Skip to main content
Chinese Journal of Mechanical Engineering
Download PDF
  • Published:

Unbalance vibratory displacement compensation for active magnetic bearings

Chinese Journal of Mechanical Engineering volume 26, pages 95–103 (2013)Cite this article

Abstract

As the dynamic stiffness of radial magnetic bearings is not big enough, when the rotor spins at high speed, unbalance displacement vibration phenomenon will be produced. The most effective way for reducing the displacement vibration is to enhance the radial magnetic bearing stiffness through increasing the control currents, but the suitable control currents are not easy to be provided, especially, to be provided in real time. To implement real time unbalance displacement vibration compensation, through analyzing active magnetic bearings (AMB) mathematical model, the existence of radial displacement runout is demonstrated. To restrain the runout, a new control scheme-adaptive iterative learning control (AILC) is proposed in view of rotor frequency periodic uncertainties during the startup process. The previous error signal is added into AILC learning law to enhance the convergence speed, and an impacting factor β influenced by the rotor rotating frequency is introduced as learning output coefficient to improve the rotor control effects. As a feed-forward compensation controller, AILC can provide one unknown and perfect compensatory signal to make the rotor rotate around its geometric axis through power amplifier and radial magnetic bearings. To improve AMB closed-loop control system robust stability, one kind of incomplete differential PID feedback controller is adopted. The correctness of the AILC algorithm is validated by the simulation of AMB mathematical model adding AILC compensation algorithm through MATLAB soft. And the compensation for fixed rotational frequency is implemented in the actual AMB system. The simulation and experiment results show that the compensation scheme based on AILC algorithm as feed-forward compensation and PID algorithm as close-loop control can realize AMB system displacement minimum compensation at one fixed frequency, and improve the stability of the control system. The proposed research provides a new adaptive iterative learning control algorithm and control strategy for AMB displacement minimum compensation, and provides some references for time-varied displacement minimum compensation.

References

  1. SCHWEITZER G, TRAXLER A, BLEULER H. Magnetic bearings: theory, design, and application to rotating machinery[M]. Berlin: Springer, 2009.

    Google Scholar 

  2. JING Minqing, LI Zixin, LUO Min, et al. Unbalance response and touch-rubbing threshold speed of rotor subjected to nonlinear magnetic forces[J]. Chinese Journal of Mechanical Engineering, 2008, 21(2): 1–4.

    Article  Google Scholar 

  3. HU Yefa, GAO Xiaoming, WU Huachun. The study of unbalance compensation for the rotor of magnetic bearings[J]. Machinery, 2006, 44(504): 24–26. (in Chinese)

    Google Scholar 

  4. TAGUCHI N, ISHIMATSU T, WOO S J, et al. Unbalance compensation of magnetic bearings[C]//20th International Conference on Industrial Electronics, Control and Instrumentation, Industrial, Bologna, Italy, September 5–9, 1994: 2 051–2 056.

  5. LUM K Y, COPPOLA V T, BERNSTEIN D S. Adaptive autocentering control for an active magnetic bearing supporting a rotor with unknown mass imbalance[J]. IEEE Transactions on Control Systems Technology, 1996, 4(5): 587–597.

    Article  Google Scholar 

  6. MIZUNO T. An unified approach to controls for unbalanced compensation in active magnetic bearings[C]//Proceedings of the 1998 IEEE International Conference on Control Applications, Trieste, Italy, September 1–4, 1998: 1 063–1 067.

  7. NONAMI, LIU Zihe. Adaptive unbalance vibration control of magnetic bearing system using frequency estimation for multiple periodic disturbances with noise. Proceedings of the 1999 IEEE International Conference on Control Applications, Kohala Coast, HI, USA, August 22–27, 1999: 576–581.

  8. ARIAS M M, SILVA N G. Finite element modeling and unbalance compensation for a two disks asymmetrical rotor system[C]//5th International Conference on Electrical Engineering, Computing Science and Automatic Control, Mexico City, Mexico, November 12–14, 2008: 386–391.

