考虑界面接触的磁悬浮轴承-转子系统建模及鲁棒控制

周扬; 周瑾; 王艺宇; 张越; 徐园平

doi:10.3969/j.issn.0258-2724.20230510

考虑界面接触的磁悬浮轴承-转子系统建模及鲁棒控制

doi: 10.3969/j.issn.0258-2724.20230510

南京航空航天大学机电学院，江苏南京 210016

基金项目: 国家自然科学基金（52075239）；南京市级重大科技专项（202209011）

详细信息

作者简介:
周扬（1996—），男，博士研究生，研究方向为磁悬浮轴承、界面接触，E-mail：zhouyang0216@nuaa.edu.cn

通讯作者:
周瑾（1972—），女，教授，研究方向为磁悬浮技术、旋转机械、机电系统控制、振动控制，E-mail：zhj@nuaa.edu.cn

中图分类号: TH133.3
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- 被引次数: 0
出版历程
- 收稿日期: 2023-09-30
- 修回日期: 2024-04-08
- 网络出版日期: 2024-05-18
- 刊出日期: 2024-04-18

Modeling and Robust Control of Magnetic Bearing-Rotor System Considering Interface Contact

College of Mechanical & Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

摘要

摘要:
磁悬浮轴承-转子系统中，螺栓连接装配形成的界面接触会在转子悬浮状态下激发弯曲模态振动，同时振动频率随转速明显变化. 为实现全转速范围内对弯曲模态振动的主动控制，提出一种考虑频率不确定性的H∞鲁棒控制器设计方法. 首先，通过建立考虑界面接触的动力学模型进行仿真预测，获得振动频率的变化范围；其次，通过频响拟合的方式对转子传递函数进行重构，并将仿真得到的振动频率变化范围以加性不确定性方式引入到重构传递函数中，得到考虑模态频率不确定性的被控对象模型；最后，基于该模型设计兼顾参数摄动和外力扰动的鲁棒性、闭环系统稳定性和防止控制电压饱和等多功能的H∞ 鲁棒控制器. 数值仿真结果表明：该控制器在模态频率处具有宽频带阻的频响特性，能够抑制磁悬浮轴承转子系统的弯曲模态振动；采用该方法设计的H∞ 鲁棒控制器后，转子弯曲模态振动幅值最少减小90%.
- 主动磁悬浮轴承 /
- 界面接触 /
- 模态振动 /
- 鲁棒控制
Abstract:
In magnetic bearing-rotor systems, the bending mode vibration may be excited by the interface contact formed by bolt joints during rotor levitation, and the vibration frequency varies with rotation speed. To actively control bending mode vibration at any speed, the design method of a robust H∞ controller considering frequency uncertainty was proposed. Firstly, the dynamic model considering interface contact was established for numerical simulation, and the vibration frequency variation was obtained. Then, the rotor transfer function was reconstructed by frequency response fitting, and the variation range of vibration frequency obtained by simulation was introduced into the reconstructed transfer function by means of additive uncertainty. As a result, a controlled object model considering mode frequency uncertainty was obtained. Finally, based on the model, the robust H∞ controller was designed by taking the robustness to parameter perturbations and external disturbance, closed-loop system stability, control voltage saturation, and other functions into account. The numerical simulation results show that the controller has the frequency response characteristic of wide band resistance at the mode frequency, which is able to suppress the bending mode vibration of the magnetic bearing-rotor system. After the robust H∞ controller designed by this method is used, the bending mode vibration amplitude of the rotor is reduced by more than 90%.
- active magnetic bearing /
- interface contact /
- mode vibration /
- robust control

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图 1 磁悬浮轴承-转子实验台

Figure 1. Magnetic bearing-rotor test rig

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图 2 磁悬浮轴承-转子系统动力学模型

Figure 2. Dynamics model of magnetic bearing-rotor system

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图 3 径向磁悬浮轴承结构

Figure 3. Radial magnetic bearing structure

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图 4 界面接触示意

Figure 4. Interface contact

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图 5 转子和盘接触面实际接触状态示意

Figure 5. Actual contact between rotor and disk

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图 6 磁悬浮轴承转子系统静态悬浮仿真响应

Figure 6. Static levitation simulation response of magnetic bearing-rotor system

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图 7 磁悬浮轴承转子系统静态悬浮实验响应

Figure 7. Static levitation experiment response of magnetic bearing-rotor system

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图 8 磁悬浮轴承-转子系统升速仿真

Figure 8. Run-up simulation of magnetic bearing-rotor system

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图 9 混合灵敏度控制框图

Figure 9. Mixed sensitivity control

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图 10 S(s)和W₁⁻¹(s)奇异值曲线

Figure 10. Singular value curves of S(s) and W₁⁻¹(s)

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图 11 T(s)和W₃⁻¹(s)奇异值曲线

Figure 11. Singular value curves of T(s) and W₃⁻¹(s)

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图 12 等效传递函数框图

Figure 12. Equivalent transfer function

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图 13 被控对象扫频试验原理框图

Figure 13. Sweep frequency experiment principle for controlled object

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图 14 被控系统频响曲线

Figure 14. Frequency response curves of controlled system

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图 15 加性不确定的近似

Figure 15. Approximation with additive uncertainty

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图 16 控制器频响特性

Figure 16. Frequency response characteristics of controller

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图 17 闭环系统动态柔度

Figure 17. Dynamic compliance of closed-loop system

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图 18 转子静态悬浮仿真响应

Figure 18. Static levitation simulation response of rotor

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图 19 转子升速仿真响应

Figure 19. Run-up simulation response of rotor

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图 20 转子静态悬浮实验响应

Figure 20. Static levitation experiment response of rotor

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图 21 转子升速实验响应

Figure 21. Run-up experiment response of rotor

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表 1 径向磁悬浮轴承结构参数

Table 1. Structural parameters of radial magnetic bearing

参数取值

单个磁极匝数 N/匝 75

单个磁极面积 A/m² 4.05 × 10^－4

偏置电流 I₀/A 2

单边气隙 C₀/mm 0.25

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表 2 理论和试验弯曲模态频率

Table 2. Theoretical and experimental bending mode frequencies Hz

弯曲模态阶数理论值试验值

1 91.26 91.83

2 255.14 257.12

3 526.41 519.53

4 816.02 817.46

5 1046.77 1032.57

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