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 theβ-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.

This article mainly investigates the model design, field programmable gate array (FPGA) implementation, and prescribed-time fault-tolerant control of a fractional-order (FO) decoupled dual-mass micro-electro-mechanical system (MEMS) gyro with deferred constraints. First, the structure of such MEMS gyro is designed to eliminate the linear acceleration in the sensing direction and its mathematical model is built based on the Lagrange’s equation. The dynamical analysis shows that such gyro can generate unpredictable, random, and disorder motions under various FOs, stiffness cross the coupling coefficients and proof masses. The designed FPGA circuit further demonstrates the undesirable chaotic oscillations of such MEMS gyro and good hardware resources utilization, avoiding the time consuming and board redesign. Second, to better solve the problems of constraints, actuator faults, uncertainties, drive couplings, and chaotic oscillations, a dependent deferred-error function superimposed to a prescribed-time function is used to guarantee no violation of constraints after a finite time. Furthermore, a$\beta $-cut type-2 fuzzy logic system (T2FLS) is employed to solve the uncertainty, and an FO hyperbolic tangent tracking differentiator (HTTD) is utilized to deal with the direct FO derivative and repeated derivative in the framework of the backstepping control. Then, a prescribed-time fault-tolerant control scheme of the FO decoupled dual-mass MEMS gyro is proposed under the actuator fault. Finally, the abundant simulation experimental results verify the feasibility and effectiveness of our scheme.