Quadrilateral modelling and robust control of a nonlinear piezoelectric cantilever

IEEE Transactions on Control Systems Technology

Volumn 17, Issue 3, 2009, Pages 528-539

  Rakotondrabe, Micky ^a   Haddab, Yassine ^a   Lutz, Philippe ^a  

^a FEMTO ST INSTITUTE   (France)

Author keywords

Hysteresis and creep; Micromanipulation; Piezoelectric devices; Quadrilateral approximate model; Robust control

Indexed keywords

DEGREE OF FREEDOM; DEVELOPED MODEL; DYNAMIC HYSTERESIS; HYSTERESIS CURVE; LINEAR DYNAMICS; MICROMANIPULATION; NEW MODEL; NON-LINEARITY; PIEZOELECTRIC CANTILEVERS; POSITIONING ACCURACY; QUADRILATERAL APPROXIMATE MODEL; ROBUST CONTROLLERS; ROBUST H; TEMPERATURE CHANGES;

ATOMIC FORCE MICROSCOPY; CONTROLLERS; CREEP; HYSTERESIS; MICROMANIPULATORS; NANOCANTILEVERS; PIEZOELECTRIC TRANSDUCERS; PIEZOELECTRICITY; THERMAL EFFECTS;

ROBUST CONTROL;

EID: 67349263452     PISSN: 10636536     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCST.2008.2001151     Document Type: Article

References (33)

