The problem of sensor runout in magnetic bearing systems has been largely overlooked due to similarities with mass unbalance in creating periodic disturbances. While the effect of mass unbalance can be significantly reduced, if not eliminated, through rotor balancing, sensor runout disturbance is unavoidable since it originates from physical nonconcentricity between rotor and stator. Sensor runout is also caused by nonuniform electrical and magnetic properties around the sensing surface. To improve performance of magnetic bearings, we present an adaptive algorithm for sensor runout compensation. It guarantees asymptotic stability of the rotor geometric center and on-line feedforward cancellation of runout disturbances using persistent excitation. Some of the advantages of our algorithm include simplicity of design and implementation, stability, and robustness to plant parameter uncertainties. The stability and robustness properties are derived from passivity of the closed-loop system. Numerical simulations are presented to demonstrate efficacy of the algorithm and experimental results confirm stability and robustness for large variation in plant parameters.
Issue Section:
Technical Papers
1.
Setiawan, J. D., Mukherjee, R., Maslen, E. H., and Song, G., 1999, “Adaptive Compensation of Sensor Runout and Mass Unbalance in Magnetic Bearing Systems,” Proc. IEEE/ASME Int. Conf. on Advanced Intelligent Mechatronics, Atlanta, GA.
2.
Batty, R., 1988, “Notch Filter Control of Magnetic Bearings,” MS thesis, Massachussetts Institute of Technology, Cambridge, MA.
3.
Knospe, C. R., 1991, “Stability and Performance of Notch Filters for Unbalance Response,” Proc. Int. Symp. on Magnetic Suspension Technology, NASA Langley Research Center, Hampton, VA, NASA Conference Publication 3152.
4.
Bleuler
, H.
, Gahler
, C.
, Herzog
, R.
, Larsonneur
, R.
, Mizuno
, T.
, Siegwart
, R.
, and Woo
, S.-J.
, 1994
, “Application of Digital Signal Processors for Industrial Magnetic Bearings
,” IEEE Trans. Control Syst. Technol.
, 2
, No. 4
, pp. 280
–289
.5.
Na
, H.-S.
, and Park
, Y.
, 1997
, “An Adaptive Feedforward Controller for Rejection of Periodic Disturbances
,” J. Sound Vib.
, 201
, No. 4
, pp. 427
–435
.6.
Shafai
, B.
, Beale
, S.
, Larocca
, P.
, and Cusson
, E.
, 1994
, “Magnetic Bearing Control Systems and Adaptive Forced Balancing
,” IEEE Control Systems
, 14
, pp. 4
–13
.7.
Hu
, J.
, and Tomizuka
, M.
, 1993
, “A New Plug-in Adaptive Controller for Rejection of Periodic Disturbances
,” ASME J. Dyn. Syst., Meas., Control
, 115
, pp. 543
–546
.8.
Herzog
, R.
, Buhler
, P.
, Gahler
, C.
, and Larsonneur
, R.
, 1996
, “Unbalance Compensation Using Generalized Notch Filters in Multivariable Feedback of Magnetic Bearings
,” IEEE Trans. Control Syst. Technol.
, 4
, No. 5
, pp. 580
–586
.9.
Sacks
, A.
, Bodson
, M.
, and Khosla
, P.
, 1996
, “Experimental Results of Adaptive Periodic Disturbance Cancellation in a High Performance Magnetic Disk Drive
,” ASME J. Dyn. Syst., Meas., Control
, 118
, pp. 416
–424
.10.
Lum
, K.-Y.
, Coppola
, V.
, and Bernstein
, D.
, 1996
, “Adaptive Autocentering Control for an Active Magnetic Bearing Supporting a Rotor with Unknown Mass Imbalance
,” IEEE Trans. Control Syst. Technol.
, 4
, No. 5
, pp. 587
–597
.11.
