Nonlinear vibrations and their control are critical in improving the magnetic bearings system performance and in the more widely spread use of magnetic bearings system. Multiple objective genetic algorithms (MOGAs) simultaneously optimize a vibration control law and geometrical features of a set of nonlinear magnetic bearings supporting a generic flexible, spinning shaft. The objectives include minimization of the actuator mass, minimization of the power loss, and maximization of the external static load capacity of the rotor. Levitation of the spinning rotor and the nonlinear vibration amplitude by rotor unbalance are constraint conditions according to International Organization for Standardization (ISO) specified standards for the control law search. The finite element method (FEM) was applied to determine the temperature distribution and identify the hot spot of the actuator during steady-state operation. Nonlinearities include magnetic flux saturation, and current and voltage limits of power amplifiers. Pareto frontiers were applied to identify and visualize the best-compromised solutions, which give a most compact design with minimum power loss whose vibration amplitudes satisfy ISO standards.

References

1.
Provenza
,
A. J.
,
Montague
,
G. T.
,
Jansen
,
M. J.
,
Palazzolo
,
A. B.
, and
Jansen
,
R. H.
,
2005
, “
High Temperature Characterization of a Radial Magnetic Bearing for Turbomachinery
,”
ASME J. Eng. Gas Turbines Power
,
127
(
2
), pp.
437
444
.
2.
Chinta
,
M.
, and
Palazzolo
,
A.
,
1998
, “
Stability and Bifurcation of Rotor Motion in a Magnetic Bearing
,”
J. Sound Vib.
,
214
(
5
), pp.
793
803
.
3.
El Hajjaji
,
A.
, and
Ouladsine
,
M.
,
2001
, “
Modeling and Nonlinear Control of Magnetic Levitation Systems
,”
IEEE Trans. Ind. Electron.
,
48
(
4
), pp.
831
838
.
4.
Kang
,
K.
, and
Palazzolo
,
A.
,
2012
, “
Homopolar Magnetic Bearing Saturation Effects on Rotating Machinery Vibration
,”
IEEE Trans. Magn.
,
48
(
6
), pp.
1984
1994
.
5.
Defoy
,
B.
,
Alban
,
T.
, and
Mahfoud
,
J.
,
2014
, “
Experimental Assessment of a New Fuzzy Controller Applied to a Flexible Rotor Supported by Active Magnetic Bearings
,”
ASME J. Vib. Acoust.
,
136
(
5
), p.
051006
.
6.
Carlson-Skalak
,
S.
,
Maslen
,
E.
, and
Teng
,
Y.
,
1999
, “
Magnetic Bearing Actuator Design Using Genetic Algorithms
,”
J. Eng. Des.
,
10
(
2
), pp.
143
164
.
7.
Chang
,
H.
, and
Chung
,
S.-C.
,
2002
, “
Integrated Design of Radial Active Magnetic Bearing Systems Using Genetic Algorithms
,”
Mechatronics
,
12
(
1
), pp.
19
36
.
8.
Schroder
,
P.
,
Green
,
B.
,
Grum
,
N.
, and
Fleming
,
P.
,
2001
, “
On-Line Evolution of Robust Control Systems: An Industrial Active Magnetic Bearing Application
,”
Control Eng. Pract.
,
9
(
1
), pp.
37
49
.
9.
Chen
,
H.-C.
,
2008
, “
Optimal Fuzzy PID Controller Design of an Active Magnetic Bearing System Based on Adaptive Genetic Algorithms
,”
IEEE
International Conference on Machine Learning and Cybernetics
, June 12–15, pp.
2054
2060
.
10.
Chen
,
H.-C.
,
2008
, “
Adaptive Genetic Algorithm Based Optimal PID Controller Design of an Active Magnetic Bearing System
,”
3rd International Conference on IEEE Innovative Computing Information and Control,
ICICIC'08
, June 18–20, pp.
603
603
.
11.
Chang
,
L.-Y.
, and
Chen
,
H.-C.
,
2009
, “
Tuning of Fractional PID Controllers Using Adaptive Genetic Algorithm for Active Magnetic Bearing System
,”
WSEAS Trans. Syst.
