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浙江大学学报(工学版)
浙江大学学报(工学版)  2020, Vol. 54 Issue (5): 963-971    DOI: 10.3785/j.issn.1008-973X.2020.05.014
机械工程     
基于单相坐标变换的磁悬浮转子不平衡补偿
吴海同1(),周瑾1,*(),纪历2
1. 南京航空航天大学 机电学院，江苏 南京 210016
2. 河海大学 能源与电气学院，江苏 南京 210098
Unbalance compensation of magnetically suspended rotor based on single phase coordinate transformation
Hai-tong WU1(),Jin ZHOU1,*(),Li JI2
1. College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
2. College of Energy and Electrical Engineering, Hohai University, Nanjing 210098, China
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摘要：

针对磁悬浮转子系统的不平衡振动控制问题，提出基于二阶广义积分（SOGI）和同步旋转坐标系（SRF）变换的不平衡补偿算法. 利用SOGI实现单相位移误差的SRF变换，避免磁悬浮轴承两自由度位移幅值不均衡造成的干扰，对变换后的直流量进行比例积分（PI）控制，并将控制量逆SRF变换后叠加到原控制器的输出中，从而实现同频位移误差的无静差跟踪控制. 分析引入补偿算法后闭环系统的稳定性，通过调整逆SRF变换的相位补角可以保证系统的稳定. 仿真和实验表明，该算法能够在宽转速范围内有效抑制磁悬浮转子的同频振动，具有较好的收敛速度和补偿精度.
关键词： 主动磁悬浮轴承;  不平衡补偿;  同步旋转坐标系;  二阶广义积分;  比例积分（PI）控制器    
Abstract:

An unbalance compensation algorithm based on the second-order generalized integrator (SOGI) and the synchronous rotating frame (SRF) transformation was proposed, for the unbalance vibration control of magnetically suspended rotor (MSR) system. The SRF transformation of single-phase displacement error was realized by SOGI, which avoided the interference caused by the displacement amplitude difference between the two-degree-of-freedom of magnetic bearing. Proportional integral (PI) controller was performed on the converted DC quantity, and the control quantity was superimposed into the output of the original controller after inverse SRF transformation, thus, the co-frequency displacement error tracking control without static error was realized. Stability of closed-loop system after introducing the compensation algorithm was analyzed. The stability of the system can be guaranteed by adjusting the phase compensation angle of the inverse SRF transform. Simulation and experiment results show that the proposed algorithm can effectively suppress the co-frequency vibration of MSR over a wide frequency range and has good convergence speed and compensation accuracy.
Key words: active magnetic bearing    unbalance compensation    synchronous rotating frame    second-order generalized integrator    proportional integral (PI) controller
收稿日期: 2019-04-23 出版日期: 2020-05-05
CLC:  TH 133  
基金资助: 国家自然科学基金资助项目（51675261）；中央高校基本科研业务费资助项目（B18020574）；南京航空航天大学研究生创新基地开放基金资助项目（kfjj20180504）
通讯作者: 周瑾     E-mail: wu_haitong@163.com;zhj@nuaa.edu.cn
作者简介: 吴海同（1995—），男，硕士生，从事磁悬浮轴承振动控制研究. orcid.org/0000-0003-3346-9668. E-mail： wu_haitong@163.com
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引用本文:

吴海同,周瑾,纪历. 基于单相坐标变换的磁悬浮转子不平衡补偿[J]. 浙江大学学报(工学版), 2020, 54(5): 963-971.

Hai-tong WU,Jin ZHOU,Li JI. Unbalance compensation of magnetically suspended rotor based on single phase coordinate transformation. Journal of ZheJiang University (Engineering Science), 2020, 54(5): 963-971.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2020.05.014    或    http://www.zjujournals.com/eng/CN/Y2020/V54/I5/963

图 1  磁悬浮轴承-转子截面示意图
图 2  磁悬浮轴承前馈补偿控制系统
图 3  SOGI-SRF补偿器结构图
图 4  二阶广义积分结构图
图 5  二阶广义积分伯德图
物理量 参数符号 数值 单位
转子质量 m 2.07 kg
电流刚度 ke 65.3 N/A
位移刚度 kd 0.317 N/μm
功放增益系数 ka 0.448 A/V
功放截止频率 fc 1 220 Hz
位移传感器增益 ks 20 000 V/m
保护轴承单边间隙 Cmin 0.125 mm
表 1  AMB-转子系统基本参数
图 6  AMB-转子实验台
图 7  转子结构简图
图 8  动态柔度的相频特性图
图 9  闭环系统主导根轨迹
图 10  不平衡补偿仿真结果
图 11  实际实验台动态柔度的相频特性图
图 12  相位补偿多项式拟合曲线
图 13  定速不平衡补偿效果
图 14  补偿前、后振动水平对比
图 15  补偿前、后振动位移三维频谱瀑布图
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