Cascaded Displacement-Flux Density Control for Electromagnetic Thrust Bearing Based on Coupled Stiffness
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摘要:
电磁推力轴承的高精度控制可以提高分拣机械臂或协作机器人辅助关节的协调性和稳定性，级联控制系统下磁密反馈控制被认为是一种解决高频应用的有效办法，但目前很少有合适的微型霍尔传感器能精确采集气隙的实时磁密. 为解决高频工况下传统磁密估计精度不足的问题，首先，对考虑涡流、漏磁和边缘效应的等效磁阻模型进行有理近似；其次，基于耦合刚度并结合有效电感的涡流补偿模型，设计一种以可测量位移和电流共同作为输入信号的磁密观测器，在外回路中设计考虑动态刚度的PID控制器以补偿磁密滞后，并重构磁密内部控制回路；最后，建立电磁推力轴承的级联位移-磁密控制回路，并进行验证. 结果表明，相较于电流控制策略，该磁密反馈控制方法能够将电磁推力轴承系统的增益裕度提升至35 dB，相位裕度稳定在50°以上，扩展控制带宽至400 Hz；在电流控制失稳时，该磁密反馈控制能抑制过冲在41.2%以下，并在不同参数的阶跃响应和方波跟踪测试中表现出更小的超调量和更快的稳定速度.
Abstract:High-precision control of electromagnetic thrust bearings can enhance the coordination and stability of sorting robotic arms or auxiliary joints in collaborative robots. Flux density feedback control under cascaded control systems is recognized as an effective solution for high-frequency applications; however, there are currently few suitable miniature Hall sensors capable of accurately capturing the real-time magnetic flux density of the air gap. To address the problem of insufficient accuracy in traditional flux density estimation under high-frequency operating conditions, first, a rational approximation of an equivalent reluctance model considering eddy current, magnetic leakage, and edge effects was performed. Secondly, based on the coupled stiffness and an eddy current compensation model incorporating effective inductance, a flux density observer using measurable displacement and current as joint input signals was designed. In the outer loop, a PID controller considering dynamic stiffness was designed to compensate for flux density hysteresis, and the internal flux density control loop was reconstructed. Finally, a cascaded displacement-flux density control loop for the electromagnetic thrust bearing was eXstablished and validated. The results indicate that compared to the current control strategy, the flux density feedback control method can increase the gain margin of the electromagnetic thrust bearing system to 35 dB, maintain the phase margin above 50°, and extend the control bandwidth to 400 Hz. When the current control becomes unstable, the flux density feedback control can suppress the overshoot to below 41.2%, and it demonstrates a smaller overshoot and a faster settling speed in step responses under different parameters and square-wave tracking tests.
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图 1 混合磁轴承模型及轴向磁轴承磁路划分
Figure 1. Hybrid magnetic bearing model and magnetic circuit division of axial magnetic bearing
图 2 电磁推力轴承气隙磁场的SC变换
Figure 2. SC transformation of air-gap magnetic field in electromagnetic thrust bearing
图 4 具有磁密估计反馈的级联位移-磁密推力轴承控制回路
Figure 4. Cascaded displacement-flux density control loop of thrust bearing with flux density estimation feedback
图 8 内部控制回路下电流控制和磁密控制的频率响应
Figure 8. Frequency responses of current control and flux density control under internal control loops
图 9 整体控制回路下电流控制和磁密控制的频率响应
Figure 9. Frequency responses of current control and flux density control under overall control loop
图 10 不同控制参数下电流控制和磁密控制的相位裕度、增益裕度、带宽、谐振峰
Figure 10. Phase margin, gain margin, bandwidth, and resonant peak of current control and flux density control under different control parameters
图 11 电流控制和磁密控制的阶跃响应
Figure 11. Step responses of current control and flux density control
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