This work presents a simple and robust method to construct a B-spline based Everett map, for application in the Preisach model of hysteresis, to predict static hysteresis behavior. Its strength comes from the ability to directly capture the Everett map as a well-founded closed-form B-spline surface expression, while also eliminating model artifacts that plague Everett map based Preisach models. Contrary to other works, that applied numerical descriptions for the Everett map, the presented approach is of completely analytic nature. In this work the B-spline surface fitting procedure and the necessary set of constraints are explained. Furthermore, the B-spline based Everett map is validated by ensuring that model artifacts were properly eliminated. Additionally, the model was compared with four benchmark excitations. Namely, a degaussing signal, a set of first-order reversal curves, an arbitrary excitation with high-order reversal curves, and a PWM like signal. The model was able to reproduce all benchmarks with high accuracy.

翻译：本文提出了一种简单而稳健的方法来构建基于B样条的Everett映射，并将其应用于迟滞的Preisach模型中，以预测静态迟滞行为。该方法的优势在于能够直接将Everett映射捕获为具有良好数学基础的闭式B样条曲面表达式，同时消除了困扰基于Everett映射的Preisach模型的伪影。与以往采用数值化描述Everett映射的研究不同，本方法具有完全解析的特性。本文详细阐述了B样条曲面拟合过程及必要的约束条件集。此外，通过确保模型伪影被有效消除，验证了基于B样条的Everett映射的正确性。模型还通过四类基准激励信号进行了对比验证，包括：退磁信号、一组一阶反转曲线、包含高阶反转曲线的任意激励信号以及类脉宽调制信号。模型在所有基准测试中均能实现高精度复现。