双径向洛伦兹力磁轴承动力学及解耦控制方法

李宗育; 王卫杰; 王丽芬; 任元; 樊亚洪; 李磊

doi:10.13700/j.bh.1001-5965.2023.0262

双径向洛伦兹力磁轴承动力学及解耦控制方法

doi: 10.13700/j.bh.1001-5965.2023.0262

1.
航天工程大学研究生院，北京 101416
2.
航天工程大学宇航科学与技术系，北京 101416
3.
北京控制工程研究所，北京 100190

基金项目:

国家自然科学基金(52075545)

详细信息

通讯作者:
E-mail：wangweijie@126.com

中图分类号: V448.2
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- 被引次数: 0
出版历程
- 收稿日期: 2023-05-22
- 录用日期: 2023-06-30
- 网络出版日期: 2023-09-01
- 整期出版日期: 2025-05-31

Dynamics and decoupling control method of double radial Lorentz force magnetic bearings

1.
Graduate School，Aerospace Engineering University，Beijing 101416，China
2.
Department of Aerospace Science and Technology，Aerospace Engineering University，Beijing 101416，China
3.
Beijing Institute of Control Engineering，Beijing 100190，China

Funds:

National Natural Science Foundation of China (52075545)

More Information

Corresponding author: E-mail：wangweijie@126.com

摘要

摘要:
为实现高精度磁浮转台的快速响应和振动抑制，针对洛伦兹力磁悬浮万向稳定平台的高精度解耦控制问题，首先阐明径向洛伦兹力磁轴承(RLFMB)工作原理，基于等效磁路法对单个径向洛伦兹力磁轴承进行动力学建模，构建转子四自由度平转运动动力学模型。设计一种基于内模结构的解耦控制器，通过补灵敏度函数Bode图验证内模控制器强鲁棒的特点。仿真算例结果表明，跟踪性能上，偏转、平动的响应时间分别较PID控制方法降低59.3%和28.2%；抗扰性能上，偏转、平动干扰残余量较PID控制方法降低38.8%和86.2%，此方法可应用于平台对载荷系统的高精、高稳、高动态指向控制。
- 洛伦兹力磁悬浮万向稳定平台 /
- 径向洛伦兹力磁轴承 /
- 解耦控制 /
- 补灵敏度函数 /
- 内模控制
Abstract:
In order to achieve rapid response and vibration suppression of high-precision magnetic levitation turntable and ensure high-precision decoupling control of Lorentz force magnetic levitation omnidirectional stable platform, the working principle of radial Lorentz force magnetic bearings (RLFMBs) was first elucidated. Based on the equivalent magnetic circuit method, a dynamics model of a single RLFMB was established, and a four-degree-of-freedom translational motion dynamics model of the rotor was constructed. A decoupling controller based on the internal model structure was designed, and the strong robustness of the internal model controller was verified by the Bode diagram of the complementary sensitivity function. The simulation results show that in terms of tracking performance, the response time of deflection and translation is reduced by 59.3% and 28.2%, respectively, compared with the proportion-integral-differential (PID) control method. In terms of anti-interference performance, the residual interference of deflection and translation is reduced by 38.8% and 86.2% compared to the PID control method. This method can be applied to high-precision, high-stability, and high dynamic pointing control of the platform’s load system.

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图 1 磁轴承主动控制绕X轴旋转示意图

Figure 1. Active control rotation of magnetic bearing around X-axis

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图 2 单个RLFMB截面结构示意图

Figure 2. Sectional structure of single RLFMB

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图 3 RLFMB磁路图

Figure 3. Magnetic circuit of RLFMB

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图 4 等效磁路图

Figure 4. Equivalent magnetic circuit

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图 5 x通道检测方案

Figure 5. x-channel detection scheme

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图 6 IMC模型框图

Figure 6. IMC model block diagram

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图 7 简化IMC模型框图

Figure 7. Simplified IMC model block diagram

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图 8 平转运动IMC模型框图

Figure 8. Block diagram of IMC model for translation and deflection

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图 9 洛伦兹力磁浮平台内模控制结构框图

Figure 9. Block diagram of IMC structure of Lorentz force magnetic levitation platform

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图 10 系统仿真模型

Figure 10. System simulation model

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图 11 补灵敏度函数Bode图

Figure 11. Bode diagram of complementary sensitivity function

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图 12 偏转响应曲线对比

Figure 12. Comparison of deflection response curves

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图 13 平动响应曲线对比

Figure 13. Comparison of translation response curves

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图 14 偏转干扰曲线对比

Figure 14. Comparison of deflection interference curves

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图 15 平动干扰曲线对比

Figure 15. Comparison of translation interference curves

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表 1 洛伦兹力平台系统参数

Table 1. Lorentz force platform system parameters

参数	数值	参数	数值
$ {K_{\text{i}}} $/(N·A⁻¹)	52.5	$ {J}_y/({\text{kg}}\cdot {\mathrm{m}}^{2}) $	1.76
$ {J}_x/({\text{kg}}\cdot {\mathrm{m}}^{2}) $	1.76	$ m{\text{/kg}} $	14.0
$ L{\text{/m}} $	0.15	$ {L_{\text{s}}}{\text{/m}} $	0.20
$ {\lambda _{\text{1}}} $	0.001	$ {\lambda _{\text{2}}} $	0.005
$ {\lambda _{\text{3}}} $	0.05	$ {\lambda _{\text{4}}} $	0.05

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表 2 偏转跟踪实验动态性能指标

Table 2. Dynamic performance index of deflection tracking experiment

控制系统	调节时间/s	响应时间/s	超调量/%
PID	2.56	0.81	12.7
IMC	0.47	0.33	0

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表 3 平动跟踪实验动态性能指标

Table 3. Dynamic performance index of translation tracking experiment

控制系统	调节时间/s	响应时间/s	超调量/%
PID	2.78	1.35	8.3
IMC	1.25	0.97	0

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