Rotating mass imbalance causes harmful vibration of high-speed machine tools, turbomachinery, etc. Constant speed, steady-state influence coefficient control allows active balancing systems to suppress this vibration if the influence matrix is estimated accurately. An optimal strategy for multiple-plane active balancing control is presented here that improves control robustness to modeling and estimation errors. The vibration controller objectively trades off residual vibration, control effort, and control rate of change. Penalizing control effort and rate of change is shown to enhance control stability margin, with certain performance trade-offs. Experimental results illustrate the improvement in control robustness compared with traditional weighted least squares optimal control.

1.
Vande Vegte
,
J.
, and
Lake
,
R. T.
,
1978
, “
Balancing of Rotating Systems During Operation
,”
J. Sound Vib.
,
57
, No.
2
, pp.
225
235
.
2.
Pardivala, D., Dyer, S. W., and Bailey, C. D., 1998, “Design Modifications and Active Balancing On An Integrally Forged Steam Turbine Rotor To Solve Serious Reliability Problems,” Proceedings of the 27th Turbomachinery Symposium, Houston, Texas, Texas A & M University, pp. 67–75.
3.
Bishop
,
R. E. D.
,
1982
, “
On the Possibility of Balancing Rotating Flexible Shafts
,”
Journal of Engineering Science
,
24
, No.
4
, pp.
215
220
.
4.
Lee
,
C. W.
,
Joh
,
Y. D.
, and
Kim
,
Y. D.
,
1990
, “
Automatic Modal Balancing of Flexible Rotors During Operation: Computer Controlled Balancing Head
,”
Proceedings of the Institute of Mechanical Engineers
,
204
, pp.
19
25
.
5.
Knospe
,
C. R.
,
Hope
,
R. W.
,
Fedigan
,
S. J.
, and
Williams
,
R. D.
,
1995
, “
Experiments in the Control of Unbalance Response Using magnetic Bearings
,”
Mechatronics
,
5
, No.
4
, pp.
385
400
.
6.
Manchala, D. W., Palazzolo, A. B., Kascak, A. F., Montague, G. T., and Brown, G. V., 1994, “Active Vibration Control of Sudden Mass Imbalance in Rotating Machinery,” DE-Vol. 75, Active Control of Vibration and Noise, ASME, pp. 133–148.
7.
Machala
,
D.
,
Palazzolo
,
A.
,
Kascak
,
A.
, and
Montague
,
G.
,
1997
, “
Constrained Quadratic Programming, Active Control of Rotating Mass Imbalance
,”
J. Sound Vib.
,
205
, No.
5
, Sept. 4, pp.
561
580
.
8.
Goodman
,
T. P.
,
1964
, “
A Least-Squares Method for Computing Balance Corrections
,”
ASME J. Ind.
,
pp.
273
279
.
9.
Darlow, M. S., 1989, Balancing of High-Speed Machinery, Springer-Verlag, New York.
10.
Knospe
,
C. R.
,
Hope
,
R. W.
,
Tamer
,
W. M.
, and
Fedigan
,
S. J.
,
1996
, “
Robustness of Adaptive Unbalance Control of Rotors With Magnetic Bearings
,”
J. Vib. Control
,
2
, pp.
33
52
.
11.
Lewis, F. L., 1992, Applied Optimal Control & Estimation: Digital Design and Implementation, Prentice Hall, Englewood Cliffs, New Jersey.
12.
Dyer, S. W., and Ni, J., 1999, “Adaptive Influence-Coefficient Control of Single-Plane Active Balancing Systems,” Manufacturing Science and Engineering, ASME-IMECE 1999, MED-10, pp. 747–755.
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