Modeling and H∞ Composite Control of the Coupled Hysteretic Dynamics in Piezoelectric Micro-displacement Systems

Liang Tang, Lei Liu, Xin Guan

Abstract

This paper investigates the modeling and H∞ composite control of the coupled hysteretic dynamics in a piezoelectric micro-displacement system (PMS). First, the coupled multi-field hysteretic dynamics with physical meanings is presented for PMS. Next, the composite control analysis of the hysteretic dynamics is proposed. Then, a H∞ synthesis controller is designed by using the simplified hysteretic dynamics. To enhance the H∞ performance, the inversion-based feedforward compensation is augmented. The proposed H∞ feedback control and the inversion-based feedforward can be designed separately. Finally, the experimental studies are provided to demonstrate the proposed H∞ composite control approach.

References

  1. Brokate, M. and Sprekels, J. (1996). Hysteresis and Phase Transitions. Springer-Verlag, Berlin-HeidelbergNewYork.
  2. Clayton, G., T. S. L. K.-Z. Q. and Devasia, S. (2009). A review of feedforward control approaches in nanopositioning for high-speed SPM. ASME J. Dyn. Syst. Control, 131(6):061101.
  3. Devasia, S., E. E. and Moheimani, S. (2007). A survey of control issues in nanopositioning. IEEE Trans. Control Syst. Technol., 15(5):802-823.
  4. Dewella, L., P. N. and Blaurockb, C. (2005). Precision telescope pointing and spacecraft vibration isolation for the terrestrial planet finder coronagraph. Preceding of SPIE conference on UV/Optical/IR Space Telescopes: Innovative Technologies and Concepts. Bellingham, 2005, vol. 5899, pp. 589902.
  5. Fleming, A. (2010). Nanapositioning system with force feedback for high performance tracking and vibration control. IEEE/ASME Trans. Mechatron., 15(3):433- 446.
  6. Janaiden, M. and Rakheja, S. (2008). Development of the rate-dependent Prandtl-Ishlinskii model for smart actuators. Smart Mater. Struc., 7:035026.
  7. Jiang, H., J. H. Q. J. and Chen, Y. (2010). A modified Prandtl-Ishlinskii model for modeling asymmetric hysteresis of piezoelectric actuators. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 57(5):1200-1210.
  8. Kamesha, D., P. R. and Ghosalb, A. (2010). Modeling, design and analysis of low frequency platform for attenuating micro-vibration in spacecraft. Journal of Sound and Vibration, 329(17):3431-3450.
  9. Laneand, S. and Lacy, S. (2008). Active vibration control of a deployable optical telescope. Journal of Spacecraft and Rocket, 45(3):568-586.
  10. Leaning, K. K. and Devasia, S. (2007). Feedback linearized inverse feedforward for creep, hysteresis and vibration compensation in AFM piezoactuators. IEEE Trans. Control Syst. Technol., 15(5):927-935.
  11. Liaw, H. and Shirinzadeh, B. (2009). Neural network motion tracking control of piezo actuated flexure based mechanisms for micro nanomanipulation. IEEE/ASME Trans. Mechatron., 14(5):517-27.
  12. Liu, L., T. K. and Lee, T. H. (2012). SVD-based preisach hysteresis identification and composite control of piezo actuators. ISA Trans., 51(3):430-438.
  13. Liu, L., T. K. C. S.-L. T. C. and Lee, T. H. (2013a). Discrete composite control of piezoelectric actuators for high speed precision scanning. IEEE Transactions on Industrial Informatics, 9(3):859-868.
  14. Liu, L., T. K. T. C.-C. S.-L. and Lee, T. H. (2013b). Development of an approach toward comprehensive identification of hysteretic dynamics in piezoelectric actuators. IEEE Trans. Control Syst. Technol., 21(5):1834- 1845.
  15. Maillarda, T., C. F. and LeLettya, R. (2009). Piezo mechatronic based systems in aircraft, space and defense applications. Space Exploration Technologies II, 2009, vol. 7331, pp. 73310K.
  16. Mayergozy, I. (2003). Mathematical Modeling of Hysteresis and Their Application. Elsevier, Amsterdam, 2nd edition.
  17. McMickell, M., K. T. and Hansen, E. (2007). Optical payload isolation using the Miniature Vibration Isolation System (MVIS-II). SPIE Industrial and Commercial Applications of Smart Structures Technologies, vol. 6527, pp.652703.
  18. Nagashima, M. and Agrawal, B. (2014). Active control of adaptive optics system in a large segmented mirror telescope. International Journal of Systems Science, 45(2):159-175.
  19. Neat, G., A. A. and Goullioud, R. (1998). Overview of the micro precision interferometer testbed. Philadelphia. American Control Conference, pp.1563-1568.
  20. Shieh, H.-J. and Hsu, C.-H. (2008). An adaptive approximator-based backstepping control approach for piezoactuator-driven stages. IEEE Trans. Ind. Electron., 55(4):1729-38.
  21. Skogestad, S. and Postlethwaite, I. (2005). Multivariable Feedback Control: Design and Analysis. John Wiley and Sons Ltd, Chichester, 2nd edition.
  22. Tan, U., L. W. S. C.-R. C. N. and Ang, W. T. (2009). Feedforward controller of ill-conditioned hysteresis using singularity-free Prandtl-Ishlinskii model. IEEE/ASME Trans. Mechatron., 14(5):598-605.
  23. Wu, Y. and Zou, Q. (2009). Robust inversion-based 2- DOF control design for output tracking: piezoelectricactuator example. IEEE Trans. Control. Syst. Technol., 17(5):1069-1082.
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Paper Citation


in Harvard Style

Tang L., Liu L. and Guan X. (2014). Modeling and H∞ Composite Control of the Coupled Hysteretic Dynamics in Piezoelectric Micro-displacement Systems . In Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 978-989-758-039-0, pages 441-449. DOI: 10.5220/0005015204410449


in Bibtex Style

@conference{icinco14,
author={Liang Tang and Lei Liu and Xin Guan},
title={Modeling and H∞ Composite Control of the Coupled Hysteretic Dynamics in Piezoelectric Micro-displacement Systems},
booktitle={Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},
year={2014},
pages={441-449},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005015204410449},
isbn={978-989-758-039-0},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,
TI - Modeling and H∞ Composite Control of the Coupled Hysteretic Dynamics in Piezoelectric Micro-displacement Systems
SN - 978-989-758-039-0
AU - Tang L.
AU - Liu L.
AU - Guan X.
PY - 2014
SP - 441
EP - 449
DO - 10.5220/0005015204410449