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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Gad-el-Hak, M. , 2005, MEMS: Applications, CRC Press, Boca Raton, FL.
Bell, D. J. , Lu, T. , Fleck, N. A. , and Spearing, S. M. , 2005, “ MEMS Actuators and Sensors: Observations on Their Performance and Selection for Purpose,” J. Micromech. Microeng., 15(7), p. S153. [CrossRef]
Chiou, J.-C. , Lin, Y.-J. , and Kuo, C.-F. , 2007, “ Extending the Traveling Range With a Cascade Electrostatic Comb-Drive Actuator,” J. Micromech. Microeng., 18(1), p. 015018. [CrossRef]
Olfatnia, M. , Sood, S. , Gorman, J. J. , and Awtar, S. , 2013, “ Large Stroke Electrostatic Comb-Drive Actuators Enabled by a Novel Flexure Mechanism,” J. Microelectromech. Syst., 22(2), pp. 483–494. [CrossRef]
Trivedi, R. , Pawaskar, D. N. , and Shimpi, R. , 2016, “ Optimization of Static and Dynamic Travel Range of Electrostatically Driven Microbeams Using Particle Swarm Optimization,” Adv. Eng. Software, 97, pp. 1–16. [CrossRef]
Ye, W. , Mukherjee, S. , and MacDonald, N. C. , 1998, “ Optimal Shape Design of an Electrostatic Comb Drive in Microelectromechanical Systems,” J. Microelectromech. Syst., 7(1), pp. 16–26. [CrossRef]
Shirazi, F. A. , Velni, J. M. , and Grigoriadis, K. M. , 2011, “ An LPV Design Approach for Voltage Control of an Electrostatic MEMS Actuator,” J. Microelectromech. Syst., 20(1), pp. 302–311. [CrossRef]
Chen, H. , Sun, W. , Chen, A. , Yeow, J. , and Sun, Z. , “ High Performance Closed-Loop Control of a 2D MEMS Micromirror With Sidewall Electrodes for a Laser Scanning Microscope System,” International Conference on Manipulation, Manufacturing and Measurement on the Nanoscale (3M-NANO), Taipei, Taiwan, Oct. 27–31, pp. 12–17.
Chen, H. , Sun, W. , Sun, Z. , and Yeow, J. , 2012, “ Second-Order Sliding Mode Control of a 2D Torsional MEMS Micromirror With Sidewall Electrodes,” J. Micromech. Microeng., 23(1), p. 015006. [CrossRef]
Gronle, M. , Zhu, G. , and Saydy, L. , “ Sliding Mode Tracking Control of an Electrostatic Parallel-Plate MEMS,” IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Montreal, ON, Canada, July 6–9, pp. 999–1004.
Zhu, G. , Saydy, L. , Hosseini, M. , Chianetta, J.-F. , and Peter, Y.-A. , 2008, “ A Robustness Approach for Handling Modeling Errors in Parallel-Plate Electrostatic MEMS Control,” J. Microelectromech. Syst., 17(6), pp. 1302–1314. [CrossRef]
Pouly, G. , Huynh, T.-H. , Lauffenburger, J.-P. , and Basset, M. , 2011, “ State Feedback Fuzzy Adaptive Control for Active Shimmy Damping,” Eur. J. Control, 17(4), pp. 370–393. [CrossRef]
Hacioglu, Y. , Arslan, Y. Z. , and Yagiz, N. , 2011, “ MIMO Fuzzy Sliding Mode Controlled Dual Arm Robot in Load Transportation,” J. Franklin Inst., 348(8), pp. 1886–1902. [CrossRef]
Vatankhah, R. , and Asemani, M. H. , 2017, “ Output Feedback Control of Piezoelectrically Actuated Non-Classical Micro-Beams Using TS Fuzzy Model,” J. Franklin Inst., 354(2), pp. 1042–1065. [CrossRef]
Radgolchin, M. , Moeenfard, H. , and Ghasemi, A. H. , 2016, “ A Two-Level Adaptive Fuzzy Control Algorithm for Beyond Pull-in Stabilization of Electrostatically Actuated Microplates,” ASME Paper No. DSCC2016-9841.
Chiou, J. , Lin, Y. , and Wu, S. , 2002, “ Closed-Loop Fuzzy Control of Torsional Micromirror With Multiple Electrostatic Electrodes,” IEEE/LEOS International Conference on Optical MEMs, Lugano, Switzerland, Aug. 20–23, pp. 85–86.
