Preisach Model

Among hysterons, the most important are probably the nonideal relay nonlinearities, or, as they are also called, the thermostat nonlinearities. The simplest block-diagrams are essentially those of standard parallel connections of a number of hysterons, or their continuous analogue. This leads to the so called Preisach nonlinearity, which will be discussed in this chapter.

A Preisach model was first suggested almost two thirds of a century years ago [19] to describe ferromagnetism. It is the continuous analog of a finite parallel connection of relays.

The Preisach model appears to be extremely successful, and is now recognized as a fundamental toolkit in describing a wide range of hysteresis phenomena in quite different subject areas (physics, mechanics, superconductivity, tectonics, economics, etc.) The interested reader might like to consult the recent special issue of Physica B [16], and the bibliography therein. The modern explanation of the pivotal role of Preisach nonlinearity is based on an operational, phenomenological approach and on special identification theorems

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