Optimal Design of a Stable Fuzzy Controller for Beyond Pull-In Stabilization of Electrostatically Actuated Circular Microplates

Abstract

The current paper aims to provide an optimal stable fuzzy controller to extend the travel range of a pair of flexible electrostatically actuated circular microplates beyond their pull-in limit. The single mode assumption is utilized to derive the equation of motion of the system based on a Lagrangian approach. The static behavior of the system is studied using the proposed model, and the utilized assumption and the relevant results are closely verified by nonlinear finite element simulations. The open-loop dynamic analysis is also performed to derive the linguistic rules governing the voltage-deflection behavior of the system. The mentioned rules are then employed for designing a fuzzy controller, which controls the deflection of the microplates. The controller is then optimized to provide better response specifications. The performance of the optimal fuzzy controller is compared with that of the optimal proportional–integral–derivative (PID) controller and obvious superiorities in terms of noise suppression and stability enhancement are observed. To guarantee the stability of the closed-loop system, another higher level controller is designed to oversee the behavior of the fuzzy controller. Simulation results reveal that the superintended fuzzy controller can prevent instability, while fairly extending the travel range of system and providing it with a better transient response. The suggested design approach proposed in this paper may be used to improve the performance of many nano/micro devices and nano/micro positioning systems.