JACIII Vol.20 No.2 pp. 223-230
doi: 10.20965/jaciii.2016.p0223


Asymmetric Prandtl-Ishlinskii Hysteresis Model for Giant Magnetostrictive Actuator

Zhuoyun Nie*, Chanjun Fu*, Ruijuan Liu**, Dongsheng Guo*, and Yijing Ma*

*School of Information Science and Engineering, National Huaqiao University
Xiamen 361021, China
**School of Applied Mathematics, Xiamen University of Technology
Xiamen 361024, China

November 10, 2015
December 10, 2015
Online released:
March 18, 2016
March 20, 2016
asymmetric play operator, asymmetric Prandtl–Ishlinskii model, giant magnetostrictive actuator

An asymmetric Prandtl–Ishlinskii (API) hysteresis model for a giant magnetostrictive actuator (GMA) is proposed in this paper. The classical Prandtl–Ishlinskii (PI) model is analyzed and divided into two parts: linear function and operator summation. To enhance model asymmetry, a polynomial function is used in the API model as the center curve of the hysteresis instead of the linear function. The remaining curve of the hysteresis is modeled by a new operator that provides some basic asymmetric hysteresis. In this manner, the proposed API model requires relatively less operators and fewer parameters to describe the asymmetric hysteresis behavior of the GMA. All parameters of the API model are identified by a standard least square method. Simulation results show that the API model is very successful in formulating an asymmetric hysteresis of the GMA. In addition, it provides better identification results compared with the classical PI model.

  1. [1]  G. Xue, Z. He, D. Li, Z. Yang, and Z. Zhao, “Analysis of the giant magnetostrictive actuator with strong bias magnetic field,” J. of Magnetism & Magnetic Materials, Vol.394, pp. 416-421, 2015.
  2. [2]  A. G. Jennera, R. J. E. Smitha, A. J. Wilkinsonb, and R. D. Greenougha, “Actuation and transduction by giant magnetostrictive alloys,” Mechatronics, Vol.10, No.4–5, pp. 457-466, 2000.
  3. [3]  X. B. Tan and J. S. Baras, “Modeling and control of hysteresis in magnetostrictive actuators,” Automatica, Vol.40, No.8, pp. 1469-1480, 2004.
  4. [4]  D. Jiles and D. Atherton, “Theory of ferromagnetic hysteresis,” J. of Magnetism and Magnetic Materials, Vol.61, No.1–2, pp. 48-60, 1986.
  5. [5]  F. T. Calklns, R. C. Smlth, A. B. Flatau, Y. J. Liu, D. Q. Wang, and F. Ding, “Energy-Based hysteresis model for magnetostrictive transducers,” IEEE. Trans. Magn, Vol.36, No.1, pp. 429-439, 2000.
  6. [6]  J. B. Restorff, H. T. Savage, and A. E. Clark, “Preisach modeling of hysteresis in Terfenol,” J. of Applied Physics, Vol.67, No.8, pp. 5016-5018, 1990.
  7. [7]  R. Iyer and X. B. Tan, “Control of hysteretic systems through inverse compensation,” IEEE Control Syst. Mag., Vol.29, No.1, pp. 83-99, 2009.
  8. [8]  R. Dong and Y. Tan, “A modified Prandtl-Ishlinskii modeling method for hysteresis,” Phys. B, Vol.404, No.8-11, pp. 1336-1342, 2009.
  9. [9]  K. Kuhnen, “Modeling,identification and compensation of complex hysteretic nonlinearities: A modified Prandtl-Ishlinskii approach,” European J. of Control, Vol.8, pp. 407-418, 2003.
  10. [10]  M. A. Janaideh, S. Rakheja, and C. Y. Su, “A generalized Prandtl-Ishlinskii model for characterizing the hysteresis and saturation nonlinearities of smart actuators,” J. of Smart Materials and Structures, Vol.18, No.4, pp. 1-9, 2009.
  11. [11]  Z. Zhang, Q. W. Chen, and J. Q. Mao, “Generalized Prandtl-Ishlinskii model for Rate-dependent hysteresis:modeling and its inverse compensation for giant magnetostrictive actuator,” Proc. of the 31st Chineae Control Conf., 2012.
  12. [12]  G. Y. Gu, L. M. Zhu, and C. Y. Su, “Modeling and compensation of asymmetric hysteresis nonlinearity for Piezoceramic Actuators with a modified Prandtl-Ishlinskii model,” IEEE Trans. on Industrial Electronics, Vol.61, No.3, 2014.
  13. [13]  H. Jiang, H. Ji, J. Qiu, and Y. Chen, “A modified Prandtl-Ishlinskii model for modeling asymmetric hysteresis of piezoelectric actuators,” IEEE Trans. Ultrason., Ferroelectr., Freq. Control, Vol.57, No.5, pp. 1200-1210, 2010.
  14. [14]  Y. X. Guo, J. Q. Mao, and K. M. Zhou, “Modeling and control of giant magnetostrictive actuator based on Bouc-Wen model,” Proc. of 2011 8th Asian Control Conf., 2011.
  15. [15]  X. S. Wang, X. J. Wang, and Y. Mao, “Hysteresis Compensation in GMA actuators using Duhem model,” Proc. of the 7th World Congress on Intelligent Control and Automation, 2008.
  16. [16]  P. Krejci and K. Kuhnen, “Inversecontrol of systems with hysteresis and creep,” Proc. Inst. Elect. Eng. Control Theory Appl., Vol.148, pp. 185-192, 2001.
  17. [17]  Z. Li, Y. Feng, T. Y. Chai, and C. Y. Su, “Modeling and compensation of asymmetric hysteresis nonlinearity for magnetostrictive actuators with an asymmetric shifted Prandtl-Ishlinskii model,” American Control Conf. (ACC), pp. 1658-1663, 2012.
  18. [18]  Y. J. Liu, D. Q. Wang, and F. Ding, “Least-squares based iterative algorithms for identifying Box-Jenkins models with finite measurement data,” Digital Signal Processing, Vol.20, No.4, pp. 1458-1467, 2010.

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Last updated on Mar. 28, 2017