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.
Issue Section:
Research Papers
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
.10.1080/0954482992613623.
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)00068-45.
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)00087-36.
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/s00202-009-0121-210.
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)00101-913.
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
.10.1109/4235.99601715.
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.2008.92579816.
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.2007.12.02820.
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.2003.80941525.
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.2003.80941526.
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
.Copyright © 2015 by ASME
You do not currently have access to this content.
