Applied Mechatronics: On Mitigating Disturbance Effects in MEMS Resonators Using Robust Nonsingular Terminal Sliding Mode Controllers

Abstract

This investigation attempts to study a possible controller in improving the dynamic stability of capacitive microstructures through mitigating the effects of disturbances and uncertainties in their resultant dynamic behavior. Consequently, a nonsingular terminal sliding mode control strategy is suggested in this regard. The main features of this particular control strategy are its high response speed and its non-reliance on powerful controller forces. The stability of the controller was investigated using Lyapunov theory. For this purpose, a suitable Lyapunov function was introduced to prove the stability of a controller, and the singularity conditions and methods to overcome these conditions are presented. The achieved results proved the high capability of the applied technique in stabilizing of the microstructure as well as mitigating the effects of disturbances and uncertainties.

Chaotic vibration control of a composite cantilever beam

“…In 2019, Mobki et al 23 applied the SMC in a closed-loop control of a one-dimensional nonlinear dynamic system of a capacitive micro structure subjected to electrostatic forces; in 2020, Azizi 24 used the SMC to reduce the unwanted vibrations of buildings subjected to earthquakes; in the next year, Azizi and Mobki 25 employed the SMC for active control of car suspension systems. Based on the existing SMC, Mobki et al 26 designed an adaptive control scheme to control the vibration of a one-dimensional nonlinear dynamic system of a micro capacitor in 2020; in 2022, Azizi et al 27 also developed a nonsingular terminal SMC strategy to control the vibration of a one-dimensional nonlinear dynamic system of a micro structure. In order to mitigate the effects of uncertainties in dynamic systems, fuzzy rules were introduced into the traditional SMC in 2006, and hence a new control strategy namely the fuzzy sliding mode control (FSMC) was developed for Duffing-Holmes chaos synchronization with uncertainties 28 ; in 2011, Yau et al 29 used the FSMC approach to control the chaotic vibration of a one-dimensional nonlinear dynamic system of a micro resonator; in 2022, Wu et al 30 applied the FSMC to stabilize Makovian jump nonlinear systems; in the same year, Ramakrishnan et al 31 also applied the FSMC to synchronize a chaotic oscillator in a fractional-order circuit.…”