Rotor unbalance, common phenomenon of rotational systems, manifests itself as a periodic disturbance synchronized with the rotor's angular velocity. In active magnetic bearing (AMB) systems, feedback control is required to stabilize the open-loop unstable electromagnetic levitation. Further, feedback action can be added to suppress the repeatable runout but maintain closed-loop stability. In this paper, a plug-in time-varying resonator is designed by inverting cascaded notch filters. This formulation allows flexibility in designing the internal model for appropriate disturbance rejection. The plug-in structure ensures that stability can be maintained for varying rotor speeds. Experimental results of an AMB–rotor system are presented.

References

References
1.
Schweitzer
,
G.
,
Bleuler
,
H.
, and
Traxler
,
A.
,
1994
,
Active Magnetic Bearings—Basics, Properties and Applications of Active Magnetic Bearings
,
Vdf Hochschulverlag
,
Zurich, Switzerland
.
2.
Barney
,
P.
,
Laugger
,
J.
,
Petteys
,
R.
,
Redmond
,
J.
, and
Sullivan
,
W.
,
1999
, “
Adaptive Spindle Balancing Using Magnetically Levitated Bearings
,”
International Mechanical Engineering Congress and Expo
.
3.
Shi
,
J.
, and
Lee
,
W. S.
,
2009
, “
Analytical Feedback Design Via Interpolation Approach for the Strong Stabilization of a Magnetic Bearing System
,”
Control and Decision Conference
, Guilin, June 17–19, pp.
274
279
.
4.
Chen
,
X.
,
Ji
,
L.
, and
Liu
,
K.
,
2010
, “
A BP Neural Network Controller for Magnetic Suspended Flywheel System
,”
3rd IEEE International Conference on Computer Science and Information Technology (ICCSIT)
, Vol.
6
, pp.
448
452
.
5.
Zhang
,
X.
,
Shinshi
,
T.
,
Li
,
L.
,
Choi
,
K. B.
, and
Shimokohbe
,
A.
,
2001
, “
Precision Control of Radial Magnetic Bearing
,”
10th International Conference on Precision Engineering
, Yokohama, Japan, July 18–20, pp.
714
718
.
6.
Hoshi
,
H.
,
Shinshi
,
T.
, and
Takatani
,
S.
,
2006
, “
Third-Generation Blood Pumps With Mechanical Noncontact Magnetic Bearings
,”
Artif. Organs
,
30
(
5
), pp.
324
338
.
7.
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
(
4
), pp.
385
400
.
8.
Seto
,
H.
,
Namerikawa
,
T.
, and
Fujita
,
M.
,
2006
, “
Experimental Evaluation on h DIA Control of Magnetic Bearings With Rotor Unbalance
,”
10th International Symposium on Magnetic Bearings
, Hotel du Parc, Martigny, Switzerland, pp.
82
87
.
9.
Yang
,
G.
,
Xu
,
Y.
,
Shi
,
Z.
, and
Gu
,
H.
,
2007
, “
Characteristic Analysis of Rotor Dynamics and Experiments of Active Magnetic Bearing for HTR-10GT
,”
Nucl. Eng. Des.
,
237
(
12–13
), pp.
1363
1371
.
10.
Francis
,
B.
, and
Wonham
,
W.
,
1976
, “
The Internal Model Principle of Control Theory
,”
Automatica
,
12
(
5
), pp.
457
465
.
11.
Fukuda
,
S.
, and
Imamura
,
R.
,
2005
, “
Application of a Sinusoidal Internal Model to Current Control of Three-Phase Utility-Interface Converters
,”
IEEE Trans. Ind. Electron.
,
52
(
2
), pp.
420
426
.
12.
Kim
,
Y. H.
,
Kang
,
C. I.
, and
Tomizuka
,
M.
,
2005
, “
Adaptive and Optimal Rejection of Non-Repeatable Disturbance in Hard Disk Drives
,”
IEEE/ASME International Conference on Advanced Intelligent Mechatronics
, pp.
1
6
.
13.
Zheng
,
Q.
, and
Tomizuka
,
M.
,
2007
, “
Compensation of Dominant Frequency Components of Nonrepeatable Disturbance in Hard Disk Drives
,”
IEEE Trans. Magn.
,
43
(
9
), pp.
3756
3762
.
14.
Landau
,
I. D.
,
Constantinescu
,
A.
, and
Rey
,
D.
,
2005
, “
Adaptive Narrow Band Disturbance Rejection Applied to an Active Suspension—An Internal Model Principle Approach
,”
Automatica
,
41
(
4
), pp.
563
574
.
15.
Herzog
,
R.
,
Bühler
,
P.
,
Gähler
,
C.
, and
Larsonneur
,
R.
