基于非对称差动控制方式的磁轴承模型预测控制策略研究

doi:10.3901/JME.260268

摘要/Abstract

摘要： 为了提升磁轴承的承载能力，处理多变量耦合时变系统，研究了基于非对称差动控制方式的磁轴承模型预测控制(Model predictive control, MPC)策略。首先，对比分析了磁轴承常规差动控制方式与非对称差动控制方式的工作原理；然后，根据磁轴承转子系统状态空间方程设计了模型预测控制器，采用鲸鱼优化算法对模型预测控制器进行参数整定，以改善控制系统的性能；进一步，使用Adams-Simulink机电联合仿真验证所搭建控制系统的正确性与有效性；最后，利用所设计的控制器完成了磁轴承飞轮转子试验台的静态悬浮、实际承载力检测与高速旋转试验。试验结果表明，非对称差动控制方式使磁轴承的名义承载力提升40.0%，实际承载力提升37.5%；飞轮转子能够在12 000 r/min稳定运行，且电流波动峰值小于1 A，转子振动峰值小于10 μm。研究表明，非对称差动控制方式可以在不改变磁轴承机械结构尺寸前提下有效提升磁轴承的承载能力；模型预测控制器能够使非对称差动控制方式下的磁轴承转子系统具有较好的动态性能。

关键词: 磁轴承, 承载能力, 模型预测控制, 鲸鱼优化算法, 机电联合仿真

Abstract: To enhance the load-carrying capacity of magnetic bearings and address a multivariable-coupled, time-varying system, a model predictive control strategy based on the asymmetric differential control approach is investigated. First, the operating principles of conventional differential control and the asymmetric differential control are comparatively analyzed. Subsequently, a model predictive controller is formulated based on the state-space model of the magnetic bearing-rotor system, and its parameters are optimized using the whale optimization algorithm to improve control performance. Thereafter, the developed control system is validated for correctness and effectiveness using Adams-Simulink electromechanical co-simulation. Finally, the designed controller is applied to a magnetic bearing flywheel rotor test rig to carry out static levitation, load-carrying capacity evaluation, and high-speed rotation experiments. Experimental results show that the asymmetric differential control approach increases the nominal load-carrying capacity of the magnetic bearing by 40.0% and the actual load-carrying capacity by 37.5%. The flywheel rotor operates stably at 12,000 r/min, with a peak current ripple below 1 A and a peak rotor vibration amplitude below 10 μm. The study demonstrates that the asymmetric differential control approach significantly enhances the load-carrying capacity of magnetic bearings without altering their mechanical dimensions, while the model predictive controller ensures satisfactory dynamic performance under the asymmetric differential control approach.

Key words: magnetic bearing, load-carrying capacity, model predictive control, whale optimization algorithm, electromechanical co-simulation

中图分类号:

TH133

许绍瀚, 谢振宇, 唐玮, 谢志波. 基于非对称差动控制方式的磁轴承模型预测控制策略研究[J]. 机械工程学报, 2026, 62(9): 201-214.

XU Shaohan, XIE Zhenyu, TANG Wei, XIE Zhibo. Research on Model Predictive Control Strategy for Magnetic Bearings Based on the Asymmetric Differential Control Approach[J]. Journal of Mechanical Engineering, 2026, 62(9): 201-214.

