基于多维可视化的电磁轴承-柔性转子系统多目标优化控制

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振动与冲击 ›› 2025, Vol. 44 ›› Issue (4) : 40-51.

振动理论与交叉研究

基于多维可视化的电磁轴承-柔性转子系统多目标优化控制

程柳峰1，陈亮亮*1，靳晓光1，伍家驹1，郭至城1，李志农2

作者信息 +

Multi-objective optimal control of active magnetic bearing flexible rotor system based on multi-dimensional visualization

CHENG Liufeng1，CHEN Liangliang*1，JIN Xiaoguang1，WU Jiaju1，GUO Zhicheng1，LI Zhinong2

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文章历史 +

摘要

为有效抑制电磁轴承-柔性转子系统的振动，该文提出一种基于多维可视化的电磁轴承-柔性转子系统多目标优化控制策略。首先，通过有限元方法搭建电磁轴承-柔性转子系统数学模型，并采用模态截断法对该系统进行降阶，以减小状态变量个数，便于控制器设计。接着，设计Luenberger全维状态观测器，将传感器处位移转换为电磁轴承处位移，解决传感器与电磁轴承不同位问题，接下来利用状态反馈解耦法将多变量强耦合的电磁轴承-柔性转子系统转化为4个彼此独立的单输入单输出子系统。在此基础上，以控制系统超调量、调节时间及振动幅值为优化目标，以系统稳定、轴承气隙为约束条件，采用多维可视化法对解耦后子系统的控制器参数进行多目标寻优，得到控制参数P、D的最优可行域。最后，搭建仿真模型对本文提出的控制算法的性能进行验证。结果表明：本文提出的控制算法能够有效抑制电磁轴承-柔性转子系统振动，具有稳定性好、超调量小、调节时间短、抗干扰能力强的特点。

Abstract

In order to effectively suppress the vibration of active magnetic bearing flexible rotor system, a multi-objective optimal control strategy of active magnetic bearing flexible rotor system based on multi-dimensional visualization is proposed. Firstly, the mathematical model of active magnetic bearing flexible rotor system is built by the finite element method, and the modal truncation method is used to lower the order of the system to reduce the number of state variables and facilitate the controller design. Then, a Luenberger full-dimensional state observer is designed to convert the displacement at the sensor position into the displacement at the active magnetic bearing position, so as to solve the problem of different positions between the sensor and the active magnetic bearing. Next, the active magnetic bearing flexible rotor system with multi-variable strong coupling is transformed into four independent single-input single-output subsystems by using the state feedback decoupling method. On this basis, the system overshoot, adjustment time and vibration amplitude are taken as the optimization objectives, and the system stability and bearing air gap are taken as the constraints, the multi-dimensional visualization method is used to optimize the controller parameters of the decoupled subsystem, and the optimal feasible region of the control parameters P and D is obtained. Finally, a system simulation model is performed to verify the control performance of the proposed control strategy. The results show that the control algorithm proposed in this paper can effectively suppress the vibration of active magnetic bearing flexible rotor system, and has the characteristics of good stability, small overshoot, short adjustment time and strong anti-interference ability.

导出引用

程柳峰1, 陈亮亮1, 靳晓光1, 伍家驹1, 郭至城1, 李志农2. 基于多维可视化的电磁轴承-柔性转子系统多目标优化控制[J]. 振动与冲击, 2025, 44(4): 40-51

CHENG Liufeng1, CHEN Liangliang1, JIN Xiaoguang1, WU Jiaju1, GUO Zhicheng1, LI Zhinong2. Multi-objective optimal control of active magnetic bearing flexible rotor system based on multi-dimensional visualization[J]. Journal of Vibration and Shock, 2025, 44(4): 40-51

