Adaptive stabilization control of the fractional-order electrostatically actuated micro-electromechanical system with hysteresis characteristic

This paper addresses an adaptive stabilization control problem of the fractional-order electrostatically actuated micro-electromechanical system (EAMS) which suffers from adverse effects like chaotic oscillation, input hysteresis, time delay, modeling uncertainty and constraints of sensor and output. The phase diagrams and bifurcation diagram are presented to reveal the chaotic oscillation of the fractional-order EAMS. To enhance system performance and reduce computation burden, an adaptive stabilization control policy integrated with the fuzzy wavelet neural network (FWNN), tracking differentiator and extended state observer is proposed to switch chaotic oscillation into regular motion without full states feedback and accurate dynamical model. The tangent barrier function is used to guarantee no violation for output constraint, and the FWNN is employed to deal with insufficient knowledge of system dynamics. By integrating the tracking differentiator into the controller, the filtering accuracy is improved in contrast with the first-order filter, and the explosion of derivative term of the backstepping is well-solved. The boundedness of all signals for the fractional-order EAMS can be guaranteed by the Lyapunov–Krasovskii function. Finally, the simulations results validate the feasibility of the presented scheme.