1. D. L. Heiserman, "Piezoelectric polymer micromanipulator," U.S. Patent, No. 4 610 475, Sep. 9, 1986.
2. Y. Haddab, N. Chaillet, and A. Bourjault, "A microgripper using smart piezoelectric actuators," presented at the IEEE/RSJ Int. Conf. Intell. Robot Syst. (IROS), Takamatsu, Japan, 2000.
3. J. Agnus, J. M. Breguet, N. Chaillet, O. Cois, P. de Lit, A. Ferreira, P. Melchior, C. Pellet, and J. Sabatier, "A smart microrobot on chip: Design, identification and modeling," in Proc. IEEE/ASME Int. Conf. Adv. Intell. Mechatron. (AIM), Kobe, Japan, 2003, pp. 685-690.
4. J. Zhong, S. Seelecke, R. C. Smith, and C. Büskens, "Optimal control of piezoceramic actuators," in SPIE Smart Structures Mater.: Model., Signal Process., Control, 2003, pp. 264-274.
5. J. A. Main, E. Garcia, and D. V. Newton, "Precision position control of piezoelectric actuators using charge feedback," J. Guidance, Control Dyn., vol. 18, no. 5, pp. 1068-1073, 1995.
6. H. Jung, J. Y. Shim, and D. Gweon, "New open-loop actuating method of piezoelectric actuators for removing hysteresis and creep," Rev. Scientific Instruments, vol. 71, no. 9, pp. 3436-3440, Sep. 2000.
7. K. Kuhnen and H. Janocha, "Compensation of the creep and hysteresis effect of piezoelectric actuators with inverse systems," in Proc. 6th Int. Conf. New Actuators, 1998, pp. 426-429.
8. D. Croft, G. Shed, and S. Devasia, "Creep, hysteresis and vibration compensation for piezoactuators: Atomic Force microscopy application," ASME J. Dyn. Syst., Meas. Control, vol. 123, pp. 35-43, 2001.
9. P. Ge and M. Jouaneh, "Generalised preisach model for hysteresis nonlinearity of piezoelectric actuators," Precision Eng., vol. 20, pp. 99-111, 1997.
10. D. Hughes and J. T. Wen, "Preisach modeling of piezoceramic and shape memory alloy hysteresys," Smart Mater. Struct., vol. 6, pp. 287-300, 1997.
11. R. B. Mrad and H. Hu, "A model for voltage to displacement dynamics in piezoceramic actuators subject to dynamic-voltage excitations," IEEE Trans. Mechatronics, vol. 7, no. 4, pp. 479-489, Dec. 2002.
12. R. C. Smith and Z. Ounaies, "A hysteresis model for piezoceramic materials," NASA, Dallas, TX, NASA-ICASE Rep. 99-229, Aug. 1999.
13. Y. Gao and S. Tse, "Modelling of piezoelectric actuator based nanopositioning system under sinusoidal excitation using multi-polynomial regression," in J. Physics: Conf. Series 13, 2005, pp. 98-101.
14. M. Goldfarb and N. Celanovic, "A lumped parameter electromechanical model for describing the nonlinear behavior of piezoelectric actuators," ASME J. Dyn. Syst., Meas. Control, vol. 119, pp. 478-485, 1997.
15. S. Lining, R. Changhai, R. Weibin, C. Liguo, and K. Minxiu, "Tracking control of piezoelectric actuator based on a new mathematical model," J. Micromech. Microeng., vol. 14, pp. 1439-1444, Aug. 2004.
16. T. S. Low and W. Guo, "Modeling of a three-layer piezoelectric bimorph beam with hysteresis," J. Microelectromech. Syst., vol. 4, pp. 230-237, 1995.
17. C. W. Wong, Y. Q. Ni, and J. M. Ko, "Steady state oscillation of hysteretic differential model. i-response analysis," J. Eng. Mechan. vol. 120, pp. 2271-2298, 1994.
18. S. Chonan, Z. Jiang, and T. Yamamoto, "Nonlinear hysteresis compensation of piezoelectric ceramic actuators," J. Intell. Mater. Syst. Struct., vol. 7, pp. 150-156, 1996.
19. M. S. Tsai and J. S. Chen, "Robust tracking control of a piezoactuator using a new approximate hysteresis model," Trans. ASME J. Dyn. Syst., Meas. Control, vol. 125, pp. 96-102, 2003.
20. J. A. Main and E. Garcia, "Piezoelectric stack actuators and control system design: Strategies and pitfalls," J. Guid. Control Dyn., vol. 20, no. 3, pp. 479-485, 1997.
21. D. Croft and S. Devasia, "Hysteresis and vibration compensation for piezoactuators," J. Guid. Control Dyn., vol. 21, pp. 710-717, 1998.
22. S. Devasia, E. E. Eleftheriou, and R. Moheimani, "A survey of control issues in nanopositioning," IEEE Trans. Control Syst. Technol., vol. 15, no. 5, pp. 802-823, Sep. 2007.
23. I. D. Mayergoyz, Mathematical Models of Hysteresis and Their Applications. Amsterdam, The Netherlands: Elsevier, 2003.
24. IEEE Standard on Piezoelectricity, Std. 176-1978, 1978.
25. J. G. Smits and W. S. Choi, "The constituent equations of piezoelectric heterogeneous bimorphs," IEEE Trans. Ultrason., Ferroelectr. Freq. Control, vol. 38, no. 3, pp. 256-270, May 1991.
26. J. L. Pons, Emerging Actuator Technologies: A Micromechatronic Approach. New York: Wiley, 2005.
27. T. Chen and B. A. Francis, Optimal Sampled-Data Control Systems. London, U.K.: Springer-Verlag.
28. K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control. Englewood Cliffs, NJ: Prentice-Hall.
29. ∞ problem with a strictly proper controller," Int. J. Control, vol. 66, no. 5, pp. 747-765, 1997.
30. G. J. Balas, J. C. Doyle, K. Glover, A. Packard, and R. Smith, "μ-analysis and synthesis toolbox," The Mathworks User's Guide-3 2001.
31. ∞-norm bound and relations to risk sensivity," Syst. Control Lett., vol. 11, pp. 167-172, 1988.
32. ∞ control problems," IEEE Trans. Automat. Control, vol. AC-34, no. 8, pp. 831-846, Aug. 1989.
33. B. C. Moore, "Principal component analysis in linear systems: Controllability, observability and model reduction," IEEE Trans. Automat. Control, vol. AC-26, no. 1, pp. 17-32, Jan. 1981.