Dynamical analysis and adaptive prescribed-performance backstepping control of two electrostatically coupled MEMS resonators with optimization

This paper investigates the dynamical analysis and adaptive prescribed-performance backstepping control for the coupled MEMS resonators with nonlinear dynamics. The dynamical model of such resonators is established considering the mutual interactions. Then, we examine and reveal the inherent chaotic behaviors that noticeably influence the system sensitivity, using time histories, phase diagrams, bifurcation diagrams, and Lyapunov exponents. In the subsequent controller design, we introduce a type-2 fuzzy wavelet neural network (T2FWNN) to estimate the uncertainties in the system. In backstepping, a speed function and prescribed performance functions are employed to reconstruct the error signals thereby achieving accelerated convergence and the high-precision control. Meanwhile, an accelerated tracking differentiator (ATD) with the speed function is design to address the intrinsic problem of 'complexity explosion' of traditional backstepping. Moreover, the particle swarm optimization (PSO) is integrated to tune the control parameters and to minimize the cost function. Besides, we prove that all signals of the closed-loop system are ultimately bounded through stability analysis. Finally, simulation results verify that all control targets such as chaos suppression, accelerated convergence, prescribed performance and optimization are all achieved. Compared with existing methods, the proposed control scheme exhibits superior performance in terms of both accuracy and convergence speed, achieving RMS control errors of 0.0016, 0.1126, 0.012, and 0.1126 respectively.