Zhao Jiye, Zhou Jiqiang, Zhang Lu, Sun Jinji
School of Instrumentation Science and Optoelectronics Engineering, Beihang University, Beijing 100191, China.
Hangzhou Institute of National Extremely-Weak Magnetic Field Infrastructure, Hangzhou 310028, China.
Materials (Basel). 2024 Jul 26;17(15):3695. doi: 10.3390/ma17153695.
Hysteresis is a fundamental characteristic of magnetic materials. The Jiles-Atherton (J-A) hysteresis model, which is known for its few parameters and clear physical interpretations, has been widely employed in simulating hysteresis characteristics. To better analyze and compute hysteresis behavior, this study established a state space representation based on the primitive J-A model. First, based on the five fundamental equations of the J-A model, a state space representation was established through variable substitution and simplification. Furthermore, to address the singularity problem at zero crossings, local linearization was obtained through an approximation method based on the actual physical properties. Based on these, the state space model was implemented using the S-function. To validate the effectiveness of the state space model, the hysteresis loops were obtained through COMSOL finite element software and tested on a permalloy toroidal sample. The particle swarm optimization (PSO) method was used for parameter identification of the state space model, and the identification results show excellent agreement with the simulation and test results. Finally, a closed-loop control system was constructed based on the state space model, and trajectory tracking experiments were conducted. The results verify the feasibility of the state space representation of the J-A model, which holds significant practical implications in the development of magnetically shielded rooms, the suppression of magnetic interference in cold atom clocks, and various other applications.
磁滞是磁性材料的一个基本特性。吉尔斯 - 阿特金森（J - A）磁滞模型以其参数少和物理意义明确而闻名，已被广泛用于模拟磁滞特性。为了更好地分析和计算磁滞行为，本研究基于原始的J - A模型建立了一种状态空间表示。首先，基于J - A模型的五个基本方程，通过变量替换和简化建立了状态空间表示。此外，为了解决过零点处的奇异性问题，通过基于实际物理特性的近似方法获得了局部线性化。在此基础上，使用S函数实现了状态空间模型。为了验证状态空间模型的有效性，通过COMSOL有限元软件获得磁滞回线，并在坡莫合金环形样品上进行测试。采用粒子群优化（PSO）方法对状态空间模型进行参数辨识，辨识结果与仿真和测试结果吻合良好。最后，基于状态空间模型构建了闭环控制系统，并进行了轨迹跟踪实验。结果验证了J - A模型状态空间表示的可行性，这在磁屏蔽室的开发、冷原子钟的磁干扰抑制以及其他各种应用中具有重要的实际意义。
