Model Validation and Controller Design for Vibration Suppression of Flexible Rotor Using AMB

  • Soo Jeon (Graduate Student, Department of Mechanical Engineering, University of California at Berkeley) ;
  • Ahn, Hyeong-Joon (Research Associate, Institute of Advanced Machinery and Design, Seoul National University) ;
  • Han, Dong-Chul (Professor, School of Mechanical & Aerospace Engineering, Seoul National University)
  • Published : 2002.12.01

Abstract

This paper discusses the model validation and vibration suppression of an AMB flexible rotor via additional LQG controller. The main difficulty in the vibration suppression of the flexible rotor using AMB is to realize a controller that can minimize resonance without injuring the stabilized rigid modes. In order to solve this problem, simple scheme for system modeling and controller design are developed. Firstly, the AMB flexible rotor is stabilized with a PID controller, which leads to a new stable rotor-bearing system. Then, authors propose the model validation procedure using measured open-loop frequency responses to obtain an accurate model of the AMB flexible rotor system. After that, LQG controller with modal weighting is designed to suppress resonances of the stable rotor-bearing system. Due to the poor controllability and observability of flexible modes compared to rigid ones, balancing of two Gramians is prerequisite for the fair LQG controller design. Simulation with step disturbance and experimental results of unbalance response up to 10,000 rpm verified the effectiveness of the proposed scheme.

Keywords

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, Vol. 122, pp. 102-107 https://doi.org/10.1115/1.482433
  2. Ahn, H. J., 2001, 'A Study on System Identification and Vibration Control of the AMB Spindle for High Speed Precision Machining Using Cylindrical Capacitive Sensors,' Ph. D. Thesis, Seoul National University, Korea
  3. Gahler, C. and Mohler, M., 1996, 'Multivariable Identification of Active Magnetic Bearing Systems,' 5th Int. Symposium on Magnetic Bearings, Kanazawa, Japan, pp. 7-12
  4. Ha, Y. H. and Lee, C. W., 1997, 'In-situ Modal Testing and Parameter Identification of Active Magnetic Bearing System by Magnetic Force Measurement and the Use of Directional Frequency response functions,' Transactions of KSME A., 21 (7), pp. 1156-1165
  5. 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
  6. Lee, C. W. and Kim, J. S., 1992, 'Modal Testing and Suboptimal Vibration Control of Flexible Rotor Bearing System by Using a Magnetic Bearing,' J. Dynamic Systems, Measurement and Control, Vol. 114, pp. 244-252 https://doi.org/10.1115/1.2896521
  7. Lewis, F., 1992, Applied Optimal Control & Estimation, Prentice-Hall International, Inc.
  8. Nonami, K., 1985, 'Vibration Control of Rotor Shaft Systems by Active Control Bearings,' ASME Design Engineering Division Conf., Cincinnati, Ohio
  9. Nonami, K. and Ito, T., 1994, '${\mu}$-Synthesis of Flexible Rotor of Magnetic Bearing System,' 4th Int. Symposium on Magnetic Bearings, Zurich, Switzerland, pp. 73-78
  10. Okada, Y., Hayashi, H., Saitoh, T. and Shinoda, Y., 1997, 'Vibration Control of Flexible Rotor Supported by Magnetic Bearing,' Asia-Pacific Vibration Conference '97, Kyongju, Korea, pp. 991 - 996
  11. Pintelon, R., Guillaume, P., Vandersteen, G. and Rolain, Y., 1998, 'Analyses, Development and Applications of TLS Algorithms in Frequency Domain System Identification,' SIAM J. Matrix Anal. Appl. https://doi.org/10.1137/S0895479896309074
  12. RODAP (ROtating machine Design and Analysis Program), D&M Technology Co., Korea
  13. RK4 Rotor kit, Bently-Nevada Co., USA.
  14. Salm, J. R., 1988, 'Active Electromagnetic Suspension of an Elastic Rotor: Modeling, Control, and Experimental Results,' ASME Journal of Vibration, Acoustics, Stress, and Reliability in Design, Vol. 110, October, pp. 493-500 https://doi.org/10.1115/1.3269556
  15. Schonhoff, U., Luo, J., Li, G., Hilton, E., Nordmann, R. and Allaire, P., 2000, 'Implementation Results of ,u-Synthesis Control for an Energy Storage Flywheel Test Rig,' 7th Int. Symposium on Magnetic Bearings, Zurich, Switzerland, pp. 317 - 322
  16. Schweitzer, G., Bleuler, H. and Traxler, A., 1994, Active Magnetic Bearings, Hochschulverlag AG de ETH Zurich, Switzerland