This paper considers two issues in the vibration of rotating machines, namely, control of rotor vibration and control of the forces transmitted to the base. An adaptive multi-objective method is developed to tackle these issues simultaneously using magnetic bearings. A two-stage weighting strategy is developed, involving base weightings calculated by using a singular value decomposition of the system’s receptance matrices and an adjustable single weighting parameter tuned automatically to shift the balance between the two objective functions in accordance with performance specifications. This new real-time controller does not require measurements in addition to those required for the open-loop adaptive strategy. Frequency and time domain simulations of an existing experimental rig are used to assess the effectiveness of the proposed multi-objective adaptive controller as a precursor to an experimental study.
1.
Schweitzer
, G.
, Bleuler
, H.
, and Traxler
, A.
, 1994, Active Magnetic Bearings—Basics, Properties and Applications, vdf Hochschulverlag AG, ETH Zurich.2.
Schweitzer
, G.
, 2002, “Active Magnetic Bearings—Chances and Limitations
,” IFToMM Sixth International Conference on Rotor Dynamics
, Sydney, Australia, Vol. 1
, pp. 1
–14
.3.
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.
0967-0661, 12
(4
), pp. 491
–501
.4.
Sahinkaya
, M. N.
, Cole
, M. O. T.
, and Burrows
, C. R.
, 2001, “Fault Detection and Tolerance in Synchronous Vibration Control of Rotor-Magnetic Bearing Systems
,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
0954-4062, 215
(12
), pp. 1401
–1416
.5.
Schweitzer
, G.
, 2005, “Safety and Reliability Aspects for Active Magnetic Bearing Applications—A Survey
,” Proceedings of the Institution of Mechanical Engineers Part I-Journal of Systems and Control Engineering
, 219
(6
), pp. 383
–392
.6.
Burrows
, C. R.
, and Sahinkaya
, M. N.
, 1983, “Vibration Control of Multi-Mode Rotor-Bearing Systems
,” Proc. R. Soc. London, Ser. A
, 386
(1790
), pp. 77
–94
.7.
Sahinkaya
, M. N.
, and Burrows
, C. R.
, 1985, “Control of Stability and the Synchronous Vibration of a Flexible Rotor Supported on Oil-Film Bearings
,” ASME J. Dyn. Syst., Meas., Control
, 107
(2
), pp. 139
–144
.8.
Burrows
, C. R.
, Sahinkaya
, M. N.
, and Clements
, S.
, 1989, “Active Vibration Control of Flexible Rotors: An Experimental and Theoretical Study
,” Proc. R. Soc. London, Ser. A
, 422
(1862
), pp. 123
–146
.9.
Knospe
, C. R.
, Hope
, R. W.
, Fedigan
, S. J.
, and Williams
, R. D.
, 1995, “Experiments in the Control of Unbalance Response Using Magnetic Bearings
,” Mechatronics
, 5
(4
), pp. 385
–400
.10.
Baun
, D. O.
, Maslen
, E. H.
, Knospe
, C. R.
, and Flack
, R. D.
, 2002, “A Multiple Harmonic Open-Loop Controller for Hydro/Aerodynamic Force Measurements in Rotating Machinery Using Magnetic Bearings
,” ASME J. Eng. Gas Turbines Power
, 124
(4
), pp. 827
–834
.11.
Knospe
, C. R.
, and Tamer
, S. M.
, 1997, “Experiments in Robust Control of Rotor Unbalance Response Using Magnetic Bearings
,” Mechatronics
, 7
(3
), pp. 217
–229
.12.
Yu
, Z.
, Meng
, L. T.
, and King
, L. M.
, 1998, “Electromagnetic Bearing Actuator for Active Vibration Control of a Flexible Rotor
,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
, 212
(8
), pp. 705
–716
.13.
Keogh
, P. S.
, Cole
, M. O. T.
, and Burrows
, C. R.
, 2002, “Multi-State Transient Rotor Vibration Control Using Sampled Harmonics
,” ASME J. Vibr. Acoust.
, 124
(2
), pp. 186
–197
.14.
Abulrub
, A. G.
, Sahinkaya
, M. N.
, Keogh
, P. S.
, and Burrows
, C. R.
, 2006, “Adaptive Control of Active Magnetic Bearings to Prevent Rotor-Bearing Contact
,” 2006 ASME International Mechanical Engineering Congress and Exposition (IMECE2006)
, Chicago, IL.15.
