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

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.

Parameter Identification of Model for Piezoelectric Actuators

“…However, piezoelectric ceramic materials have hysteretic nonlinear characteristics of multi-valued mapping and frequency dependence [ 11 ]. The hysteretic nonlinearity prevents PEAs’ positioning precision from being further improved and impairs the stability of the closed-loop system [ 12 ].…”

“…The Bouc–Wen model, based on differential equations, has the advantages of fewer unknown parameters and high modeling accuracy, and it is currently widely used in the modeling and compensation of the multi-valued mapping characteristics of PEAs [ 20 , 21 , 22 , 23 ]. Reference [ 12 ] proposes an improved Bouc–Wen model that introduces the input voltage frequency, in which a more accurate description of the frequency-dependent hysteresis features is provided. Reference [ 24 ] proposes a generalized Bouc–Wen model, with a relaxation function for the static part of the Hammerstein model, which is used to describe the multi-valued mapping hysteresis characteristics of PEAs.…”