Stop Model With Input-Dependent Shape Function and Its Identification Methods

Abstract

Abstract-We propose an input-dependent shape function for the stop model to remove its property of equal vertical chords regardless of dc bias. We compare several identification methods for the stop model and show that the input-dependent shape function improves the ability to represent the stop model effectively. A least-squares identification method using both symmetric and asymmetric -loops achieves the most precise representation of hysteretic characteristics for a silicon steel sheet. However, if only symmetric loops are available for identification, a newly proposed identification method gives more accurate representation than other methods including the least-squares method.

Representation of minor hysteresis loops of a silicon steel sheet using stop and play models

“…A discretized form of the stop model with an inputdependent shape function [7] describes the hysteretic relationship between the magnetic flux density B and the magnetic field H as follows: In these equations, s Z is the stop hysteron operator with height Z, N s is the number of stop hysterons, Z n ¼ nB S =N s , g n is the input-dependent shape function for s Zn , B S is the saturation magnetic flux density, and B 0 and s 0 Z are the values of B and s Z , respectively, at the previous time-point.…”

“…[7,8] for stop and play models, respectively, where w(B) is called the weighting function. A simple weighting function…”

“…[7], where H þ M ðBÞ and H À M ðBÞ are the ascending and descending curves, respectively, of the measured major loop. Weighting function (7) improves the representation capability of stop and play models [7,8].…”

“…[7]. Introducing a product form of an input-dependent shape function, this identification method efficiently yields the shape function for the stop model.…”

Mathematical Models of Hysteresis

“…1.7.1 of this book. The models introduced in [13][14][15] are based on the superposition of stop or play operators. The ''limiting loop proximity'' hysteresis model introduced in [16] presents an algebraic model based on the relative position of the current hysteretic state with respect to the major hysteresis loop.…”