Prescribed-Time Fault-Tolerant Control of the FO Decoupled Dual-Mass MEMS Gyro With Deferred Constraints-Design and Implementation

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.