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Research Papers

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

[+] Author and Article Information
Mohsen Bakhtiari-Shahri

School of Mechanical Engineering,
Ferdowsi University of Mashhad,
Mashhad 9177948944, Iran
e-mail: m.bakhtiari@mail.um.ac.ir

Hamid Moeenfard

School of Mechanical Engineering;
Center of Excellence in Soft Computing and
Intelligent Information Processing,
Ferdowsi University of Mashhad,
Mashhad 9177948944, Iran
e-mail: h_moeenfard@um.ac.ir

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received November 25, 2017; final manuscript received September 1, 2018; published online October 8, 2018. Assoc. Editor: Maurizio Porfiri.

J. Vib. Acoust 141(1), 011019 (Oct 08, 2018) (9 pages) Paper No: VIB-17-1394; doi: 10.1115/1.4041399 History: Received November 25, 2017; Revised September 01, 2018

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.

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Figures

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Fig. 1

A schematic view of electrostatically actuated circular microplates

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Fig. 2

Voltage-deflection behavior of the microplates shown in Fig. 1

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Fig. 3

Normalized undamped dynamic response of the system to normalized voltage V=0.24

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Fig. 4

Open-loop response of the undamped system to different excitation voltages

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Fig. 5

Closed-loop response and the control voltage versus time for the case of the fuzzy controller wmax,d=0.2

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Fig. 6

Optimal values of d for some specific set-points and approximating the optimal d with a polynomial

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Fig. 7

Comparison of the performance of the optimal fuzzy controller with optimal PID controller in stabilizing the system around the within pull-in command wmax,d=0.2

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Fig. 8

Comparison of the performance of the optimal fuzzy controller with optimal PID controller in stabilizing the system around the beyond pull-in command wmax,d=0.4

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Fig. 9

Performance comparison of the fuzzy and PID controllers in dealing with multiple step commands

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Fig. 10

Noise effects on the performance of fuzzy and PID controllers

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Fig. 11

Closed-loop response of the system to set-point wmax,d=0.2, with and without supervisory controller

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Fig. 12

Closed-loop response of the system with and without supervisory controller to a large stroke harmonic set-point

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