参考文献

[1] Schweitzer G, Maslen E H. Magnetic bearings: theory, design, and application to rotating machinery[M]. Berlin, Heidelberg: Springer, 2009.
[2] Siva Srinivas R, Tiwari R, Kannababu Ch. Application of active magnetic bearings in flexible rotordynamic systems – A state-of-the-art review[J]. Mechanical Systems and Signal Processing, 2018, 106: 537-572.
[3] 刘程子, 湛江, 杨艳, 等. 主动磁悬浮轴承–柔性转子的研究和发展综述[J]. 中国电机工程学报, 2020, 40(14): 4602-4614+4739.
LIU Chengzi, ZHAN Jiang, YANG Yan, et al. Review of research status and development of flexible rotor-magnetic bearing[J]. Proceedings of the CSEE, 2020, 40(14): 4602-4614+4739.
[4] Zheng S, Li H, Peng C, et al. Experimental investigations of resonance vibration control for noncollocated AMB flexible rotor systems[J]. IEEE Transactions on Industrial Electronics, 2017, 64(3): 2226-2235.
[5] 李翁衡, 祝长生. 主动电磁轴承-柔性转子系统的不同位效应[J]. 振动工程学报, 2023, 36(5): 1179-1190.
LI Wengheng, ZHU Changsheng. Different position effects of active magnetic bearing-flexible rotor system[J]. Journal of Vibration Engineering, 2023, 36(5): 1179-1190.
[6] Kulesza Z. Virtual collocation method for a flexible rotor supported by active magnetic bearings[J]. Journal of Vibration and Control, 2015, 21(8): 1522-1538.
[7] 李翁衡, 祝长生. 主动电磁轴承-柔性转子系统振动位移的高精度跟踪和估计方法[J]. 电工技术学报, 2023, 38(12): 3151-3164.
LI Wengheng, ZHU Changsheng. A high-precision tracking and estimation method for vibration displacement of active magnetic bearing-flexible rotor system[J]. Transactions of China Electrotechnical Society, 2023, 38(12): 3151-3164.
[8] 刘峰, 王德明, 欧阳慧珉, 等. 基于交叉解耦的滑模控制在磁轴承中的应用[J]. 轴承, 2014(11): 12-15, 47.
Liu Feng，Wang Deming，Ouyang Huimin, et al. Application of sliding mode control based on cross decoupling in magnetic bearings[J]. Bearing, 2014(11): 12-15, 47.
[9] 陈亮亮, 祝长生, 王忠博. 电磁轴承高速飞轮转子模态分离–状态反馈解耦控制[J]. 中国电机工程学报, 2017, 37(18): 5461-5472, 5546.
CHEN Liangliang, ZHU Changsheng, WANG Zhongbo. Decoupling control for active magnetic bearing high-speed flywheel rotor based on mode separation and state feedback[J]. Proceedings of the CSEE, 2017, 37(18): 5461-5472, 5546.
[10] 陈亮亮, 祝长生, 王忠博. 基于逆系统解耦的电磁轴承飞轮转子系统二自由度控制[J]. 电工技术学报, 2017, 32(23): 100-114.
CHEN Liangliang, ZHU Changsheng, WANG Zhongbo. Two-Degree-of-Freedom control for active magnetic bearing flywheel rotor system based on inverse system decoupling[J]. Transactions of China Electrotechnical Society, 2017, 32(23): 100-114.
[11] Cheng X, Cheng B, Deng S, et al. State-feedback decoupling control of 5-DOF magnetic bearings based on α-order inverse system[J]. Mechatronics, 2020, 68: 102358.
[12] Noshadi A, Shi J, Lee W S, et al. Robust control of an active magnetic bearing system using H∞ and disturbance observer-based control[J]. Journal of Vibration and Control, 2017, 23(11): 1857-1870.
[13] 宋春生, 尹睿, 魏子航, 等. 磁悬浮柔性转子系统解耦控制仿真[J]. 西南交通大学学报, 2023, 58(4): 761-772.
