volume | PIER Journals

Abstract

In order to solve the problem that the unbalance vibration caused by rotor mass eccentricity of the six-pole radial hybrid magnetic bearing (HMB) seriously affects stability and security of the system, a feed-forward compensation control strategy for rotor unbalance vibration based on fuzzy least-mean-square (LMS) algorithm is proposed. Firstly, the structure, operation principle and mathematical model of the six-pole radial HMB are introduced, and the cause of rotor vibration is analyzed and the dynamic equation of rotor deduced. Secondly, an LMS self-adapting filter is improved by using a fuzzy inference system, and the step size of the LMS algorithm is combined with the fuzzy control theory. By using the Takagi-Sugeno (TS) fuzzy inference machine system to adjust the step size of the algorithm, the filter output can approach the unbalance vibration signal smoothly and quickly, and realize the vibration compensation of the rotor. Finally, the simulations and experiments are carried out to verify that the proposed method can not only effectively suppress the unbalance vibration of the six-pole radial HMB rotor in real time but also have good compensation accuracy. The results show that the vibration compensation effect of fuzzy LMS algorithm is better than that of fixed step size filtering algorithm.

1. Ju, J.-T. and H.-Q. Zhu, "Radial force-current characteristics analysis of three-pole radial-axial hybrid magnetic bearings and their structure improvement," IET Electr. Power Appl., Vol. 11, No. 9, 1548-1557, 2017.
doi:10.1049/iet-epa.2017.0106

2. Le, Y., J.-J. Sun, and B.-C. Han, "Modeling and design of 3-DOF magnetic bearing for high-speed motor including eddy-current effects and leakage effects," IEEE Trans. Ind. Electron., Vol. 63, No. 6, 3656-3665, 2016.
doi:10.1109/TIE.2016.2530778

3. Zhu, D.-H., X. Cheng, and H.-Q. Zhu, "Structure and performance analysis for AC-DC three degrees of freedom active magnetic bearings," Proc. 2009 IEEE 6th International Power Electronics and Motion Control Conference, 2005-2009, 2009.

4. Zhang, W.-Y., H.-Q. Zhu, Z.-B. Yang, et al. "Nonlinear model analysis and “switching model” of AC-DC three-degree-of-freedom hybrid magnetic bearing," IEEE/ASME Trans. Mechatronics, Vol. 21, No. 2, 1102-1115, 2016.
doi:10.1109/TMECH.2015.2463676

5. Zhang, W.-Y. and H.-Q. Zhu, "Control system design for a five-degree-of-freedom electrospindle supported with AC hybrid magnetic bearings," IEEE/ASME Trans. Mechatronics, Vol. 20, No. 5, 2525-2537, 2015.
doi:10.1109/TMECH.2014.2387151

6. Zhang, W.-Y. and H.-Q. Zhu, "Improved model and experiment for AC-DC three-degree-of-freedom hybrid magnetic bearing," IEEE Trans. Magnetics, Vol. 49, No. 11, 5554-5565, 2013.
doi:10.1109/TMAG.2013.2271754

7. Wu, H.-T., J. Zhou, and L. Ji, "Unbalance compensation of magnetically suspended rotor based on single phase coordinate transformation," Journal of Zhejiang University (Engineering Science), Vol. 54, No. 5, 963-971, 2020.

8. Inoue, T., J. Liu, Y. Yoshimura, et al. "Vibration control and unbalance estimation of a nonlinear rotor system using disturbance observer," J. Vib. Acoust., Vol. 131, No. 3, 031010-031018, 2009.
doi:10.1115/1.3085886

9. Peng, C., M.-T. Zhu, K. Wang, et al. "A two-stage synchronous vibration control for magnetically suspended rotor system in the full speed range," IEEE Trans. Ind. Electron., Vol. 67, No. 1, 480-489, 2020.
doi:10.1109/TIE.2018.2890498

10. Mao, C. and C.-S. Zhu, "A Real-time variable step size iterative unbalance compensation for active magnetic bearing-rigid rotor systems," Proceedings of the CSEE, Vol. 38, No. 13, 3960-3968, 2018.

11. Peng, C., J.-J. Sun, C.-X.Miao, and J.-C. Fang, "A novel cross-feedback notch filter for synchronous vibration suppression of an MSFW with significant gyroscopic effects," IEEE Trans. Ind. Electron., Vol. 64, No. 9, 7181-7190, 2017.
doi:10.1109/TIE.2017.2694402

12. Yoon, S.-Y., L. Di, and Z.-L. Lin, "Unbalance compensation for AMB systems with input delay: An output regulation approach," Control Eng. Practice, Vol. 46, 166-175, 2016.
doi:10.1016/j.conengprac.2015.11.002

13. Mao, C. and C.-S. Zhu, "Unbalance compensation for active magnetic bearing rotor system using a variable step size real-time iterative seeking algorithm," IEEE Trans. Ind. Electron., Vol. 65, No. 5, 4177-4186, 2018.
doi:10.1109/TIE.2017.2760844

14. Cui, P.-L., S. Li, Q.-R. Wang, et al. "Harmonic current suppression of an AMB rotor system at variable rotation speed based on multiple phase-shift notch filters," IEEE Trans. Ind. Electron., Vol. 63, No. 11, 6962-6969, 2016.
doi:10.1109/TIE.2016.2585545

15. Liu, C. and G. Liu, "Autobalancing control for MSCMG based on sliding-mode observer and adaptive compensation," IEEE Trans. Ind. Electron., Vol. 63, No. 7, 4346-4356, 2016.
doi:10.1109/TIE.2016.2551681

16. Wang, Z.-B., C. Mao, and C.-S. Zhu, "Current compensation control of multiple frequency vibrations of the rotor in active magnetic bearing high speed motors," Proceedings of the CSEE, Vol. 38, No. 1, 275-284, 2018.

17. Cui, P. and J. Cui, "Harmonic current suppression of active-passive magnetically suspended control moment gyro based on variable-step-size FBLMS," J. Vib. Control, Vol. 23, No. 8, 1221-1230, 2015.
doi:10.1177/1077546315602153

Prof. Huangqiu Zhu

Dr. Mingjie Tang