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参考文献

[1] 张维煜，朱熀秋，袁野. 磁悬浮轴承应用发展及关键技术综述[J]. 电工技术学报，2015，30(12)：12-20. ZHANG Weiyu，ZHU Huangqiu，YUAN Ye. Study on key technologies and applications of magnetic bearings[J]. Transactions of China Electrotechnical Society，2015，30(12)：12-20.
[2] MASLEN E H，SCHWEITZER G. Magnetic bearings：theory，design，and application to rotating machinery[M]. Berlin，Heidelberg：Springer Berlin Heidelberg，2009.
[3] HUANG Z，LI C，ZHOU Z，et al. Magnetic bearing：structure，model，and control strategy[J]. International Journal of Advanced Manufacturing Technology，2024，131(5-6)：3287-3333.
[4] DU Y，ZHANG G，HUA W. Review on research and development of magnetic bearings[J]. Energies，2025，18(12)：3222.
[5] HAN W，CAI Y，HAN W，et al. Review of magnetic bearing control method[C]// 2022 IEEE International Conference on Sensing，Diagnostic，Prognostics，and Control (SDPC)，August 5-7，2022，Chongqing University of Posts and Telecommunications，Chongqing，China. IEEE，2022：16-22.
[6] SARMAH N，TIWARI R. Numerical and experimental study on quantitative assessment of multiple fault parameters in a warped internally damped rotor with a transverse fatigue crack integrated with an active magnetic bearing[J]. Mechanical Systems and Signal Processing，2022，174(6)：109112.
[7] LALDINGLIANA J，BISWAS P K. Artificial intelligence based fractional order PID control strategy for active magnetic bearing[J]. Journal of Electrical Engineering and Technology，2022.
[8] 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 & Technology Transactions of Electrical Engineering，2018，42(4)：451-463.
[9] ZHANG S，ZHOU J. Integral sliding mode control with exponential approximation law for an AMB rotor system considering the alford force[J]. Applied Computational Electromagnetics Society Journal (ACES)，2024：841-847.
[10] ZHANG G，LIU M，ZOU H，et al. Vibration control of a rotor-magnetic bearing system on the moving base through H∞ control[C]// ASME Turbo Expo 2023：Turbomachinery Technical Conference and Exposition，GT2023，June 26-30，2023，Boston，Massachusetts. ASME，2023：GT2023-102528.
[11] MORSI A，ABBAS H S，AHMED S M，et al. Model predictive control based on linear parameter-varying models of active magnetic bearing systems[J]. IEEE Access，2021，9：23633-23647.
[12] 邹晋彬，易辉阳，张鹏辉，等. 基于Q-MPC的径向四自由度磁悬浮轴承控制策略[J]. 轴承，2024(7)：36-44. ZOU Jinbin，YI Huiyang，ZHANG Penghui，et al. Control strategy of radial four degree of freedom magnetic bearings based on Q-MPC[J]. Bearing，2024(7)：36-44.
[13] 袁野，朱俊俊，杨帆，等. 应用混合逻辑动态模型预测控制器的磁轴承三电平调制策略[J]. 西安交通大学学报，2024，58(8)：19-27. YUAN Ye，ZHU Junjun，YANG Fan，et al. Magnetic bearing three-level modulation strategy based on mixed logical dynamical model prediction controller[J]. Journal of Xi’an Jiaotong University，2024，58(8)：19-27.
[14] 关旭东，周瑾，金超武，等. 重载磁悬浮轴承-转子自适应控制性能[J]. 浙江大学学报，2020，54(4)：662-670. GUAN Xudong，ZHOU Jin，JIN Chaowu，et al. Adaptive control performance of heavy load magnetic bearing and rotor[J]. Journal of Zhejiang University，2020，54(4)：662-670.
[15] MUKOYAMA S，NAKAO K，SAKAMOTO H，et al. Development of superconducting magnetic bearing for 300 kW flywheel energy storage system[J]. IEEE Transactions on Applied Superconductivity，2017，27(4)：1-4.
[16] ZHANG P，FENG Y，WEN P，et al. Structure design，analysis，and optimization of 12-pole radial magnetic bearing[J]. Advances in Mechanical Engineering，2025，17(6)：1-16.
[17] 李超，谢振宇，吴传响，等. 磁悬浮轴承非定向差动控制方式研究[J]. 机械工程学报，2022，58(21)：161-170. LI Chao，XIE Zhenyu，WU Chuanxiang，et al. Research on non-directional differential control strategy of active magnetic bearing[J]. Journal of Mechanical Engineering，2022，58(21)：161-170.
[18] LEE A，FAN Y. Decentralized control of a rotor system supported by magnetic bearings[J]. International Journal of Machine Tools and Manufacture，1995，35：445-458.
[19] 胡业发. 磁力轴承的基础理论与应用[M]. 北京：机械工业出版社，2006. HU Yefa. Fundamentals and applications of magnetic bearings[M]. Beijing：China Machine Press，2006.
[20] 董永泽. 基于非对称差动控制方式的磁轴承自适应滑模控制算法研究[D]. 南京：南京航空航天大学，2024. DONG Yongze. Research on adaptive sliding mode control algorithm of magnetic bearing based on asymmetric differential control mode[D]. Nanjing：Nanjing University of Aeronautics and Astronautics，2024.
[21] 席裕庚，李德伟，林姝. 模型预测控制——现状与挑战[J]. 自动化学报，2013，39(3)：222-236. XI Yugeng，LI Dewei，LIN Shu. Model predictive control — status and challenges[J]. Acta Automatica Sinica，2013，39(3)：222-236.
[22] SCHWENZER M，AY M，BERGS T，et al. Review on model predictive control：an engineering perspective[J]. International Journal of Advanced Manufacturing Technology，2021，117(5-6)：1327-1349.
[23] AXEHILL D，HANSSON A. A dual gradient projection quadratic programming algorithm tailored for model predictive control[C]// The 47th IEEE Conference on Decision and Control，December 9-11，2008，Cancun，Mexico. Cancun：IEEE，2008：3057-3064.
[24] MIRJALILI S，LEWIS A. The whale optimization algorithm[J]. Advances in Engineering Software，2016，95(12)：51-67.