New realisation of Preisach model using adaptive polynomial approximation

Abstract

Modelling system with hysteresis has received considerable attention recently due to the increasing accurate requirement in engineering applications. The classical Preisach model (CPM) is the most popular model to demonstrate hysteresis which can be represented by infinite but countable first-order reversal curves (FORCs). The usage of look-up tables is one way to approach the CPM in actual practice. The data in those tables correspond with the samples of a finite number of FORCs. This approach, however, faces two major problems: firstly, it requires a large amount of memory space to obtain an accurate prediction of hysteresis; secondly, it is difficult to derive efficient ways to modify the data table to reflect the timing effect of elements with hysteresis. To overcome, this article proposes the idea of using a set of polynomials to emulate the CPM instead of table look-up. The polynomial approximation requires less memory space for data storage. Furthermore, the polynomial coefficients can be obtained accurately by using the least-square approximation or adaptive identification algorithm, such as the possibility of accurate tracking of hysteresis model parameters.

Keywords:

• hysteresis
• Preisach model
• polynomial approximation

Acknowledgements

This article is in memory of Dr Mu-Huo Cheng who was a professor in the Department of Electrical and Control Engineering, National Chiao Tung University, Hsinchu, Taiwan, ROC. This research was sponsored by National Science Council of Taiwan under the Grant NSC96-2221-E-150-016.