Journal of Electroceramics

, Volume 28, Issue 4, pp 240–245 | Cite as

A hysteresis model based on ellipse polar coordinate and microscopic polarization theory



In this paper, the underlying anhysteretic polarization is derived based on Boltzmann statictics and Langevin model. The remnant polarization and the irreversible polarization are analyzed. A thermodynamic description of ferroelectric phenomena is proposed to address the coupling relationship between electrical field and mechanical field by considering the series expansion of the elastic Gibbs energy function. A simple linear mapping hysteresis model based on theory of microscopic polarization and ellipse polar coordinate is derived. In order to evaluate the effectiveness of the proposed model, a nano-positioning stage driven by the PZT in open-loop operation is used to test. The experimental results show that the proposed hysteresis model could precisely describe hysteresis phenomena. The model max relative error of full span range is about 0.5 %. The proposed model simplifies the identification procedure of its inverse model. It is experimentally demonstrated that the tracking precision is significantly improved.


Piezoelectric actuator Hysteresis Microscopic polarization Linear mapping 



The authors gratefully acknowledge financial support from the National Natural Science Foundation of China under Grant No. 61174087 and Foundation for University Key Teacher of Heilongjiang Province of China.


  1. 1.
    G. Tao, P.V. Kolotovic, IEEE Trans. Autom. Control. 40(2), 200 (1995)CrossRefGoogle Scholar
  2. 2.
    P. Ge, M. Jouaneh, IEEE Trans. Control. Syst. Technol. 4(3), 211 (1996)Google Scholar
  3. 3.
    P. Ge, M. Jouaneh, Precis. Eng. 20, 99 (1997)CrossRefGoogle Scholar
  4. 4.
    M.A. Krasnoskl’skii, A.V. Pokrovskii, (Springer-Verlag, New York, 1989)Google Scholar
  5. 5.
    G. Webb, A. Kurdila, D. Lagoudas, J. Guid. Control. Dyn. 23(3), 459 (2000)CrossRefGoogle Scholar
  6. 6.
    J. Ha, Y. Kung, R. Fung, Sensor Actuator Phys. 132, 643 (2006)CrossRefGoogle Scholar
  7. 7.
    K. Kuhnen, H. Janocha, 6th International Conference on New Actuators, (Bremen, 1998), p. 309Google Scholar
  8. 8.
    P. Kreci, K. Kuhnen, IEE Proc. Contr. Theor. Appl. 148(3), 185 (2001)CrossRefGoogle Scholar
  9. 9.
    K. Kuhnen, H. Janocha, Sensor Actuator Phys. 79, 83 (2000)CrossRefGoogle Scholar
  10. 10.
    H. Aderiaens, W. Koning, R. Baning, IEEE ASME Trans. Mechatron. 5, 331 (2000)CrossRefGoogle Scholar
  11. 11.
    M. Goldfarb, N. Celanovic, ASME J. Dyn. Syst. Meas. Contr. 119, 478 (1997)CrossRefGoogle Scholar
  12. 12.
    S. Bashash, N. Jalili, J. Appl. Phys. 100(1), 014103 (2006)CrossRefGoogle Scholar
  13. 13.
    E. James, IEEE Trans. Automat. Contr. 38, 351 (1993)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.College of AutomationHarbin Engineering UniversityHarbinChina
  2. 2.Centre of Robotics and MicrosystemSoochow UniversitySoochowChina

Personalised recommendations