Wavelet implementation of Preisach model of hysteresis

Abstract

Preisach model has enjoyed extensive applications in describing the hysteresis phenomena. However an important open question in the analysis of hysteresis using Preisach models is the determination of the model parameters. This is to determine the parameter of Preisach function and is referred as the identification problem. However, no general mathematical methods appear to be available for the identification of nonlinear hysteresis system. As a result customized identification algorithms must be developed for each specific area of applications. In order to more closely describe physical systems, it becomes increasingly difficult to compute the Preisach function and its associated parameters from experimental results as the complexity of hysteresis models increases. This paper presents a new approach -- a Wavelet identification of Preisach model. A wavelet can generate a special basis for all functions with finite energy and has some important properties such as orthogonality, symmetry, short support and accuracy. In this application the output of system and the Preisach functions are represented by a series of wavelets. The experiment data is used to determine the coefficients of the base functions. Then the Preisach function and the output of the hysteresis system can be directly calculated by using wavelet methods.