Dynamical Analysis, Circuit Design, and Fuzzy Prescribed Performance Backstepping Control of the FO Weakly Coupled MEMS Resonators

This article investigates the dynamical analysis, circuit design, and fuzzy prescribed performance backstepping control of fractional-order (FO) weakly coupled micro-electro-mechanical system (MEMS) resonators with an event-triggered input. The math model of such MEMS resonators coupled by bridge-type coupling beam is constructed based on the Lagrange motion equation and Caputo definition. The dynamical analysis reveals evolution rules and a tendency of system dynamics involved periodic/multiperiodic state and chaotic oscillation for the coupling stiffness, alternating voltage and FO. The designed FO analog circuit and digital circuit based on the field-programmable gate array further validate the mentioned dynamics and are convenient for latter engineering development. To realize stabilization control purposes like chaos suppression, accelerated convergence, high accuracy tracking, performance constraint, and communication resource saving, a fuzzy prescribed performance backstepping controller, in which the beta-cut type-2 fuzzy logic system is used to deal with unknown system function, a transfer function with prescribed performance function is proposed to guarantee the constraint boundary of the tracking error, an accelerated tracking differentiator with a speed function is established to increase convergence rate and solve the "complexity explosion," an event trigger mechanism is provided to ease the communication burden and a continuous frequency distributed model is utilized to reflect the essence of infinite dimension of such FO system, is constructed in the framework of a backstepping. The proposed scheme not only guarantees that all system signals in closed-loop system are bounded, but also achieves the mentioned stabilization control purposes. Finally, abundant simulation results validate the feasibility of the presented scheme.