A Dynamic Model for Magnetostrictive Hysteresis

The rate-dependent hysteresis present in thin magnetostrictive actuators can be captured by a dynamic model, consisting of a Preisach operator coupled to an ordinary differential equation in an unusual way. The model presents interesting problems in analysis and computation due to its special structure. In this paper, we first transform the model into a more amenable form and gain insight into the model by introducing a new hysteretic operator. Then we investigate some system-theoretic properties of the model: stability of equilibria, input-output stability, reachability and observability. Existence of periodic solutions under periodic forcing is also established. Finally, numerical integration schemes for the model are discussed.