In this article we discuss applications of the numerical integration methods to the ordinary differential equations with the Preisach nonlinearity. We use a canonical model of the iron pendulum in the magnetic field as an example of the technique. In particular we use guaranteed estimates of the integration error to rigorously prove the chaotic behaviour of the system considered. MSC 2000: Prim...

A general formulation of scalar hysteresis is proposed. This formulation is based on two steps. First, a generating function g(x) is associated with an individual system, and a hysteresis evolution operator is defined by an appropriate envelope construction applied to g(x), inspired by the overdamped dynamics of systems evolving in multistable free-energy landscapes. Second, the average hystere...

Introduction The models of magnetic devices having a magnetic core without known parameters require the core evaluation by means of sophisticated measurement procedures and systems. For certain models, higher measurement accuracy is of key importance. For the other models, additional factors (speed, cost, measurement instruments and apparatus) may strongly limit achievement of the specific meas...

This paper describes a method for the design of compensators able to reduce hysteresis in transducers, as well as two measures to quantify and compare controller performance. Rate independent hysteresis, as represented by the Preisach model of hysteresis, is seen as an input–output phase lag. The compensation is based on controllers derived from the “phaser,” a unitary gain operator that shifts...