Stability analysis in systems with Preisach hysteresis
by
Séamus P. Ó Ceallaigh
Department of Applied Mathematics, University College Cork, Ireland
Coauthors: Dmitrii Rachinskii

We consider differential equations that contain the time derivative of the Preisach operator P. Such equations appear, for example, in terrestrial hydrology and model the water flow through unsaturated soil exhibiting soil-moisture hysteresis. In particular, scalar models where P describes the hysteresis relation between the matric potential and the water content.

Equations of the similar structure model systems with ferromagnetic hysteresis elements. One example is power-electronic circuits where hysteresis in the ferromagnetic core of transformer coils can essentially affect dynamics. For such systems, coupling of the rate equations of an electrical circuit with the Preisach nonlinearity, which models the relation between the magnetic field H and magnetic induction B in the ferromagnetic core, can be used to improve the agreement of model predictions with experimental data. The resulting models contain the time derivative of the Preisach nonlinearity, which can be seen from Maxwell's equations.

We are interested in an algorithm of local linear stability analysis for periodic solutions.

Date received: June 29, 2007

Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavj-39.