Active magnetic bearing (AMB) is the device to support and control rotating shaft. Feedback linearization is one of the methods to compensate the system nonlinearity, and it is often used in the control of AMB. Some parameters in the electromagnetic force model have often been ignored or their parametric uncertainty from the nominal values has been calibrated; however, their influence on the stability has not been investigated. In this paper, the influence of the parametric uncertainty in the electromagnetic force model on the stability of AMB is investigated. The equilibrium positions and their stability are investigated and clarified analytically. Furthermore, the choice of the parameter value for improving the stability of AMB with feedback linearization is proposed, and its effectiveness is explained analytically. It is shown that the proposed choice of the parameter value also reduces the remained nonlinearity significantly. The validity of theoretical results and proposed choice of the parameter value are confirmed by experiment.

References

1.
Knight
,
J. D.
, and
Ecker
,
H.
,
1996
, “
Simulation of Nonlinear Dynamics in Magnetic Bearing
,”
Computer Simulation Conference, Portland
, OR, pp. 466–471.
2.
Chinta
,
M.
, and
Palazzolo
,
A. B.
,
1998
, “
Stability and Bifurcation of Rotor Motion in a Magnetic Bearing
,”
J. Sound Vib.
,
214
(
5
), pp.
793
803
.
3.
Steinschaden
,
N.
, and
Springer
,
H.
,
1999
, “
Some Nonlinear Effects of Magnetic Bearings
,”
ASME
Paper No. DETC99/VIB-8063. http://members.a1.net/nst.hsdpa/DETC99_VIB_8063.pdf
4.
Chang
,
S. C.
, and
Tung
,
P. C.
,
1999
, “
Nonlinear Identification of a Magnetic Bearing System With Closed Loop Control
,”
JSME Int. J. Ser. C
,
42
(
4
), pp.
982
990
.
5.
Ji
,
J. C.
,
Yu
,
L.
, and
Leung
,
A. Y. T.
,
2000
, “
Bifurcation Behavior of a Rotor Supported by Active Magnetic Bearing
,”
J. Sound Vib.
,
235
(
1
), pp.
133
151
.
6.
Ji
,
J. C.
, and
Hansen
,
C. H.
,
2001
, “
Non-Linear Oscillations of a Rotor in Active Magnetic Bearing
,”
J. Sound Vib.
,
240
(
4
), pp.
599
612
.
7.
Ji
,
J. C.
, and
Leung
,
A. Y. T.
,
2003
, “
Non-Linear Oscillation of a Rotor-Magnetic Bearing System Under Superharmonic Resonance Conditions
,”
Int. J. Non-Linear Mech.
,
38
(
6
), pp.
829
835
.
8.
Ji
,
J. C.
,
2003
, “
Dynamics of a Jeffcott Rotor-Magnetic Bearing System With Time Delay
,”
Int. J. Non-Linear Mech.,
38(
9
), pp.
1387
1401
.
9.
Ji
,
J. C.
,
2003
, “
Stability and Hopf Bifurcation of a Magnetic Bearing System With Time Delays
,”
J. Sound Vib.
,
259
(
4
), pp.
845
856
.
10.
Ho
,
Y. S.
,
Liu
,
H.
, and
Yu
,
L.
, “
Effect of Thrust Magnetic Bearing on Stability and Bifurcation of a Flexible Rotor Active Magnetic Bearing System
,”
ASME. J. Vib. Acoust.
,
125
(
3
), pp.
307
316
.
11.
Polajzer
,
B.
,
Stumberger
,
G.
,
Ritonja
,
J.
,
Tezak
,
O.
,
Dolinar
,
D.
, and
Hameyer
,
K.
,
2004
, “
Impact of Magnetic Nonlinearities and Cross-Coupling Effects on Properties of Radial Active Magnetic Bearings
,”
IEEE Trans. Magn.
,
40
(
2
), pp.
798
801
.
12.
Inoue
,
T.
,
Sugawara
,
Y.
, and
Sugiyama
,
M.
,
2009
, “
Modeling and Nonlinear Vibration Analysis of a Rigid Rotor System Supported by the Magnetic Bearing (Effects of Delays of Both Electric Current and Magnetic Flux)
,”
ASME J. Appl. Mech.
,
77
(
1
), p.
011005
.
13.
