A Novel Fault-Tolerant Super-Twisting Control Technique for Chaos Stabilization in Fractional-Order Arch MEMS Resonators

With the increasing demand for high-performance controllers in micro- and nano-systems, it is crucial to account for the effects of unexpected faults in control inputs during the design process. To tackle this challenge, we present a new approach that leverages an estimator-based super-twisting control technique that is capable of regulating chaos in fractional-order arch micro-electro-mechanical system (MEMS) resonators. We begin by studying the governing equation of a fractional-order arch MEMS resonator, followed by a thorough exploration of its chaotic properties. We then outline the design process for our novel control technique. The proposed technique takes into consideration the effects of uncertainty and faults in the control input by utilizing a finite time estimator and a super-twisting algorithm. The proposed technique addresses important challenges in the control of MEMS in real-world applications by providing fault tolerance, which enables the controller to withstand unexpected faults in the control input. We apply our controller to the fractional-order arch MEMS resonator, conducting numerical simulations. The numerical findings reveal that our proposed control technique is capable of stabilizing the system’s dynamics, even in the presence of a time-evolving fault in the control actuator. These results provide compelling evidence of the efficacy of our approach to control, despite the presence of an evolving fault.