Abstract
Fault tolerance is one of the practical and effective approaches to improve the reliability of magnetic bearings. The linearization of the electromagnetic force (EMF) from the redundant structures is the crucial basis of the design of a fault-tolerant controller. In this paper, we propose an accurate linearization approach for the heteropolar magnetic bearings with redundant structures by solving the Taylor series expansion equation of the current distribution matrix (W) in the nonequilibrium position and introducing a set of displacement compensation matrices to establish a unified accurate EMF model including the controlled current and rotor position. The proposed approach can effectively decrease the EMF error between the actual physical model and the linearized model compared with the existing methods for the consideration of the rotor position. Moreover, the solutions of the current distribution matrix and the relevant optimization approach have been presented on the basis of the proposed approach to help to design a high-performance fault-tolerant controller in the entire rotor displacement range. The numerical results demonstrated the noticeable accuracy advantages of the proposed EMF model.
Issue Section:
Research Papers
References
1.
Keogh
,
P.
, and
Cole
,
M. O. T.
, 2009
, “
Dynamics and Control Issues for Fault Tolerance
,” Magnetic Bearings
,
G.
Schweitzer
, and
E. H.
Maslen
, eds., Springer-Verlag Berlin and Heidelberg GmbH & Co. K, Switzerland, pp. 407
–433
.10.1007/978-3-642-00497-1_142.
Cheng
,
X.
,
Zhang
,
L.
,
Zhou
,
R.
,
Song
,
S.
,
Wang
,
B.
, and
Liu
,
H.
, 2017
, “
Analysis of Output Precision Characteristics of Digital Switching Power Amplifier in Active Magnetic Bearing System
,” Automatika
,
58
(2
), pp. 205
–215
.10.1080/00051144.2017.13901943.
Park
,
Y.
, 2014
, “
Design and Implementation of an Electromagnetic Levitation System for Active Magnetic Bearing Wheels
,” IET Control Theory A
,
8
(2
), pp. 139
–148
.10.1049/iet-cta.2013.04504.
Ren
,
Y.
, and
Fang
,
J.
, 2014
, “
High-Precision and Strong-Robustness Control for an MSCMG Based on Modal Separation and Rotation Motion Decoupling Strategy
,” IEEE Trans. Ind. Electron.
,
61
(3
), pp. 1539
–1551
.10.1109/TIE.2013.22571475.
Cheng
,
X.
,
Wang
,
B.
,
Chen
,
Q.
,
Zhang
,
L.
,
Liu
,
H.
, and
Song
,
S.
, 2017
, “
A Unified Design and the Current Ripple Characteristic Analysis of Digital Switching Power Amplifier in Active Magnetic-Levitated Bearings
,” Int. J. Appl. Electromagn. Mech.
,
55
(3
), pp. 391
–407
.10.3233/JAE-1700336.
Allaire
,
P. E.
,
Fittro
,
R. L.
,
Maslen
,
E. H.
, and
Wakefield
,
W. C.
, 1997
, “
Measured Force/Current Relations in Solid Magnetic Thrust Bearings
,” ASME J. Eng. Gas Turbines Power
,
119
(1
), pp. 137
–142
.10.1115/1.28155377.
Maslen
,
E. H.
, and
Meeker
,
D. C.
, 1995
, “
Fault Tolerance of Magnetic Bearings by Generalized Bias Current Linearization
,” IEEE Trans. Magn.
,
31
(3
), pp. 2304
–2314
.10.1109/20.3762298.
Meeker
,
D. C.
, 1996
, “
Optimal Solutions to the Inverse Problem in Quadratic Magnetic Actuators
,” Ph.D. dissertation
, University of Virginia, Charlottesville, VA.http://www.femm.info/dmeeker/pdf/cnd.pdf9.
Maslen
,
E. H.
,
Sortore
,
C. K.
,
Gillies
,
G. T.
,
Williams
,
R. D.
,
Fedigan
,
S. J.
, and
Aimone
,
R. J.
, 1999
, “
Fault Tolerant Magnetic Bearings
,” ASME J. Eng. Gas Turbines Power
,
121
(3
), pp. 504
–508
.10.1115/1.281850110.
Na
,
U. J.
, and
Palazzolo
,
A. B.
, 2000
, “
Optimized Realization of Fault-Tolerant Heteropolar Magnetic Bearings
,” ASME J. Vib. Acoust.
,
122
(3
), pp. 209
–221
.10.1115/1.130307211.
Na
,
U. J.
,
Palazzolo
,
A. B.
, and
Provenza
,
A.
, 2002
, “
Test and Theory Correlation Study for a Flexible Rotor on Fault-Tolerant Magnetic Bearings
,” ASME J. Vib. Acoust.
