Numerical Solving Method for Jiles-Atherton Model and Influence Analysis of the Initial Magnetic Field on Hysteresis

Guangming Xue (), Hongbai Bai, Tuo Li, Zhiying Ren, Xingxing Liu and Chunhong Lu
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Guangming Xue: School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou 350116, China
Hongbai Bai: School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou 350116, China
Tuo Li: Department of Unit Command, Officers College of PAP, Chengdu 610200, China
Zhiying Ren: School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou 350116, China
Xingxing Liu: School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou 350116, China
Chunhong Lu: Department of Automotive Engineering, Hebei College of Industry and Technology, Shijiazhuang 050091, China

Mathematics, 2022, vol. 10, issue 23, 1-16

Abstract: The Jiles-Atherton model was widely used in the description of the system with hysteresis, and the solution for the model was important for real-time and high-precision control. The secant method was used for solving anhysteretic magnetization and its initial values were optimized for faster convergence. Then, the Fourth Order Runge-Kutta method was employed to solve magnetization and the required computation cycles were supplied for stable results. Based on the solving method, the effect of the nonzero initial magnetic field on the magnetization was discussed, including the commonly used linear model of the square of magnetization under the medium initial value. From computations, the proposed secant iteration method, with supplied optimal initial values, greatly reduced the iterative steps compared to the fixed-point iteration. Combined with the Fourth Order Runge-Kutta method under more than three cycles of calculations, stable hysteresis results with controllable precisions were acquired. Adjusting the initial magnetic field changed the result of the magnetization, which was helpless to promote the amplitude or improve the symmetry of magnetization. Furthermore, the linear model of the square of magnetization was unacceptable for huge computational errors. The proposed numerical solving method can supply fast and high-precision solutions for the Jiles-Atherton model and provide a basis for the application scope of typical linear assumption.

Keywords: Jiles-Atherton model; numerical solving method; secant method; Runge-Kutta method; initial magnetic field; square of magnetization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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