SONG Chunsheng, YIN Rui, WEI Zihang, et al. Simulation on decoupling control of maglev flexible rotor system[J]. Journal of Southwest Jiaotong University, 2023, 58(4): 761-772.
[14] 周天豪, 祝长生. 基于特征结构配置的电磁轴承高速电机刚性转子系统鲁棒输出反馈控制器的设计[J]. 中国电机工程学报, 2022, 42(10): 3775-3786.
ZHOU Tianhao, ZHU Changsheng.Design of robust output controller for an active magnetic bearing high-speed motor rigid rotor system based on eigenstructure assignment[J]. Proceedings of the CSEE,2022, 42(10): 3775-3786.
[15] 梁杰, 专祥涛, 严家政. 基于深度强化学习TD3的PID参数自整定算法[J]. 武汉大学学报（工学版）, 2023: 1-12.
LIANG Jie, ZHUAN Xiangtao, YAN Jiazheng. PID parameter self-tuning algorithm based on deep reinforcement learning TD3[J]. Engineering Journal of Wuhan University, 2023: 1-12.
[16] 冯浩, 姜金叶, 宋倩玉, 等. 电液伺服系统多PID控制器参数整定优化[J]. 控制理论与应用.
https://link.cnki.net/urlid/44.1240.tp.20230928.1132.088
FENG Hao, JIANG Jinye, SONG Qianyu, et al. Multi-PID controller parameters optimization of electro hydraulic servo system[J]. Control Theory & Applications.
https://link.cnki.net/urlid/44.1240.tp.20230928.1132.088
[17] Wei C, Soffker D. Optimization strategy for PID-controller design of AMB rotor systems[J]. IEEE Transactions on Control Systems Technology, 2016, 24(3): 788-803.
[18] Dhyani A, Panda M K, Jha B. Moth-Flame Optimization-based Fuzzy-PID controller for optimal control of active magnetic bearing system[J]. Iranian Journal of Science and Technology, Transactions of Electrical Engineering, 2018, 42(4): 451-463.
[19] 蒋凌云, 魏庆来, 张峰华, 等. 基于改进粒子群优化算法的PID控制器参数整定[J]. 控制工程, 2024, 31(3): 470-477.
JIANG Lingyun, WEI Qinglai, ZHANG Fenghua, et al. PID controller parameter tuning based on improved particle swarm optimization algorithm[J]. Control Engineering of China, 2024, 31(3): 470-477.
[20] 伍家驹, 陈亮亮作. 磁性器件的优化设计及其可视化算法[M]. 北京: 科学出版社, 2023.
WU Jiaju, CHEN Liangliang.Optimization design of magnetic devices and its visualization algorithm[M]. Beijing: Science Press, 2023.
[21] 伍家驹, 蔡智恒, 谢光元, 等. 小型变压器优化设计的可视化算法[J]. 高电压技术, 2023, 49(12): 5282-5291.
WU Jiaju, CAI Zhiheng, XIE Guangyuan, et al. Visualization algorithm for the optimization design of miniature transformers[J]. High Voltage Engineering, 2023, 49(12): 5282-5291.
[22] 黄维健, 陈亮亮, 靳晓光, 等. 一种电磁轴承-转子系统多目标优化控制方法: CN115048750B[P]. 2022-11-08.
HUANG Weijian, CHEN Liangliang, JIN Xiaoguang, et al. A multi-objective optimal control method for active magnetic bearing-rotor system: CN115048750B[P]. 2022-11-08.
[23] 涂之艺, 陈亮亮, 伍家驹, 等. 基于多维可视化的高速永磁电机转子强度优化设计[J]. 振动与冲击, 2022, 41(18): 236-243.
TU Zhiyi, CHEN Liangliang, WU Jiaju, et al. Optimal strength design of a high-speed permanent magnet motor rotor based on multi-dimensional visualization[J]. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(18): 236-243.
[24] 袁惠群. 转子动力学基础[M]. 北京: 冶金工业出版社, 2013.
YUAN Huiqun. Fundamentals of rotor dynamics[M]. Beijing: Metallurgical Industry Press, 2013.
[25] Friswell M I, Penny J E T, Garvey S D, et al. Dynamics of rotating machines[M]. New York: Cambridge University Press, 2010.