Advertisement

Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

System modeling and robust control of an AMB spindle : part II a robust controller design and its implementation

  • 178 Accesses

  • 7 Citations

Abstract

This paper discusses an entire procedure for a robust controller design and its implementation of an AMB (active magnetic bearing) spindle, which is part II of the papers presenting details of system modeling and robust control of an AMB spindle. Since there are various uncertainties in an AMB system and reliability is the most important factor for applications, robust control naturally gains attentions in this field. However, tight evaluations of various uncertainties based on experimental data and appropriate performance weightings for an AMB spindle are still ongoing research topics. In addition, there are few publications on experimental justification of a designed robust controller. In this paper, uncertainties for the AMB spindle are classified and described based on the measurement and identification results of part I, and an appropriate performance weighting scheme for the AMB spindle is developed. Then, a robust control is designed through the mixedμ synthesis based on the validated accurate nominal model of part I, and the robust controller is reduced considering its closed loop performance. The reduced robust controller is implemented and confirmed with measurements of closed-loop responses. The AMB spindle is operated up to 57,600 rpm and performance of the designed controller is compared with a benchmark PID controller through experiments. Experiments show that the robust controller offers higher stiffness and more efficient control of rigid modes than the benchmark PID controller.

This is a preview of subscription content, log in to check access.

Abbreviations

A :

System matrix

C(s) :

Controller

d :

Plant input disturbance

D :

D scaling for theμ synthesis

e :

Error

F l :

LFT

G.G(s) :

Plant

M :

General plant

n :

Noise

S :

Sensitivity function

T :

Complementary sensitivity function

U :

Controller input

w :

Controller input disturbance

W :

Weighting functions

δ :

Parameter variation

ω :

Natural frequency

ξ :

Damping

References

  1. Ahn, H. J., Jeon, S. and Han. D. C., 2000, “Error Analysis of the Cylindrical Capacitive Sensor for Active Magnetic Bearing Spindles,”J. of Dynamics systems, measurement, and control, trans, of ASME, March, Vol. 122, pp. 102–107. Balas, G. J., Doyle, J. C, Glover, K., Packard,

  2. A. K. and Smith, R., μ-Analysis and Synthesis toolbox, the MathWorks, Natick, MA, 1995.

  3. Balas, G. J. and Young, P. M., 1995, “Control Design for Variations in Structural Natural Frequencies,”Journal of Guidance, Control and Dynamics, Vol. 18, No. 2, pp. 325–332.

  4. Carrere, F., Font, S. and Due, G., 1994.“H∞, Control Design of Flexible Rotor Magnetic Bearing System,”Proceedings of the 4 th IS MB, Zurich, Switzerland, pp. 65-71.

  5. Cui, W. M. and Nonami, K., 1992,“H∞ Control of Flexible Rotor-Magnetic Bearing Systems,”Proceedings of the 3 rd ISMB, Alexandria, Virginia, USA, pp. 504-514

  6. Doyle, J., Packard, A. and Zhou, K., 1991, “Review of LFTs, LMIs, andμ,” Proceedings of the 30 th Conference on Decision and Control, Brington, England.

  7. Fittro, R. L., 1998, “A High Speed Machining Spindle with Active Magnetic Bearings: Control Theory, Design, and Application,” Ph. D. dissertation, University of Virginia, USA.

  8. Innovative Integration Co., 1998. M44 DSP Hardware manual, USA.

  9. Jeon, S., Ahn, H. J., Chang, I. B. and Han, D. C., 2001, “A New Design of Cylindrical Capacitive Sensor for On-line Precision Control of AMB Spindle,”IEEE Transactions on Instrumentation and measurement, Vol. 50, No. 3, pp. 757–763.

  10. Jeon, S., Ahn, H. J. and Han, D. C., 2003, “Control of Flexible Rotor with Active Magnetic Bearing System,” KSME International Journal, 16(12), pp. 1583–1593.

  11. Kim, S. J. and Lee, C. W., 1998. “On-line Identification of Position and Current Stiffnesses in Active Magnetic Bearing System Equipped with Built-in Force Transducers by LMS Algorithm,”Transactions of KSME A., 22(12), pp. 2261–2268.

  12. Losch, F., Gahler, C. and Herzog, R., 1998, “μ- Synthesis Controller Design For a 3MW Pump Running In AMBs,”Proceedings of the 6 th ISMB, MIT, Massachusetts, USA, pp. 415–428.

  13. Namerikawa. T., Fugita, M. and Matsumura, F., 1998, “Uncertainty Structure and μ-Design of a Magnetic Suspension System,”Proceedingsof the 6 th ISMB, MIT, Boston, MA. USA, pp. 439–447.

  14. Nonami. K., Ueyama, H. and Yutaka, S., 1994, “H∞ Control of Milling AMB Spindle,”Proceedings of the 4 th ISMB, Zurich, Switzerland, pp. 531-536.

  15. Nonami, K., Takayuki, I., 1994, “μ Synthesis of Flexible Rotor Magnetic Bearing Systems,”Proceedings of the 4 th ISMB, Zurich, Switzerland, pp. 73-78.

  16. Stephens. L. S., 1995, “Design and Control of Active Magnetic Bearings for a High Speed Machining Spindle,” Ph. D. dissertation. University of Virginia, USA.

  17. Schonhoff, U., Luo, J., Li, G., Hilton. E., Nordmann, R. and Allaire, P. E., 2000, “Implementation Results of μ-Synthesis Control for an Energy Storage Flywheel Test Rig,”Proceedings of the 7 th ISMB, Zurich, Switzerland, pp. 317-322.

  18. Texas Instruments Co., 1995, TMS 320C4x User’s Guide, USA.

  19. Van Den Braembussche, P., 1998, “Robust Motion Control of High Performance Machine Tools with Linear Motors,” Ph. D. dissertation, Katholieke Universiteit Leuven, Belgium.

  20. Wortelboer, P. M. R., 1994, “Frequency-weighted Balanced Reduction of Closed-loop Mechanical Servo- systems: Theory and Tools,” Ph. D. dissertation, Delft University of Technology, Nederland.

  21. Young, P. M., 1996, “Controller Design with Real Parametric Uncertainty,”International Journal of Control, Vol. 65, No. 3, pp. 469–509.

Download references

Author information

Correspondence to Hyeong-Joon Ahn.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Ahn, H., Han, D. System modeling and robust control of an AMB spindle : part II a robust controller design and its implementation. KSME International Journal 17, 1855–1866 (2003). https://doi.org/10.1007/BF02982424

Download citation

Key Words

  • Robust Control
  • Uncertainty Description and Active Magnetic Bearing