Realization of Preisach model using adaptive polynomial approximation method

Modeling of systems with hysteresis has received considerable attention recently due to the increasing accuracy requirement in engineering applications. The classical Preisach model (CPM) is the most popular model to characterize hysteresis which can be represented by infinite but countable first order reversal curves (FORC). In practice, one approach to realize the CPM uses data tables; the data of which correspond with the samples of a finite number of FORC. This approach, however, suffers from two drawbacks: it requires a large amount of memory in order to obtain an accurate prediction of hysteresis and it is difficult to derive efficient ways to modify the data table in order to reflect the aging or timing effect of elements with hysteresis. To overcome these drawbacks, this paper proposes to use a set of polynomials instead of data tables for realization of the CPM. The proposed approach reduces the required memory because it only requires to store a small number of polynomial coefficients. Furthermore, the polynomial coefficients can be obtained using the least-square approximation or the adaptive identification algorithm such that the tracking of hysteresis model parameters is possible. The proposed approach has been verified by the computer simulations; the resulting realization compared with the table method yields close effect in model accuracy and has tracking ability for a changed CPM.