Modeling Rate-Dependent Hysteresis for Magnetostrictive Actuator


Article Preview

The rate-dependent hysteresis exhibited by magnetostrictive actuator (MA) presents a challenge in modeling of these actuators. In this paper, a novel rate-dependent hysteresis model was proposed for magnetostrictive actuator. In the model, the modified Prandtl-Ishlinskii operator (PI) is combined with a second order ordinary differential equation in a cascaded structure. The modified PI operator is used to account for the static hysteresis, the connection between ODE and the rate-dependent energy loss was established, including the classical eddy current loss and the mechanical dynamics. Simulation results show a good agreement with the experiment ones.



Materials Science Forum (Volumes 546-549)

Edited by:

Yafang Han et al.




Z. Zhen and J. Q. Mao, "Modeling Rate-Dependent Hysteresis for Magnetostrictive Actuator", Materials Science Forum, Vols. 546-549, pp. 2251-2256, 2007

Online since:

May 2007




[1] Xiao Tan and John S Baras: Modeling and control of a magnetostrictive actuator, Proceedings of the 41st IEEE Conference on Decision and Control Las Vegas, Nevada USA, December 2002, pp.866-872.


[2] G. Bertotti: General properties of power losses in soft ferromagnetic materials, IEEE TRANSACTIONS ON MAGNETICS, VOL. 24, NO. I, JANUARY 1988, pp.621-630.


[3] D. C. Jiles: Frequency dependence of hysteresis curves in conducting magnetic materials, J. Appl. Phys. 76(10), 15 November 1994, pp.5849-5855.


[4] K. Kuhnen: Modeling, Identification and Compensation of complex hysteretic Nonlinearities - A modified Prandtl-Ishlinskii approach, European Journal of Control, Vol. 9, Nr. 4, 2003, S. 407-418.


[5] J. C. Slaughter et al Modeling of a Terfenol-D ultrasonic transducer, Proceedings of SPIE Vol. 3985 (2000), pp.366-377.

[6] M. J. Dapino, F. T. Calkins and A. B. Flatau: On identification and analysis of fundamental issues in Terfenol-D transducer modeling, Proceedings of SPIE Vol. 3329 (1998), pp.185-197.


[7] R. Venkataraman, in: Modeling and adaptive control of magnetostrictive actuators, PhD Dissertation (1998).

[8] D. C. Jiles and D. L. Atherton Theory of ferromagnetic hysteresis, Journal of Magnetism and Magnetic Materials, vol. 61, pp.48-60, (1986).

[9] I. D. Mayergoyz, in: Mathematical Models of Hysteresis, Springer Verlag, New York, (1991).

[10] M. A. Krasnosel'skii and A. V. Pokrovskii, Systems with Hysteresis, Springer Verlag, (1989).

[11] Ray W. Clough, Joseph Penzien, in: Dynamics of structures New York McGraw-Hill, (1993).

[12] Wei Tech Ang, Francisco Alija Garmbn, Pradeep K. Khosla, and Cameron N. Riviere, Modeling Rate-dependent Hysteresis in Piezoelectric Actuators", Proceedings of the 2003 IEEE/RSJ. Conference on Intelligent Robots and Systems Las Vegas, Nevada , October (2003).