Using Padé Approximation in Takács Hysteresis Model

Abstract

The application of the modified Takacs hysteresis model for numerical modeling of measured hysteresis loops of ferromagnetic material is investigated. In order to better approximate measured hysteresis loops, the Takacs model is modified using parameterized Pade approximations of the hyperbolic tangent function. That way, several variants of the modified model are constructed. The experimental data are fitted with the original model, as well as with the modified model, and the quality of conformance between empirical data and the models is assessed. Three numerical criteria are used for comparison: 1) the coefficient of determination; 2) percent error of the residual vector; and 3) percent errors at the five characteristic points on the hysteresis loop. The proposed method shows improvement in cases when hysteresis loops are not reaching saturation, while maintaining accuracy in the saturation. The performance of the modified model is verified by theoretical data.