Semilinear Duhem model for rate-independent and rate-dependent hysteresis

• Published in: IEEE transactions on automatic control Vol. 50; no. 5; pp. 631 - 645
• Main Authors: JinHyoung Oh, Bernstein, D.S.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.2005; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Aerodynamics; Applied sciences; Computer science; control theory; systems; Control theory. Systems; Duhem; Exact sciences and technology; Frequency; hysteresis; Linear systems; Magnetic fields; Magnetic flux density; Magnetic hysteresis; Magnetic materials; Nonlinear dynamical systems; rate dependence; Springs; Terminology; Rate function; Duhem; Low frequency; Modeling; Hysteresis; rate dependence; Input output model
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2005.847035

The classical Duhem model provides a finite-dimensional differential model of hysteresis. In this paper, we consider rate-independent and rate-dependent semilinear Duhem models with provable properties. The vector field is given by the product of a function of the input rate and linear dynamics. If the input rate function is positively homogeneous, then the resulting input-output map of the model is rate independent, yielding persistent nontrivial input-output closed curve (that is, hysteresis) at arbitrarily low input frequency. If the input rate function is not positively homogeneous, the input-output map is rate dependent and can be approximated by a rate-independent model for low frequency inputs. Sufficient conditions for convergence to a limiting input-output map are developed for rate-independent and rate-dependent models. Finally, the reversal behavior and orientation of the rate-independent model are discussed.