,
8
(
1
), pp.
158
167
.
12.
Jastrzębski
,
R. P.
, and
Pöllänen
,
R.
,
2009
, “
Centralized Optimal Position Control for Active Magnetic Bearings: Comparison With Decentralized Control
,”
Electr. Eng.
,
91
(
2
), pp.
101
114
.
13.
Deb
,
K.
,
Pratap
,
A.
,
Agarwal
,
S.
, and
Meyarivan
,
T.
,
2002
, “
A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II
,”
IEEE Trans. Evol. Comput.
,
6
(
2
), pp.
182
197
.
14.
Zitzler
,
E.
,
Laumanns
,
M.
,
Thiele
,
L.
,
Zitzler
,
E.
,
Zitzler
,
E.
,
Thiele
,
L.
, and
Thiele
,
L.
,
2001
, “
SPEA2: Improving the Strength Pareto Evolutionary Algorithm
,” Eidgenössische Technische Hochschule Zürich (ETH), Institut für Technische Informatik und Kommunikationsnetze (TIK), Zurich, Switzerland.
15.
Watanabe
,
S.
,
Hiroyasu
,
T.
, and
Miki
,
M.
, 2003, “
NCGA: Neighborhood Cultivation Genetic Algorithm for Multi-Objective Optimization Problems
,”
GECCO Late Breaking Papers
, pp.
458
465
.
16.
Shelke
,
S.
, and
Chalam
,
R.
,
2011
, “
Optimum Power Loss Analysis of Radial Magnetic Bearing Using Multi-Objective Genetic Algorithm
,”
Int. J. Comput. Appl.
,
27
(
6
), pp. 20–27.
17.
Rao
,
J. S.
, and
Tiwari
,
R.
,
2009
, “
Design Optimization of Double-Acting Hybrid Magnetic Thrust Bearings With Control Integration Using Multi-Objective Evolutionary Algorithms
,”
Mechatronics
,
19
(
6
), pp.
945
964
.
18.
Zhong
,
W.
, and
Palazzolo
,
A.
,
2015
, “
Magnetic Bearing Rotordynamic System Optimization Using Multi-Objective Genetic Algorithms
,”
ASME J. Dyn. Syst. Meas. Control
,
137
(
2
), p.
021012
.
19.
ISO
,
2004
, “
Mechanical Vibration-Vibrations of Rotating Machinery Equipped With Active Magnetic Bearings Part—2: Evaluation of Vibration
,” International Organization for Standardization, Geneva, Switzerland, Standard, No. 14839-2: 2004.
20.
ISO
,
2004
, “
Mechanical Vibration-Vibration of Rotating Machinery Equipped With Active Magnetic Bearings Part—3: Evaluation of Stability Margin
,” Geneva, Switzerland, ISO Standard No. 14839-3: 2006 (E).
21.
Lei
,
S. L.
, and
Palazzolo
,
A.
,
2008
, “
Control of Flexible Rotor Systems With Active Magnetic Bearings
,”
J. Sound Vib.
,
314
(
1–2
), pp.
19
38
.
22.
Kasarda
,
M. E.
,
1997
,
The Measurement and Characterization of Power Losses in High Speed Magnetic Bearings
,
University of Virginia
,
Charlottesville, VA
.
23.
Haupt
,
R. L.
, and
Werner
,
D. H.
,
2007
,
Genetic Algorithms in Electromagnetics
,
Wiley
, Hoboken, NJ.
24.
Gen
,
M.
, and
Cheng
,
R.
,
2000
, Genetic Algorithms and Engineering Optimization,
Wiley
, Hoboken, NJ.
25.
Sivaraj
,
R.
, and
Ravichandran
,
T.
,
2011
, “
A Review of Selection Methods in Genetic Algorithm
,”
Int. J. Eng. Sci. Technol. (IJEST)
,
3
(
5
), pp.
3792
3797
.
26.
Schweitzer
,
G.
, and
Maslen
,
E. H.
, eds.,
2009
, Magnetic Bearings: Theory, Design and Application to Rotating Machinery (POD), Springer, Zurich, Switzerland.
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