Electromagnetic-suspension (EMS)-type maglev, based on long stator linear synchronous motor (LSLSM), suffers from the flux linkage and thrust ripple. This is due to the non-sinusoidal airgap magnetic field distribution caused by the slot effect and end effect. In this article, it is intended to address this issue by establishing a nonlinear mathematical model of LSLSM for real-time simulation and controller design, considering the spatial harmonics and core saturation. The Euler–Lagrange (EL) model is improved by means of coenergy and then applied to obtain the general equations of LSLSM. At first, the variation in coenergy in LSLSM regarding the mover position and stator current are analyzed, in the presence of spatial harmonics and core saturation. Afterward, an analytical model of coenergy is constructed by two Fourier basis vectors of mover position and torque angle, and a coefficient matrix polynomial of stator current magnitude. Then, a new model of LSLSM is derived based on the coenergy model and EL method. The parameters of the model can be obtained from the numerical data of coenergy in all operation ranges via finite-element analysis (FEA). Finally, the new model of LSLSM and its propulsion system are integrated in MATLAB/Simulink setup. The simulation results show that the improved EL model can achieve satisfactory accuracy compared with the FEA results well, whereas the computational efficiency is improved largely.

中文翻译：

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解析磁余能重构法改进长定子直线同步电机EL模型

电磁悬浮（EMS）型磁悬浮基于长定子直线同步电机（LSLSM），存在磁链和推力纹波。这是由于槽效应和端部效应引起的非正弦气隙磁场分布。在本文中，旨在通过建立用于实时仿真和控制器设计的 LSLSM 非线性数学模型来解决这个问题，同时考虑空间谐波和磁芯饱和。欧拉-拉格朗日 (EL) 模型通过协能改进，然后应用到 LSLSM 的一般方程。首先，在存在空间谐波和磁芯饱和的情况下，分析了 LSLSM 中关于动子位置和定子电流的协能变化。之后，由动子位置和转矩角的两个傅立叶基向量和定子电流幅值的系数矩阵多项式构建了协能解析模型。然后，基于余能模型和EL方法推导出LSLSM的新模型。该模型的参数可以通过有限元分析（FEA）从所有运行范围内的协能数值数据中获得。最后，将新的 LSLSM 模型及其推进系统集成到 MATLAB/Simulink 设置中。仿真结果表明，与有限元分析结果相比，改进后的EL模型可以达到令人满意的精度，同时大大提高了计算效率。该模型的参数可以通过有限元分析（FEA）从所有运行范围内的协能数值数据中获得。最后，将新模型的 LSLSM 及其推进系统集成到 MATLAB/Simulink 设置中。仿真结果表明，与有限元分析结果相比，改进后的EL模型可以达到令人满意的精度，同时大大提高了计算效率。该模型的参数可以通过有限元分析（FEA）从所有运行范围内的协能数值数据中获得。最后，将新模型的 LSLSM 及其推进系统集成到 MATLAB/Simulink 设置中。仿真结果表明，与有限元分析结果相比，改进后的EL模型可以达到令人满意的精度，同时大大提高了计算效率。