform to better characterize two Duffing-type MEMS gyros. Based on this, we explore nonlinear dynamic behaviors through phase and time history diagrams from the DSP platform as well as Lyapunov exponents under different coupling and damping coefficients, thereby identifying the existence of harmful chaotic phenomena in such gyros. Subsequently, to address chaotic oscillations along with overcoming the troubles of state constraints, uncertain disturbances and communication burden in the system, we incorporate the integral barrier Lyapunov function (IBLF) to limit the position of the proof mass within the physical limit. Furthermore, a type-2 sequential fuzzy neural network (T2SFNN) is used to approximate unknown nonlinear terms and the switching threshold event-triggered (STET) mechanism is utilized to save communication bandwidth. Then, an event-triggered neural backstepping controller is proposed to successfully achieve safety, high-precision and low resource consumption control of such gyros, ensuring that all signals in the closed-loop system remain bounded. Finally, simulation results and comparative experiments demonstrate the effectiveness and superiority of our proposed control scheme.