Technical Briefs

Robust H Control of Hysteresis in a Piezoelectric Stack Actuator1

[+] Author and Article Information
Ning Chuang

e-mail: ning1@tpg.com.au

Ian R. Petersen

e-mail: i.r.petersen@gmail.com
School of Engineering and Information Technology,
University of New South Wales
at Australian Defence Force Academy,
Canberra, ACT 2600, Australia

1A preliminary version of this paper appeared in the Proceedings of the 17th IFAC World Congress, Seoul, July 2008.

2Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received November 3, 2011; final manuscript received June 13, 2013; published online August 23, 2013. Assoc. Editor: Nader Jalili.

J. Dyn. Sys., Meas., Control 135(6), 064501 (Aug 23, 2013) (10 pages) Paper No: DS-11-1344; doi: 10.1115/1.4024811 History: Received November 03, 2011; Revised June 13, 2013

This paper describes an H control method for controlling hysteresis in a piezoelectric stack actuator. The actuator used is a high-performance monolithic multilayer piezoelectric stack actuator. The proposed control method involves the use of a capacitor in series with the piezoelectric actuator to provide a measured output voltage which is proportional to the charge on the piezoelectric actuator. The controller is designed based on a model of the hysteresis nonlinearity constructed using experimental data. The parameters in the nonlinear model of the system are obtained from the measurements on the piezoelectric actuator circuit. Our focus in this paper is to develop a tracking controller based on a charge output of the piezoelectric actuator system and to reduce the hysteresis nonlinearity. The paper considers a robust H tracking controller to control the piezoelectric actuator based on an uncertain system model. Experimental results show that the hysteresis can be significantly reduced and the measured output can closely track a 5 Hz sawtooth reference input signal when the H controller is used.

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Croft, D., Shedd, G., and Devasia, S., 2000, “Creep, Hysteresis, and Vibration Compensation for Piezoactuators: Atomic Force Microscopy Application,” Proceedings of American Control Conference ACC’00, Vol. 3, pp. 2123–2128.
Leang, K., and Devasia, S., 2006, “Design of Hysteresis-Compensating Iterative Learning Control for Piezo-Positioners: Application to Atomic Force Microscopes,” Mechatronics, 16(3–4), pp. 141–158. [CrossRef]
Goldfarb, M., and Celanovic, N., 1997, “Modeling Piezoelectric Stack Actuators for Control of Micromanipulation,” IEEE Control Syst. Mag., 17(3), pp. 69–79. [CrossRef]
Sebastian, A., and Salapaka, S., 2005, “Design Methodologies for Robust Nano-Positioning,” IEEE Trans. Control Syst. Technol., 13(6), pp. 868–876. [CrossRef]
Ru, C., and Sun, L., 2005, “Improving Positioning Accuracy of Piezoelectric Actuators by Feedforward Hysteresis Compensation Based on a New Mathematical Model,” Rev. Sci. Instrum., 76(9), p. 095111. [CrossRef]
Jung, H., Shim, J., and Gweon, D., 2001, “Tracking Control of Piezoelectric Actuators,” Nanotechnology, 12(1), pp. 14–20. [CrossRef]
Banning, R., de Koning, W., Adriaens, H., and Koops, R., 2001, “State-Space Analysis and Indentification for a Class of Hysteresis Systems,” Automatica, 37, pp. 1883–1892. [CrossRef]
Fleming, A., and Moheimani, R., 2005, “A Grounded-Load Charge Amplifier for Reducing Hysteresis in Piezoelectric Tube Scanners,” Rev. Sci. Instrum., 76(7), p. 073707. [CrossRef]
Furutaniy, K., Urushibata, M., and Mohri, N., 1998, “Displacement Control of Piezoelectric Element by Feedback of Induced Charge,” Nanotechnology, 9, pp. 93–98. [CrossRef]
Moheimani, R., and Vautier, B., 2005, “Resonant Control of Structural Vibration Using Charge-Driven Piezoelectric Actuators,” IEEE Trans. Control Syst. Technol., 13(6), pp. 1021–1035. [CrossRef]
Jang, M., Chen, C., and Lee, J., 2009, “Modeling and Control of a Piezoelectric Actuator Driven System With Asymmetric Hysteresis,” J. Franklin Inst., 346, pp. 17–32. [CrossRef]
Adriaens, H., de Koning, W., and Banning, R., 2000, “Modeling Piezoelectric Actuators,” IEEE/ASME Trans. Mech., 5(4), pp. 331–341. [CrossRef]
Xie, L., Fu, M., and de Souza, C., 1992, “H Control and Quadratic Stabilization of Systems With Parameter Uncertainty via Output Feedback,” IEEE Trans. Autom. Control, 37(8), pp. 1253–1256. [CrossRef]
Xie, L., and de Souza, C., 1992, “Robust H Control for Linear Systems With Norm-Bounded Time-Varying Uncertainty,” IEEE Trans. Autom. Control, 37(8), pp. 1188–1191. [CrossRef]
Petersen, I., Anderson, B., and Jonckeere, E., 1991, “A First Principles Solution to the Non-Singular H Control Problem,” Int. J. Robust Nonlinear Control, 1(3), pp. 171–185. [CrossRef]
Chuang, N., Petersen, I., and Pota, H., 2011, “Robust H Control in Fast Atomic Force Microscopy,” Proceedings of IEEE American Control Conference ACC’11, pp. 2258–2265.
Fleming, A., 2011, “Dual-Stage Vertical Feedback for High-Speed Scanning Probe Microscopy,” IEEE Trans. Control Syst. Technol., 19(1), pp. 156–165. [CrossRef]
Zhou, K., Doyle, J., and Glover, K., 1996, Robust and Optimal Control, Prentice-Hall, Englewood Cliffs, NJ.
Green, M., and Limebeer, D., 1995, Linear Robust Control, Prentice-Hall, Englewood Cliffs, NJ.
Baser, T., and Bernhard, P., 1995, H Optimal Control and Related Minimax Design Problem: A Dynamic Game Approach, Birhauser, Boston, MA.


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Fig. 1

Electromechanical model for the piezoelectric actuator

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Fig. 2

Graph of the relationship between i and U·h

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Fig. 3

Valid region of the model

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Fig. 4

Piezoelectric stack actuator model

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Fig. 5

Simplified equivalent circuit model

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Fig. 6

Measured and model frequency responses for the piezoelectric actuator circuit

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Fig. 7

Experimental test setup to measure the hysteresis in the piezoelectric actuator circuit

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Fig. 8

Hysteresis plot of U2 versus U obtained from experimental data and model simulation

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Fig. 9

Sector bounded nonlinearity in the piezoelectric stack actuator model

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Fig. 10

Block diagram illustrating the robust H tracking control problem formulation

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Fig. 11

Bode plot of the feedback controller transfer function H1(s)

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Fig. 12

Bode plot of the feedforward controller transfer function H2(s)

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Fig. 13

Block diagram of piezoelectric stack actuator with the H tracking controller

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Fig. 14

Bode plot of the closed loop transfer function from the reference w to the output y

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Fig. 15

Bode plot of the loop gain transfer function corresponding to the robust H controller

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Fig. 16

Experimentally measured hysteresis curves with a 5 Hz sinusoidal reference input w

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Fig. 17

System output U2 corresponding to a 5 Hz sawtooth reference input compared to an ideal sawtooth output

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Fig. 18

Output tracking error versus time for a 5 Hz sawtooth reference input



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