Multiple objective genetic algorithms (MOGAs) simultaneously optimize a control law and geometrical features of a set of homopolar magnetic bearings (HOMB) supporting a generic flexible, spinning shaft. The minimization objectives include shaft dynamic response (vibration), actuator mass and total actuator power losses. Levitation of the spinning rotor and dynamic stability are constraint conditions for the control law search. Nonlinearities include magnetic flux saturation, and current and voltage limits. Pareto frontiers were applied to identify the best-compromised solution. Mass and vibration reductions improve with a two control law approach.

References

References
1.
Schweitzer
,
G.
, and
Maslen
,
E. H.
,
2009
,
Magnetic Bearings: Theory, Design and Application to Rotating Machinery (POD), Springer
, Berlin, Heidelberg, Germany.
2.
Carlson-Skalak
,
S.
,
Maslen
,
E.
, and
Teng
,
Y.
,
1999
, “
Magnetic Bearing Actuator Design Using Genetic Algorithms
,”
J. Eng. Des.
,
10
(
2
), pp.
143
164
.10.1080/095448299261362
3.
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
), p.
20
.
4.
Chang
,
H.
, and
Chung
,
S.-C.
,
2002
, “
Integrated Design of Radial Active Magnetic Bearing Systems Using Genetic Algorithms
,”
Mechatronics
,
12
(
1
), pp.
19
36
.10.1016/S0957-4158(00)00068-4
5.
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
.10.1016/S0967-0661(00)00087-3
6.
Chen
,
H.-C.
,
2008
, “
Optimal Fuzzy PID Controller Design of an Active Magnetic Bearing System Based on Adaptive Genetic Algorithms
,”
IEEE Machine Learning and Cybernetics, International Conference
, Kunming, China, July 12–15, pp.
2054
2060
.
7.
Chen
,
H.-C.
,
2008
, “
Adaptive Genetic Algorithm Based Optimal PID Controller Design of an Active Magnetic Bearing System
,”
IEEE ICICIC'08 3rd International Conference Innovative Computing Information and Control
, Dalian, Liaoning, China, June 18–20, pp.
603
603
.
8.
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
.
9.
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
.10.1007/s00202-009-0121-2
10.
Hsiao
,
F. Z.
,
Fan
,
C. C.
,
Chieng
,
W. H.
, and
Lee
,
A. C.
,
1996
, “
Optimum Magnetic Bearing Design Considering Performance Limitations
,”
JSME Int. J. Ser. C
,
39
(
3
), pp.
586
596
.
11.
Lee
,
A.-C.
,
Hsiao
,
F.-Z.
, and
Ko
,
D.
,
1994
, “
Performance Limits of Permanent-Magnet-Biased Magnetic Bearings
,”
JSME Int. J. Ser. C,
37-C
(
4
), pp.
783
794
.
12.
Fan
,
Y.-H.
,
Lee
,
A.-C.
, and
Hsiao
,
F.-Z.
,
1997
, “
Design of a Permanent/Electromagnetic Magnetic Bearing-Controlled Rotor System
,”
J. Franklin Inst.
,
334
(
3
), pp.
337
356
.10.1016/S0016-0032(96)00101-9
13.
Knowles
,
J.
, and
Corne
,
D.
,
1999
, “
The Pareto Archived Evolution Strategy: A New Baseline Algorithm for Pareto Multiobjective Optimisation
,”
IEEE Evolutionary Computation, CEC 99, Proceedings of the 1999 Congress
, Washington, DC, July 6–9.
14.
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
.10.1109/4235.996017
15.
Li
,
H.
, and
Zhang
,
Q.
,
2009
, “
Multiobjective Optimization Problems With Complicated Pareto Sets, MOEA/D, and NSGA-II
,”
IEEE Trans.Evol. Comput.
,
13
(
2
), pp.
284
302
.10.1109/TEVC.2008.925798
16.
Sharma
,
D.
,
Kumar
,
A.
,
Deb
,
K.
, and
Sindhya
,
K.
,
2007
, “
Hybridization of SBX Based NSGA-II and Sequential Quadratic Programming for Solving Multi-Objective Optimization Problems
,”
IEEE Evolutionary Computation, CEC 2007, IEEE Congress
, Singapore, Sept. 25–28, pp.
3003
3010
.
17.
Deb
,
K.
, and
Karthik
,
S.
, “
Dynamic Multi-Objective Optimization and Decision-Making Using Modified NSGA-II: A Case Study on Hydro-Thermal Power Scheduling
,”
Evolutionary Multi-Criterion Optimization
,
Springer
, Berlin, Heidelberg, Germany, pp.
803
817
.
18.
Lin
,
C.-T.
, and
Jou
,
C.-P.
,
2000
, “
GA-Based Fuzzy Reinforcement Learning for Control of a Magnetic Bearing System
,”
IEEE Trans. Syst., Man, Cybernetics, Part B
,
30
(
2
), pp.
276
289
.
19.
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
.10.1016/j.jsv.2007.12.028
20.
Gen
,
M.
, and
Cheng
,
R.
,
2000
,
Genetic Algorithms and Engineering Optimization
,
Wiley
, Hoboken, NJ.
21.
Sivaraj
,
R.
, and
Ravichandran
,
T.
,
2011
, “
A Review of Selection Methods in Genetic Algorithm
,”
Int. Eng. Sci. Technol.
,
3
(
5
), pp. 3792–3797.
22.
Kasarda
,
M. E.
,
1997
, “
The Measurement and Characterization of Power Losses in High Speed Magnetic Bearings
,” University of Virginia, Charlottesville, VA.
23.
Carpenter Technology
,
Magnetic Alloys
,
Carpenter Technology, Reading
,
PA
.
24.
Standard
,
A.
,
2004
, “617, 2002,”
Axial and Centrifugal Compressors and Expander-Compressors for Petroleum, Chemical and Gas Industry Services
,
7th ed.
,
American Petroleum Institute
,
Washington, DC
.10.1109/TIE.2003.809415
25.
Kim
,
O.-S.
,
Lee
,
S.-H.
, and
Han
,
D.-C.
,
2003
, “
Positioning Performance and Straightness Error Compensation of the Magnetic Levitation Stage Supported by the Linear Magnetic Bearing
,”
IEEE Trans.Ind. Electron.
,
50
(
2
), pp.
374
378
.10.1109/TIE.2003.809415
26.
Levine
,
J.
,
Lottin
,
J.
, and
Ponsart
,
J.-C.
,
1996
, “
A Nonlinear Approach to the Control of Magnetic Bearings
,”
IEEE Trans. Control Syst. Technol.
,
4
(
5
), pp.
524
544
.
You do not currently have access to this content.