Recent experimental results have demonstrated the effectiveness of adaptive open-loop control algorithms for the suppression of unbalance response on rotors supported in active magnetic hearings. Herein, tools for the analysis of stability and performance robustness of this algorithm with respect to structured uncertainty are derived. The stability and performance robustness analysis problems are shown to be readily solved using a novel application of structured singular values. An example problem is presented which demonstrate the efficacy of this approach in obtaining tight bounds on stability margin and worst case performance.

1.
Beatty, R., 1988, “Notch Filter Control of Magnetic Bearings to Improve Rotor Synchronous Response,” M.S. thesis, M.I.T., May.
2.
Burrows
C. R.
and
Sahinkaya
M. N.
,
1983
, “
Vibration Control of Multi-Mode Rotor-Bearing Systems
,”
Proceedings of the Royal Society of London
, Vol.
386
, pp.
77
94
.
3.
Burrows
C. R.
,
Sahinkaya
M. N.
, and
Clements
S.
,
1989
, “
Active Vibration Control of Flexible Rotors: an Experimental and Theoretical Study
,”
Proceedings of the Royal Society of London
, Vol.
422
, pp.
123
146
.
4.
Haberman, H. and Brunet, M., 1984, “The Active Magnetic Bearing Enables Optimum Damping of Flexible Rotors,” ASME Paper 84-GT-117.
5.
Hope, R., 1994, “Adaptive Open Loop Control of Synchronous Rotor Vibration using Magnetic Bearings,” M.S. thesis. University of Virginia, August.
6.
Higuchi, T., Otsuka, M., Mizuno, T., and Ida, T., 1990, “Application of Periodic Learning Control with Inverse Transfer Function Compensation in Totally Active Magnetic Bearings,” Proceedings of the 2nd International Symposium on Magnetic Bearings, Tokyo, Japan, July 12–14, 1990.
7.
Knospe, C., Hope, R., Fedigan, S., and Williams, R., 1994, “New Results in the Control of Rotor Synchronous Vibration,” Proceedings of the Fourth International Symposium on Magnetic Bearings, vdf Hochschulverlag AG, Zurich, Switzerland, Aug. 23–26.
8.
Knospe
C.
,
Hope
R.
,
Fedigan
S.
, and
Williams
R.
,
1995
, “
Experiments in the Control of Unbalance Response Using Magnetic Bearings
,”
Mechatronics
, Vol.
5
, No.
4
, pp.
385
400
.
9.
Larsonneur, R. and Herzog, R., 1994, “Feedforward Compensation of Unbalance; New Results and Application Experiences,” IUTAM Symposium on the Active Control of Vibration, Bath, UK, Sept.
10.
Maslen
E. H.
, and
Bielk
J. R.
,
1992
, “
A Stability Model for Flexible Rotors with Magnetic Bearings
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
114
, No.
1
, Mar. pp.
172
175
.
11.
Matsumura, F., Fujita, M., and Okawa, K., 1990, “Modeling and Control of Magnetic Bearing Systems Achieving a Rotation around the Axis of Inertia,” Proceedings of the 2nd International Symposium on Magnetic Bearings, Tokyo, Japan, July 12–14.
12.
Shafai
B.
,
Beale
S.
,
LaRocca
P.
, and
Cusson
E.
,
1994
, “
Magnetic Bearing Control Systems and Adaptive Forced Balancing
,”
IEEE Control Systems
, Vol.
14
, No.
2
, pp.
4
13
, April.
13.
Zhou, K., Doyle, J., and Glover, K., 1996, Robust and Optimal Control, Prentice-Hall.
This content is only available via PDF.
You do not currently have access to this content.