Stability Control of Electrodynamic Suspension with Permanent Magnet and Electromagnet Hybrid Halbach Array
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摘要:
为了研究不同控制方法下永磁电磁混合Halbach阵列的电动悬浮稳定性，首先，利用电磁场理论对系统悬浮力2D解析式进行了推导，并搭建有限元模型对其进行了验证；其次，建立了系统垂向动力学模型，设计了基于气隙反馈的定气隙PID控制器和变气隙PID控制器；最后，仿真分析了系统受到外界扰动时的悬浮气隙及线圈电流波形. 研究结果表明：当系统受到1 mm轨道沉降扰动时，两种控制器均能使系统稳定运行于额定状态，且动态过程一致；当系统受到 ±1000 N扰动力作用时，定气隙PID控制器可使系统稳定悬浮于额定气隙30 mm位置，且稳态线圈电流分别为2.12 A/mm2和 −2.17 A/mm2，变气隙PID控制器则使系统分别稳定悬浮于28.5 mm及31.6 mm位置，且稳态线圈电流均为0.
Abstract:In order to study the suspension stability of the electrodynamic suspension (EDS) with permanent magnet (PM) and electromagnet hybrid halbach array under different control methods, Firstly, the 2D levitation force analytical expression was derived by using the electromagnetic field theory and the corresponding finite element model (FEM) was built to verify the suspension force analytical expression. Secondly, the vertical dynamic model of the system was established, and the fixed air gap PID controller and variable air gap PID controller based on the air gap feedback were designed respectively. Finally, the system suspension air gap and current density waveforms under external disturbances were simulated and analyzed. The simulation results indicate that both controllers can make the system suspend stably at the rated state and have the same dynamic process under the 1 mm track settlement disturbance. When the system is disturbed by the ± 1000 N disturbing force, the fixed air gap PID controller can make the system suspend stably at the 30 mm rated air gap, and apply the steady state coil current of 2.12 A/mm2 and −2.17 A/mm2 respectively. The variable air gap PID controller makes the system suspend stably at 28.5 mm and 31.6 mm respectively, and applies the steady-state coil current of 0.
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图 1 永磁电磁混合Halbach阵列电动悬浮示意
Figure 1. Diagram of PM and electromagnet hybrid Halbach array EDS system
图 7 悬浮气隙及线圈电流密度(变气隙)
Figure 7. Suspension air gap and coil current density (variable air gap )
表 1 模型参数
Table 1. Model parameters
参数 数值 参数 数值 永磁体剩磁 Br/T 1.25 线圈宽度/mm 10 永磁体横向宽度/mm 200 线圈电流体密度 J/
（ A•mm−2)）6 永磁体长度/mm 80 导体板横向宽度/mm 200 永磁体高度/mm 100 导体板长度/mm 1600 一对极模块数 m 4 导体板厚度 d/mm 20 阵列总长度/mm 800 导体板电导率/
（S•m−1）3.8 × 107 阵列模块数 N 8 气隙 g/mm 30 
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