,
124
(3
), pp. 359
–366
.10.1115/1.146765212.
Noh
,
M. D.
,
Cho
,
S.-R.
,
Kyung
,
J.-H.
,
Ro
,
S.-K.
, and
Park
,
J.-K.
, 2005
, “
Design and Implementation of a Fault-Tolerant Magnetic Bearing System for Turbo-Molecular Vacuum Pump
,” IEEE-ASME Trans. Mechatronics
,
10
(6
), pp. 626
–631
.10.1109/TMECH.2005.85983013.
Na
,
U. J.
, and
Palazzolo
,
A. B.
, 2001
, “
The Fault-Tolerant Control of Magnetic Bearings With Reduced Controller Outputs
,” ASME J. Dyn. Sys. Meas. Control
,
123
(2
), pp. 219
–224
.10.1115/1.136935614.
Meeker
,
D. C.
,
Maslen
,
E. H.
, 1996
,
M. D.
, and
Noh
, “
An Augmented Circuit Model for Magnetic Bearings Including Eddy Currents, Fringing and Leakage
,” IEEE Trans. Magn.
,
32
(4
), pp. 3219
–3227
.10.1109/20.50838515.
Na
,
U. J.
, and
Palazzolo
,
A. B.
, 2000
, “
Fault Tolerance of Magnetic Bearings With Material Path Reluctances and Fringing Factors
,” IEEE Trans. Magn.
,
36
, pp. 3939
–3946
.10.1109/20.91434316.
Meeker
,
D. C.
,
Filatov
,
A. V.
, and
Maslen
,
E. H.
, 2004
, “
Effect of Magnetic Hysteresis on Rotational Losses in Heteropolar Magnetic Bearings
,” IEEE Trans. Magn.
,
40
(5
), pp. 3302
–3307
.10.1109/TMAG.2004.83166417.
Kasarda
,
M. E. F.
,
Allaire
,
P. E.
,
Norris
,
P. M.
,
Mastrangelo
,
C.
, and
Maslen
,
E. H.
, 1999
, “
Experimentally Determined Rotor Power Losses in Homopolar and Heteropolar Magnetic Bearings
,” ASME J. Eng. Gas Turbines Power
,
121
(4
), pp. 697
–702
.10.1115/1.281852918.
Sortore
,
C. K.
,
Allaire
,
P. E.
,
Maslen
,
E. H.
, and Humphris, R. R., 1990
, “
Permanent Magnet Biased Magnetic Bearings—Design, Construction and Testing
,” Proceedings of the Second International Symposium on Magnetic Bearings
,
Tokyo, Japan
, July 12–14, pp. 175
–182
.19.
Allaire
,
P. E.
,
Maslen
,
E. H.
,
Humphris
,
R. R.
, Sortore, C. K., and Studer, P. A., 1992
, “
Low Power Magnetic Bearing Design for High Speed Rotating Machinery
,” Proceedings of the NASA International Symposium on Magnetic Suspension Technology
, Charlottesville, VA, May 1, pp. 317
–329
.https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19920018496.pdf20.
Maslen
,
E. H.
,
Allaire
,
P. E.
,
Noh
,
M. D.
, and
Sortore
,
C. K.
, 1996
, “
Magnetic Bearing Design for Reduced Power Consumption
,” ASME J. Tribol.
,
118
(4
), pp. 839
–846
.10.1115/1.283161721.
Lee
,
A. C.
,
Hsiao
,
F. Z.
, and
Ko
,
D.
, 1994
, “
Analysis and Testing of a Magnetic Bearing With Permanent Magnets for Bias
,” JSME Int. J. Ser. C
,
37
, pp. 774
–782
.10.1299/jsmec1993.37.77422.
Lee
,
A. C.
,
Hsiao
,
F. Z.
, and
Ko
,
D.
, 1994
, “
Performance Limits of Permanent-Magnet-Biased Magnetic Bearings
,” JSME Int. J. Ser. C
,
37
, pp. 783
–794
.10.1299/jsmec1993.37.78323.
Fan
,
Y.
,
Lee
,
A.
, and
Hsiao
,
F.
, 1997
, “
Design of a Permanent/Electromagnetic Magnetic Bearing-Controlled Rotor System
,” J. Frankl. Inst.
,
334
(3
), pp. 337
–356
.10.1016/S0016-0032(96)00101-924.
Na
,
U. J.
, 2004
, “
Fault Tolerance of Homopolar Magnetic Bearings
,” J. Sound Vib.
,
272
(3–5
), pp. 495
–511
.10.1016/S0022-460X(03)00379-125.