Inoue
,
T.
, and
Sugawara
,
Y.
,
2010
, “
Nonlinear Vibration Analysis of a Rigid Rotating Shaft Supported by the Magnetic Bearing (Influence of the Integral Feedback in the PID Control of the Vertical Shaft)
,”
J. Syst. Des. Dyn.
,
4
(
3
), pp.
471
483
.
14.
Nijmeijer
,
H.
, and
Van der Schaft
,
A.
,
1990
,
Nonlinear Dynamical Control Systems
, Vol.
175
,
Springer-Verlag
,
New York
.
15.
Ueno
,
S.
, and
Necip Sahinkaya
,
M.
, 2012, “
Variable Bias Current Control and Adaptive Parameter Estimation in Active Magnetic Bearings
,”
13th International Symposium on Magnetic Bearings, Arlington, VA
, Aug. 6–9, p.
301
.
16.
Chen
,
M.
, and
Knospe
,
C. R.
,
2005
, “
Feedback Linearization of Active Magnetic Bearings: Current-Mode Implementation
,”
IEEE/ASME Trans. Mechatronics
,
10
(
6
), pp.
632
639
.
17.
Kin
,
J.-L.
, and
Tho
,
B.-C.
,
1998
, “
Analysis and μ-Based Controller Design for an Electromagnetic Suspension System
,”
IEEE Trans. Educ.
,
41
(
2
), pp.
116
129
.
18.
Lindlau
,
J. D.
, and
Knospe
,
C. R.
,
2002
, “
Feedback Linearization of an Active Magnetic Bearing With Voltage Control
,”
IEEE Trans. Control Syst. Technol.
,
10
(
1
), pp.
21
31
.
19.
Yang
,
Z.-J.
,
Miyazaki
,
K.
,
Kanae
,
S.
, and
Wada
,
K.
,
2004
, “
Robust Position Control of a Magnetic Levitation System Via Dynamic Surface Control Technique
,”
IEEE Trans. Ind. Electron.
,
51
(
1
), pp.
26
34
.
20.
Minihan
,
T. P.
,
Lei
,
S.
,
Sun
,
G.
,
Palazzolo
,
A.
,
Kascak
,
A. F.
, and
Calvert
,
T.
,
2003
, “
Large Motion Tracking Control for Thrust Magnetic Bearings With Fuzzy Logic, Sliding Mode, and Direct Linearization
,”
J. Sound Vib.
,
263
(
3
), pp.
549
567
.
21.
Ishida
,
Y.
, and
Yamamoto
,
T.
,
2012
, “
Linear and Nonlinear Rotordynamics, a Modearn Treatment With Applications
,”
Second Enlarged and Improved Edition
,
Wiley-VCH
, Hoboken, NJ.
22.
Ahrens
,
M.
,
Kucera
,
L.
, and
Larsonneur
,
R.
,
1996
, “
Performance of a Magnetically Suspended Flywheel Energy Storage Device
,”
IEEE Trans. Control Syst. Technol.
,
4
(
5
), pp.
494
502
.
23.
JSME
,
1995
,
The Basis and Application of the Magnetic Bearings
, Japan Society Mechanical Engineers, Tokyo, Japan (in Japanese).
24.
Schweitzer
,
G.
,
Bleuler
,
H.
, and
Traxler
,
A.
, 1994,
Active Magnetic Bearings
,
Hochschulverlag AG an der ETH
,
Zurich, Switzerland
.
25.
IEEJ
,
1993
,
Magnetic Levitation and Magnetic Bearings
,
Japan Society of Mechanical Engineers, Tokyo, Japan
(in Japanese).
26.
Morishida
,
M.
,
Azukizawa
,
T.
,
Kanda
,
S.
,
Tamura
,
N.
, and
Yokoyama
,
T.
,
1989
, “
A New Maglev System for Magnetically Levitated Carrier System
,”
IEEE Trans. Veh. Technol.
,
38
(
4
), pp.
230
236
.
27.
Shih-Kang
,
K.
,
Ximin
,
S.
, and
Chia-Hsiang
,
M.
,
2003
, “
Large Travel Ultra Precision x – y − θ Motion Control of a Magnetic-Suspension Stage
,”
IEEE/ASME Trans. Mechatronics
,
8
(
3
), pp.
334
341
.
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