DOI QR코드

DOI QR Code

Modeling of Dynamic Hysteresis Based on Takagi-Sugeno Fuzzy Duhem Model

  • Lee, Sang-Yun (School of Electrical and Electronic Engineering, Yonsei University) ;
  • Park, Mignon (School of Electrical and Electronic Engineering, Yonsei University) ;
  • Baek, Jaeho (Advanced R&D Team (Digital Appliances), Samsung Electronics Co. Ltd.)
  • Received : 2013.11.21
  • Accepted : 2013.12.25
  • Published : 2013.12.25

Abstract

In this study, we propose a novel method for modeling dynamic hysteresis. Hysteresis is a widespread phenomenon that is observed in many physical systems. Many different models have been developed for representing a hysteretic system. Among them, the Duhem model is a classical nonlinear dynamic hysteresis model satisfying the properties of hysteresis. The purpose of this work is to develop a novel method that expresses the local dynamics of the Duhem model by a linear system model. Our approach utilizes a certain type of fuzzy system that is based on Takagi-Sugeno (T-S) fuzzy models. The proposed T-S fuzzy Duhem model is achieved by fuzzy blending of the linear system model. A simulated example applied to shape memory alloy actuators, which have typical hysteretic properties, illustrates the applicability of our proposed scheme.

Keywords

References

  1. S. M. Dutta, F. H. Ghorbel, and J. B. Dabney, "Modeling and control of a shape memory alloy actuator," in Proceedings of the 20th IEEE International Symposium on Intelligent Control, Limassol, Cyprus, June 27-29, 2005, pp. 1007-1012. http://dx.doi.org/10.1109/.2005.1467151
  2. I. D. Mayergoyz, "The classical preisach model of hysteresis," in Mathematical Models of Hysteresis, I. D. Mayergoyz, Ed. New York, NY: Springer-Verlag, 1991, pp. 1-63. http://dx.doi.org/10.1007/978-1-4612-3028-1_1
  3. I. Mayergoyz and G. Friedman, "Generalized preisach model of hysteresis," IEEE Transactions on Magnetics, vol. 24, no. 1, pp. 212-217, 1988. https://doi.org/10.1109/20.43892
  4. J.W. Macki, P. Nistri, and P. Zecca, "Mathematical models for hysteresis," SIAM Review, vol. 35, no. 1, pp. 94-123, Mar. 1993. http://dx.doi.org/10.1137/1035005
  5. S. M. Dutta, "Dynamic hysteresis modeling and applications," M.S. thesis, Rice University, Houston, TX, 2004.
  6. R. Bouc, "Forced vibration of mechanical systems with hysteresis," in Preceedings of the 4th International Conference on Nonlinear Oscillations, Prague, Czechoslovakia, 1967.
  7. Y. K. Wen, "Method for random vibration of hysteretic systems," ASCE Journal of the Engineering Mechanics Division, vol. 102, no. 2, pp. 249-263, Apr. 1976.
  8. B. D. Coleman and M. L. Hodgdon, "On a class of constitutive relations for ferromagnetic hysteresis," Archive for Rational Mechanics and Analysis, vol. 99, no. 4, pp. 375-396, Dec. 1987. http://dx.doi.org/10.1007/BF00282052
  9. L. O. Chua and K. A. Stromsmoe, "Mathematical model for dynamic hysteresis loops," International Journal of Engineering Science, vol. 9, no. 5, pp. 435-450, May 1971. http://dx.doi.org/10.1016/0020-7225(71)90046-2
  10. K. Tanaka and H. O.Wang, Fuzzy Control Systems Design and Analysis: a Linear Matrix Inequality Approach, New York, NY: Wiley, 2001.
  11. L. X. Wang, A Course in Fuzzy Systems and Control, Upper Saddle River, NJ: Prentice Hall PTR, 1997.
  12. S. W. Jun, D. W. Kim, and H. J. Lee, "Design of T-S fuzzy-model-based controller for control of autonomous underwater vehicles," Journal of Korean Institute of Intelligent Systems, vol. 21, no. 3, pp. 302-306, Jun. 2011. http://dx.doi.org/10.5391/JKIIS.2011.21.3.302
  13. H. J. Kim, Y. H. Joo, and J. B. Park, "Controller design for continuous-time Takagi-Sugeno fuzzy systems with fuzzy lyapunov functions: LMI approach," International Journal of Fuzzy Logic and Intelligent Systems, vol. 12, no. 3, pp. 187-192, Sep. 2012. http://dx.doi.org/10.5391/IJFIS.2012.12.3.187
  14. M. K. Song, J. B. Park, J. K. Kim, and Y. H. Joo, "Delay-range-dependent stability analysis and stabilization for nonlinear systems: T-S fuzzy model approach," Journal of Korean Institute of Intelligent Systems, vol. 19, no. 3, pp. 337-342, Jun. 2009. http://dx.doi.org/10.5391/JKIIS.2009.19.3.337
  15. H. J. Lee, Y. H. Joo, S. Y. Lee, and J. B. Park, "Stochastic stabilization of TS fuzzy system with Markovian input delay," Journal of Korean Institute of Intelligent Systems, vol. 11, no. 6, pp. 459-464, Dec. 2001.
  16. Y. Feng, C. A. Rabbath, and C. Y. Su, "Inverse Duhem model based robust adaptive control for flap positioning system with SMA actuators," in Proceedings of the 18th IFAC World Congress, Milano, Italy, August 28-September 2, 2011, pp. 8126-8131. http://dx.doi.org/10.3182/20110828-6-IT-1002.01744

Cited by

  1. Inverse Hysteresis Modeling for Piezoelectric Stack Actuators with Inverse Generalized Prandtl-Ishlinskii Model vol.24, pp.2, 2014, https://doi.org/10.5391/JKIIS.2014.24.2.193
  2. Comprehensive analysis of magnetization, magnetostriction, hysteresis and kinematical characteristics for precision magnetostrictive actuator vol.17, pp.12, 2016, https://doi.org/10.1007/s12541-016-0186-6