Acceleration Feedback Control of Bilateral Permanent Magnet and Electromagnetic Hybrid Electrodynamic Suspension
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摘要:
为提升永磁电动悬浮动态稳定性及减小低速运行时的阻力，提出一种双边永磁电磁混合型电动悬浮系统. 首先，基于麦克斯韦方程组推导系统电磁力2D解析式，对解析结果进行有限元数值计算验证，并对比单、双边结构电磁力特性；然后，建立系统悬浮动力学模型，并设计加速度反馈悬浮控制器；最后，利用Simulink仿真，对比分析在加速度反馈悬浮控制和气隙反馈PID控制下，系统受到轨道及载荷扰动时的气隙、加速度及电流波形. 研究结果表明：双边结构可有效增加系统浮阻比，100 km/h运行时单、双边结构浮阻比分别为3.18和15.43；当系统受到±1 mm轨道扰动时，控制器能使系统振动加速度及悬浮气隙分别快速稳定于0和20 mm额定位置；当系统受到±
2000 N载荷扰动时，加速度反馈悬浮控制器可使系统悬浮气隙分别快速稳定于19.05 mm和20.96 mm，而PID控制器则使得线圈电流分别稳定于4.43 A/mm2和−4.66 A/mm2；当系统稳定运行时，加速度反馈悬浮控制下的线圈稳态电流均为0，而PID控制下的稳态悬浮气隙均为0，且当各种扰动消除后，系统均可快速恢复到初始额定运行状态.Abstract:To improve the dynamic stability of the permanent magnet (PM) electrodynamic suspension (EDS) and reduce the drag during low-speed operation, a bilateral PM and electromagnetic hybrid EDS system was proposed. Firstly, a 2D analytical expression of the system electromagnetic force was derived based on Maxwell’s equations. The analytical results were verified by finite element numerical calculations, with a comparison of the electromagnetic force characteristics between unilateral and bilateral structures. Secondly, a suspension dynamic model of the system was established, and an acceleration feedback suspension controller was designed. Finally, a comparative analysis of the air gap, acceleration, and current waveforms under acceleration feedback suspension control and air gap feedback PID control was carried out through Simulink simulation when the system was subjected to track and load disturbances. The results show that the bilateral structure effectively increases the system float-to-drag ratio. At an operating speed of 100 km/h, the float-to-drag ratio for the unilateral and bilateral structures are 3.18 and 15.43, respectively. When the system is subjected to ± 1 mm track disturbances, the controller enables the system vibration acceleration and suspension air gap to quickly stabilize at rated positions of 0 and 20 mm, respectively. When the system is subjected to ± 2 000 N load disturbances, the acceleration feedback suspension controller allows the suspension air gap to quickly stabilize at 19.05 mm and 20.96 mm, respectively, while the PID controller stabilizes the coil current at 4.43 A/mm2 and −4.66 A/mm2, respectively. During stable operation, the steady-state coil current under the acceleration feedback suspension control is 0, while the steady-state suspension air gap under the PID control is 0. The system quickly returns to its initial rated operating state after the disturbances are eliminated.
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图 4 磁感应强度矢量图（vx=100 km/h）
Figure 4. Vector diagram of magnetic induction intensity （vx = 100 km/h）
图 8 加速度反馈悬浮控制系统框图
Figure 8. Block diagram of acceleration feedback suspension control system
图 9 加速度反馈悬浮控制仿真框图
Figure 9. Simulation block diagram of acceleration feedback suspension control
图 10 轨道扰动下的绝对气隙、悬浮气隙、振动加速度及线圈电流
Figure 10. Absolute air gap, suspended air gap, vibration acceleration, and coil current under track disturbances
图 11 载荷扰动下的绝对气隙、悬浮气隙、振动加速度及线圈电流
Figure 11. Absolute air gap, suspended air gap, vibration acceleration, and coil current under load disturbances
表 1 系统参数
Table 1. System parameters
参数 数值 参数 数值 Br/T 1.27 J/（ A·mm−2） 3 w1/mm 300 w2/mm 300 lm/mm 80 l2/mm 1800 h/mm 100 d/mm 5 M/块 4 γ2/（S·m−1） 3.77 × 107 N/块 8 c1/mm 20 δ/mm 10 c2/mm 40 
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