,
1996
, “
Unbalance Compensation Using Generalized Notch Filters in the Multivariable Feedback of Magnetic Bearings
,”
IEEE Trans. Control Syst. Technol.
,
4
(
5
), pp.
580
586
.
16.
Tomizuka
,
M.
,
Tsao
,
T. C.
, and
Chew
,
K. K.
,
1989
, “
Analysis and Synthesis of Discrete-Time Repetitive Controllers
,”
ASME J. Dyn. Syst. Meas. Control
,
111
(
3
), pp.
353
358
.
17.
Tsao
,
T. C.
, and
Tomizuka
,
M.
,
1994
, “
Robust Adaptive and Repetitive Digital Tracking Control and Application to a Hydraulic Servo for Noncircular Machining
,”
ASME J. Dyn. Syst. Meas. Control
,
116
(
1
), pp.
24
32
.
18.
Yu
,
S. H.
, and
Hu
,
J. S.
,
2000
, “
Asymptotic Rejection of Periodic Disturbances With Fixed or Varying Period
,”
ASME J. Dyn. Syst. Meas. Control
,
123
(
3
), pp.
324
329
.
19.
Tammi
,
K.
,
Hätönen
,
J.
, and
Daley
,
S.
,
2007
, “
Novel Adaptive Repetitive Algorithm for Active Vibration Control of a Variable-Speed Rotor
,”
J. Mech. Sci. Technol.
,
21
(
6
), pp.
855
859
.
20.
Wang
,
Y.
,
Wang
,
D.
,
Zhang
,
B.
, and
Zhou
,
K.
,
2007
, “
Fractional Delay Based Repetitive Control With Application to PWM DC/AC Converters
,”
IEEE
International Conference on Control Applications
, Singapore, Oct. 1–3, pp.
928
933
.
21.
Wang
,
Y.
,
Chu
,
K.
, and
Tsao
,
T. C.
,
2009
, “
An Analysis and Synthesis of Internal Model Principle Type Controllers
,”
American Control Conference
, St. Louis, MO, June 10–12, pp.
488
493
.
22.
Kang
,
C.
, and
Tsao
,
T. C.
,
2014
, “
Control of Magnetic Bearings With Plug-In Time-Varying Harmonic Resonators
,”
American Control Conference
, Portland, OR, June 4–6, pp.
4237
4242
.
23.
Brown
,
L. J.
, and
Zhang
,
Q.
,
2004
, “
Periodic Disturbance Cancellation With Uncertain Frequency
,”
Automatica
,
40
(
4
), pp.
631
637
.
24.
Bodson
,
M.
, and
Douglas
,
S. C.
,
1997
, “
Adaptive Algorithms for the Rejection of Sinusoidal Disturbance With Unknown Frequency
,”
Automatica
,
33
(
12
), pp.
2213
2221
.
25.
Tsao
,
T. C.
,
Qian
,
Y.-X.
, and
Nemani
,
M.
,
2000
, “
Repetitive Control for Asymptotic Tracking of Periodic Signals With an Unknown Period
,”
ASME J. Dyn. Syst. Meas. Control
,
122
(
2
), pp.
364
369
.
26.
Paden
,
B.
,
Morse
,
N.
, and
Smith
,
R.
,
1996
, “
Magnetic Bearing Experiment for Integrated Teaching and Research Laboratories
,”
IEEE
International Conference on Control Applications
, Dearborn, MI, Sept. 15–18, pp.
421
425
.
27.
Chu
,
K.
,
Wang
,
Y.
,
Wilson
,
J.
,
Lin
,
C. Y.
, and
Tsao
,
T. C.
,
2010
, “
Modeling and Control of a Magnetic Bearing System
,”
American Control Conference
, Baltimore, MD, June 30–July 2, pp.
2206
2211
.
28.
Tomizuka
,
M.
,
1987
, “
Zero Phase Error Tracking Algorithm for Digital Control
,”
ASME J. Dyn. Syst. Meas. Control
,
109
(
1
), pp.
65
68
.
29.
Butterworth
,
J. A.
,
Pao
,
L. Y.
, and
Abramovitch
,
D. Y.
,
2012
, “
Analysis and Comparison of Three Discrete-Time Feedforward Model-Inverse Control Techniques for Nonminimum-Phase Systems
,”
Mechatronics
,
22
(
5
), pp.
577
587
.
30.
Rigney
,
B. P.
,
Pao
,
L. Y.
, and
Lawrence
,
D. A.
,
2009
, “
Nonminimum Phase Dynamic Inversion for Settle Time Applications
,”
IEEE Trans. Control Syst. Technol.
,
17
(
5
), pp.
989
1005
.
You do not currently have access to this content.