Khadembashi, M. , Moeenfard, H. , and Ghasemi, A. H. , 2016, “ Deflection Control OF Electrostatically Actuated Micro Cantilevers Via Fuzzy Controller,” ASME Paper No. DSCC2016-9838.
Feng, G. , Cao, S. , Rees, N. , and Chak, C. , 1997, “ Design of Fuzzy Control Systems With Guaranteed Stability,” Fuzzy Sets Syst., 85(1), pp. 1–10. [CrossRef]
Chen, C.-S. , and Chen, W.-L. , 1998, “ Robust Adaptive Sliding-Mode Control Using Fuzzy Modeling for an Inverted-Pendulum System,” IEEE Trans. Ind. Electron., 45(2), pp. 297–306. [CrossRef]
Lei, D. , Wang, T. , Di, C. , and Fei, J. , 2016, “ Adaptive Dynamic Surface Control of MEMS Gyroscope Sensor Using Fuzzy Compensator,” IEEE Access, 4, pp. 4148 –4154. [CrossRef]
Fei, J. , and Zhou, J. , 2012, “ Robust Adaptive Control of MEMS Triaxial Gyroscope Using Fuzzy Compensator,” IEEE Trans. Syst., Man, Cybern., Part B (Cybern.), 42(6), pp. 1599–1607. [CrossRef]
Radgolchin, M. , and Moeenfard, H. , 2016, “ Development of a Multi-Level Adaptive Fuzzy Controller for Beyond Pull-In Stabilization of Electrostatically Actuated Microplates,” J. Vib. Control, 24(5), pp. 860–878.
Rigatos, G. , Zhu, G. , Yousef, H. , and Boulkroune, A. , 2016, “ Flatness-Based Adaptive Fuzzy Control of Electrostatically Actuated MEMS Using Output Feedback,” Fuzzy Sets Syst., 290, pp. 138–157. [CrossRef]
Rao, S. S. , 2007, Vibration of Continuous Systems, Wiley, Hoboken, NJ.
Reddy, J. N. , 2006, Theory and Analysis of Elastic Plates and Shells, CRC Press, Boca Raton, FL.
Soedel, W. , 2004, Vibrations of Shells and Plates, Marcel Dekker, New York.
Nader, M. , Gattringer, H. , Krommer, M. , and Irschik, H. , 2003, “ Shape Control of Flexural Vibrations of Circular Plates by Shaped Piezoelectric Actuation,” ASME J. Vib. Acoust., 125(1), pp. 88–94. [CrossRef]
Philen, M. K. , and Wang, K. , 2005, “ Active Stiffeners for Vibration Control of a Circular Plate Structure: Analytical and Experimental Investigations,” ASME J. Vib. Acoust., 127(5), pp. 441–450. [CrossRef]
Vogl, G. W. , 2006, “ Nonlinear Dynamics of Circular Plates Under Electrical Loadings for Capacitive Micromachined Ultrasonic Transducers (CMUTs),” Ph.D. dissertation, Virginia Polytechnic Institute, Blacksburg, VA.
Gani, A. , and Salami, M. , 2002, “ A LabVIEW Based Data Acquisition System for Vibration Monitoring and Analysis,” Student Conference on Research and Development (SCOReD), Shah Alam, Malaysia, July 17, pp. 62–65.
Wang, L.-X. , 1999, A Course in Fuzzy Systems, Prentice Hall Press, Upper Saddle River, NJ.
Solihin, M. I. , Kamal, M. , and Legowo, A. , “ Objective Function Selection of GA-Based PID Control Optimization for Automatic Gantry Crane,” International Conference on Computer and Communication Engineering (ICCCE), Kuala Lumpur, Malaysia, May 13–15, pp. 883–887.
Valluru, S. K. , and Singh, M. , 2018, “ Performance Investigations of APSO Tuned Linear and Nonlinear PID Controllers for a Nonlinear Dynamical System,” J. Electr. Syst. Inf. Technol. (in press).
Verma, O. P. , Manik, G. , and Jain, V. K. , 2017, “ Simulation and Control of a Complex Nonlinear Dynamic Behavior of Multi-Stage Evaporator Using PID and Fuzzy-PID Controllers,” J. Comput. Sci., 25, pp. 238–251. [CrossRef]
Yang, Z. , Matsumoto, S. , Goto, H. , Matsumoto, M. , and Maeda, R. , 2001, “ Ultrasonic Micromixer for Microfluidic Systems,” Sens. Actuators A: Phys., 93(3), pp. 266–272. [CrossRef]


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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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