At the very heart of the successful phenomenological model of magnetic hysteresis there is the so called Preisach distribution. In the existing literature it is implicitly assumed, that this distribution has a mirror symmetry. We show, by simple and convincing example, that this common assumption is plainly wrong. Dropping it, we gain the ability to model not only the usual hysteresis loops (ma...

Brokate and Sprekels introduced the notion of hysteresis operators of the Preisach type (HOPTs), that are more general than (and include as a subset) the classical Preisach operator. In this paper, we provide a mathematical framework to the important representation problem for HOPTs by presenting two results on the approximation of the output function on the set of memory curves. One of the res...

The motivation for this research arises from recent interest in actuators made from \smart mate-rials" such as shape memory alloys and piezoceram-ics. One common characteristic among these new materials is that they exhibit complex hysteresis non-linearities. The input-output nature of the Preisach model of hysteresis results in a simple model for which identiication strategies are known, and i...

Ionic polymer-metal composites (IPMCs) generate large bending motions under a low driving voltage (about 1 V). In this paper quasi-static actuation of IPMC is investigated with the goal of precise positioning. It is found that IPMC exhibits hysteresis between its bending curvature and the applied quasi-static voltage. The Preisach operator is proposed to model the hysteresis, and its density fu...

[cu+ P[u]]t − div(a·∇u) = f, with Preisach hysteresis P . The functions c, a, and the density function ψ of the Preisach operator are allowed to depend also on the space variable x. The equation is homogenized by considering a sequence of equations with spatially periodic data c , a , andψ , where the spatial period converges to 0. Properties of hysteresis operators and the concept of two-scale...

In this paper we give a formal deenition of dissipative systems that is considerably more general than earlier deenitions. The measured output is irrelevant in this formulation. The key component of dissipation is an appropriate work rate. We also deene cyclo-dissipation and show how it can be used to obtain a suitable work rate. Using this idea, we propose a new work rate for the Preisach hyst...

Preisach model has been used extensively since the model has been initially developed by Ferenc Preisach about 75 years ago, especially for ferromagnetic materials. When the model has been analyzed from a mathematical point of view by Krasnoselskii and Pokrovskii and after them by Mayergoys and other scientists it was stated that, in fact, the model is “the best hysteresis model at our disposal...

A novel dynamic model is proposed for the hysteresis in magnetostrictive actuators by coupling a Preisach operator to an ordinary di0erential equation, and a parameter identi2cation method is described. An e3cient inversion algorithm for a class of Preisach operators with piecewise uniform density functions is then introduced, based upon which an inverse control scheme for the dynamic hysteresi...

We consider a di erential equation describing the mass balance in a soil hydrology model with noninvertible Preisach-type hysteresis. We approximate the singular Preisach operator by regular ones and show, as main result, that the solutions of the regularized problem converge to a solution of the original one as the regularization parameter tends to zero. For monotone right hand sides, we prove...