Matsumura, F., Fujita, M., and Okawa, K., 1990, “Modeling and Control of Magnetic Bearing Systems Achieving a Rotation Around the Axis of Inertia,” Second Int. Symp. on Magnetic Bearings, Tokyo, Japan, pp. 273–280.
12.
Hisatani, M., and Koizumi, T., 1994, “Adaptive Filtering for Unbalance Vibration Suppression,” Fourth Int. Symp. on Magnetic Bearings, ETH Zurich, Switzerland.
13.
Song, G., and Mukherjee, R., 1996, “Integrated Adaptive Robust Control of Active Magnetic Bearing,” IEEE Int. Conf. on System, Man, and Cybernetics, Beijing, China.
14.
Reining
, K. D.
, and Desrochers
, A. A.
, 1986
, “Disturbance Accomodating Controllers for Rotating Mechanical Systems
,” ASME J. Dyn. Syst., Meas., Control
, 108
, pp. 24
–31
.15.
Mizuno, T., and Higuchi, T., 1990, “Design of Magnetic Bearing Controllers Based on Disturbance Estimation,” Proc. 2nd Int. Symp. on Magnetic Bearings, Tokyo, Japan, pp. 281–288.
16.
Knospe
, C. R.
, Hope
, R. W.
, Tamer
, S. M.
, and Fedigan
, S. J.
, 1996
, “Robustness of Adaptive Unbalance Control of Rotors With Magnetic Bearings
,” J. Vib. Control
, 2
, pp. 33
–52
.17.
Knospe
, C. R.
, Tamer
, S. M.
, and Fedigan
, S. J.
, 1997
, “Robustness of Adaptive Rotor Vibration Control to Structured Uncertainty
,” ASME J. Dyn. Syst., Meas., Control
, 119
, pp. 243
–250
.18.
Fujita, M., Hatake, K., and Matsumura, F., 1993, “Loop Shaping Based Robust Control of a Magnetic Bearing,” IEEE Control Systems, pp. 57–65.
19.
Rutland, N. K., Keogh, P. S., and Burrows, C. R., 1994, “Comparison of Controller Designs for Attenuation of Vibration in a Rotor Bearing System Under Synchronous and Transient Conditions,” Fourth Int. Symp. on Magnetic Bearings, ETH Zurich, Switzerland, pp. 107–112.
20.
Mohamed A. M., Matsumura, M., Namerikawa, T., and Lee, J., 1997, “Q-Parameterization Control of Vibrations in a Variable Speed Magnetic Bearing,” Proc. 1997 IEEE Int. Conf. on Control Applications, Hartford, CT.
21.
Paul, M., Hoffman, W., and Steffani, H. F., 1998, “Compensation for Unbalances With Aid of Neural Networks,” Sixth Int. Symp. on Magnetic Bearings, Cambridge, MA.
22.
Kim
, C.-S.
, and Lee
, C.-W.
, 1997
, “In Situ Runout Identification in Active Magnetic Bearing System by Extended Influence Coefficient Method
,” IEEE/ASME Trans. on Mechatronics
, 2
, No. 1
, pp. 51
–57
.23.
Narendra, K. S., and Annaswamy, A. M., 1989, Stable Adaptive Systems, Prentice-Hall, Englewood Cliffs, NJ 07632.
24.
Chen
, D.
, and Paden
, B.
, 1993
, “Adaptive Linearization of Hybrid Step Motors: Stability Analysis
,” IEEE Trans. Autom. Control
, 38
, No. 6
, pp. 874
–887
.25.
Siegwart, R., 1992, “Design and Applications of Active Magnetic Bearings (AMB) for Vibration Control,” Von Karman Institute Fluid Dynamics Lecture Series 1992-06, Vibration and Rotor Dynamics.
26.
Khalil, H., 1996, Nonlinear Systems, 2nd Ed., Prentice-Hall, Upper Saddle River, NJ 07458.
27.
Krstic, M., Kanellakopoulos, I., and Kokotovic, P., 1995, Nonlinear and Adaptive Control Design, Wiley Interscience, New York, NY.
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