Won
,
J. S.
, and
Na
,
U. J.
, 2006
, “
Design of Flux Invariant, Fault Tolerant Homopolar Magnetic Bearings
,” SICI-ICASE International Joint Conference
,
Busan, Korea
, Oct. 18–21, pp. 3470
–3473
.10.1109/SICE.2006.31516626.
Li
,
M.-H.
,
Palazzolo
,
A. B.
,
Kenny
,
A.
,
Provenza
,
A. J.
,
Beach
,
R. F.
, and
Kascak
,
A. F.
, 2004
, “
Fault Tolerant Homopolar Magnetic Bearings
,” IEEE Trans. Magn.
,
40
(5
), pp. 3308
–3318
.10.1109/TMAG.2004.83342827.
Phi Nguyen
,
N.
, and
Hong
,
S. K.
, 2018
, “
Sliding Mode Thau Observer for Actuator Fault Diagnosis of Quadcopter UAVs
,” Appl. Sci.
,
8
(10
), p. 1893
.10.3390/app810189328.
Nguyen
,
N.
, and
Hong
,
S.
, 2019
, “
Fault Diagnosis and Fault-Tolerant Control Scheme for Quadcopter UAVs With a Total Loss of Actuator
,” Energies
,
12
(6
), p. 1139
.10.3390/en1206113929.
Glowacz
,
A.
, 2018
, “
Recognition of Acoustic Signals of Commutator Motors
,” Appl. Sci.
,
8
(12
), p. 2630
.10.3390/app812263030.
Shahnazari
,
H.
, and
Mhaskar
,
P.
, 2018
, “
Actuator and Sensor Fault Detection and Isolation for Nonlinear Systems Subject to Uncertainty
,” Int. J. Robust Nonlinear Control
,
28
(6
), pp. 1996
–2013
.10.1002/rnc.399631.
Zhao
,
K.
,
Li
,
P.
,
Zhang
,
C.
,
Li
,
X.
,
He
,
J.
, and
Lin
,
Y.
, 2017
, “
Sliding Mode Observer-Based Current Sensor Fault Reconstruction and Unknown Load Disturbance Estimation for PMSM Driven System
,” Sensors
,
17
(12
), p. 2833
.10.3390/s1712283332.
Yan
,
X.
,
Sun
,
Z.
,
Zhao
,
J.
,
Shi
,
Z.
, and
Zhang
,
C.-A.
, 2019
, “
Fault Diagnosis of Active Magnetic Bearing–Rotor System Via Vibration Images
,” Sensors
,
19
(2
), p. 244
.10.3390/s1902024433.
Cole
,
M. O. T.
,
Keogh
,
P. S.
,
Sahinkaya
,
M. N.
, and
Burrows
,
C. R.
, 2004
, “
Towards Fault-Tolerant Active Control of Rotor-Magnetic Bearing Systems
,” Control Eng. Pract.
,
12
(4
), pp. 491
–501
.10.1016/S0967-0661(03)00173-434.
Na
,
U. J.
, 2005
, “
Fault Tolerant Control of Magnetic Bearings With Force Invariance
,” KSME J. Mech. Sci. Technol.
,
19
(3
), pp. 731
–742
.10.1007/BF0291612235.
Na
,
U. J.
, 2006
, “
Fault Tolerant Homopolar Magnetic Bearings With Flux Invariant Control
,” KSME J. Mech. Sci. Technol.
,
20
(5
), pp. 643
–651
.10.1007/BF0291598136.
Agarwal
,
P. K.
, and
Chand
,
S.
, 2009
, “
Fault Tolerant Control of Three-Pole Active Magnetic Bearing
,” Expert Syst. Appl.
,
36
(10
), pp. 12592
–12604
.10.1016/j.eswa.2009.05.05237.
Cheng
,
X.
,
Chen
,
Q.
,
Zeng
,
H.
,
Wang
,
X.
, and
Zhou
,
R.
, 2016
, “
Reconfiguration Rules for Loosely-Coupled Redundant Supporting Structure in Radial Magnetic Bearings
,” Int. J. Appl. Electromagn. Mech.
,
51
(2
), pp. 91
–106
.10.3233/JAE-15010338.
Cheng
,
X.
,
Liu
,
H.
,
Song
,
S.
,
Hu
,
Y.
,
Wang
,
B.
, and
Li
,
Y.
, 2017
, “
Reconfiguration of Tightly-Coupled Redundant Supporting Structure in Active Magnetic Bearings Under the Failures of Electromagnetic Actuators
,” Int. J. Appl. Electromagn. Mech.
,
54
(3
), pp. 421
–432
.10.3233/JAE-16011339.
Meeker
,
D.
, 2017
, “
A Generalized Unbiased Control Strategy for Radial Magnetic Beatings
,” Actuators
,
6
(1
), p. 1
.10.3390/act6010001Copyright © 2020 by ASME
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