Preisach model

The Preisach model is a mathematical model for describing hysteresis curves . It was first published in 1935 by the Hungarian physicist Ferenc Preisach under the title About the magnetic aftermath in the Zeitschrift für Physik . It was initially developed to describe the hysteresis properties of ferromagnetic materials, but it is now also used in other physical areas.

General

Put simply, the Preisach model consists of a collection of many simple rectangular hysteresis curves with the hysteresis operator . ${\displaystyle R_{\alpha ,\beta }}$

The output of these hysteresis functions is as follows:

${\displaystyle y(x)={\begin{cases}1&{\mbox{ wenn }}x\geq \beta \\0&{\mbox{ wenn }}x\leq \alpha \\k&{\mbox{ wenn }}\alpha <x<\beta \end{cases}}}$

This is the so-called memory function, which contains the previous value of the output function . ${\displaystyle k}$ ${\displaystyle y(t)}$

If you now integrate a large number of such rectangular hysteresis curves and weight them with a distribution factor, the Preisach model is obtained in continuous form:

${\displaystyle y(t)=\Gamma \cdot x(t)=\iint _{\beta \geq \alpha }\mu (\alpha ,\beta )\mathbb {R} _{\alpha ,\beta }x(t){\mbox{d}}\alpha {\mbox{d}}\beta }$

where represent the input variable and the output variable. is the weighting function (also called the price function or distribution function) and the hysteresis operator. ${\displaystyle x(t)}$ ${\displaystyle y(t)}$ ${\displaystyle \mu (\alpha ,\beta )}$ ${\displaystyle R_{\alpha ,\beta }}$

literature

• I. Mayergoyz: Mathematical Models of Hysteresis and their Applications . 2nd Edition. Elsevier, 2003, ISBN 978-0-12-480873-7 .
• Ferenc Vajda, Edward Della Torre: Ferenc Preisach, In Memoriam . In: IEEE Transactions on Magnetics . March 1995, doi : 10.1109 / TMAG.1995.6570665 (English, researchgate.net [PDF]).

Web links

• Price according to model. ( Memento from September 22, 2013 in the Internet Archive ) In: Hysteresis Tutorial . University College, Cork (English)

Individual evidence

1. ↑ F. Preisach: About the magnetic aftermath . In: Journal of Physics . tape 94 , 1935, pp. 277-302 , doi : 10.1007 / BF01349418 ( springer.com [PDF]).