  9. JASTRZEBSKI R P, POLLANEN R. Compensation of nonlinearities in active magnetic bearings with variable force bias for zero and reduced-bias operation[J]. Mechatronics, 2009, 19(5): 629–638.

    Article  Google Scholar 

  10. INOUE T, LIU Jun, ISHIDA Y, et al. Vibration control and unbalance estimation of a nonlinear rotor system using disturbance observer[J]. Journal of Vibration and Acoustics, 2009, 131(3): 1–8.

    Google Scholar 

  11. COSTIC B T, QUEIROZ M S, DAWSON D N. A new learning control approach to the active magnetic bearing benchmark system[C]//Proceedings of 2000 American Control Conference, Chicago, IL, USA, June 28–30, 2000: 2 639–2 643.

  12. CHIARINI H G, MANDOLESI P S. Unbalance compensation for active magnetic bearings using ILC[C]//Proceedings of the 2001 IEEE International Conference on Control Applications, Mexico City, Mexico, September 5–7, 2001: 58–63.

  13. BI Chao, WU Dezheng, JIANG Quan, et al. Automatic learning control for unbalance compensation in active magnetic bearings[J]. IEEE Transactions on Magnetics, 2005, 41(7): 2 270–2 280.

    Google Scholar 

  14. GU Jialiu. Rotor dynamic[M]. Beijing: National Defense Industry Press, 1985.

    Google Scholar 

  15. KOSAKII T, SANO M, TANAKA K. Model-based fuzzy control system design for magnetic bearings[C]//Proceedings of the Sixth IEEE International Conference on Fuzzy Systems, Barcelona, Spain, July 1–5, 1997: 895–899.

  16. SUN Yanhua, HO Y S, YU Lie. Dynamic stiffnesses of active magnetic thrust bearing including eddy-current effects[J]. IEEE Transactions on Magnetics, 2009, 45(1): 139–149.

    Article  Google Scholar 

  17. HU Yefa. Magnetic bearings basic theory and application[M]. Beijing: China Machine Press, 2006.

    Google Scholar 

  18. JUNG H M, TAE Y D, MYUNG J C. An iterative learning controls scheme for manipulators[C]//Proceedings of the 1997 IEEE/RSJ International Conference on Intelligent Robot and Systems, Grenoble, France, September 7–11, 1997: 759–765.

  19. BRIAN E, LEE H C, DOUGLAS A, et al. Combined H∞-feedback control and iterative learning control design with application to nanopositioning systems[J]. IEEE Transactions on Control System Technical, 2010, 18(2): 336–351.

    Article  Google Scholar 

  20. AHN H S, CHEN Y Q. Periodic adaptive learning compensation of state-dependent disturbance[J]. IET Control Theory Application, 2010, 4(4): 529–538.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Hui Gao, Longxiang Xu & Yili Zhu

Authors
  1. Hui Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Longxiang Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yili Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hui Gao.

Additional information

This project is supported by National Natural Science Foundation of China (Grant No. 50437010), National Hi-tech Research and Development Program of China (863 Program, Grant No. 2006AA05Z205), and Fund of Aeronautics Science of China (Grant No. 2008ZB52018)

GAO Hui, born in 1981, is currently a PhD candidate at College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, China. His research interest is vibration compensation control of AMB system when the rotor high-speed rotating.

XU Longxiang, born in 1959, is currently a professor at College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, China.

ZHU Yili, born in 1987, is currently a PhD candidate at College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, China. His research interest is vibration compensation control of AMB system when the rotor high-speed rotating. His research interest is dynamics.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gao, H., Xu, L. & Zhu, Y. Unbalance vibratory displacement compensation for active magnetic bearings. Chin. J. Mech. Eng. 26, 95–103 (2013). https://doi.org/10.3901/CJME.2013.01.095

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3901/CJME.2013.01.095

Key words