Abulrub
, A. G.
, Sahinkaya
, M. N.
, Keogh
, P. S.
, and Burrows
, C. R.
, 2006, “Contact Dynamics and Recursive Open Loop Adaptive Control to Recover Rotor Position
,” The Tenth International Symposium on Magnetic Bearings (ISMB10)
, Martigny, Switzerland.16.
Keogh
, P. S.
, Burrows
, C. R.
, and Berry
, T.
, 1996, “On-Line Controller Implementation for Attenuation of Synchronous and Transient Rotor Vibration
,” ASME J. Dyn. Syst., Meas., Control
, 118
(2
), pp. 315
–321
.17.
Lum
, K. Y.
, Coppola
, V. T.
, and Bernstein
, D. S.
, 1998, “Adaptive Virtual Autobalancing for a Rigid Rotor With Unknown Mass Imbalance Supported by Magnetic Bearings
,” ASME J. Vibr. Acoust.
, 120
(2
), pp. 557
–570
.18.
Nonami
, K.
, Fan
, Q. F.
, and Ueyama
, H.
, 1998, “Unbalance Vibration Control of Magnetic Bearing Systems Using Adaptive Algorithm With Disturbance Frequency Estimation
,” JSME Int. J., Ser. C
, 41
(2
), pp. 220
–226
.19.
Herzog
, R.
, Buhler
, P.
, Gahler
, C.
, and Larsonneur
, R.
, 1996, “Unbalance Compensation Using Generalized Notch Filters in the Multivariable Feedback of Magnetic Bearings
,” IEEE Trans. Control Syst. Technol.
, 4
(5
), pp. 580
–586
.20.
Houlston
, P. R.
, Garvey
, S. D.
, and Popov
, A. A.
, 2007, “Modal Control of Vibration in Rotating Machines and Other Generally Damped Systems
,” J. Sound Vib.
, 302
(1–2
), pp. 104
–116
.21.
Matsumura
, F.
, Namerikawa
, T.
, Hagiwara
, K.
, and Fujita
, M.
, 1996, “Application of Gain Scheduled H∞ Robust Controllers to a Magnetic Bearing
,” IEEE Trans. Control Syst. Technol.
, 4
(5
), pp. 484
–493
.22.
Glover
, K.
, and Doyle
, J. C.
, 1988, “State-Space Formulae for All Stabilizing Controllers That Satisfy an H∞-Norm Bound and Relations to Relations to Risk Sensitivity
,” Syst. Control Lett.
, 11
(3
), pp. 167
–172
.23.
Doyle
, J. C.
, Glover
, K.
, Khargonekar
, P. P.
, and Francis
, B. A.
, 1989, “State-Space Solutions to Standard H2 and H∞ Control Problems
,” IEEE Trans. Autom. Control
, 34
(8
), pp. 831
–847
.24.
Keogh
, P. S.
, Mu
, C.
, and Burrows
, C. R.
, 1995, “Optimized Design of Vibration Controllers for Steady and Transient Excitation of Flexible Rotors
,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
, 209
(C3
), pp. 155
–168
.25.
Gahinet
, P.
, and Apkarian
, P.
, 1994, “A Linear Matrix Inequality Approach to H∞ Control
,” Int. J. Robust Nonlinear Control
, 4
(4
), pp. 421
–448
.26.
Chen
, Y. J.
, and Zhu
, C. S.
, 2008, “Active Vibration Control Based on Linear Matrix Inequality for Rotor System Under Seismic Excitation
,” J. Sound Vib.
, 314
(1–2
), pp. 53
–69
.27.
Schlotter
, M.
, and Keogh
, P. S.
, 2008, “The Vibration Control of Speed-Dependent Flexible Rotor/Magnetic Bearing Systems Using Linear Matrix Inequality Gain-Scheduled H∞ Design
,” Proceedings of the Institution of Mechanical Engineers Part I-Journal of Systems and Control Engineering
, 222
(2
), pp. 97
–107
.28.
Nonami
, K.
, and Ito
, T.
, 1996, “μ Synthesis of Flexible Rotor-Magnetic Bearing Systems
,” IEEE Trans. Control Syst. Technol.
, 4
(5
), pp. 503
–512
.29.
Schonhoff
, U.
, Luo
, J.
, Li
, G.
, Hilton
, E.
, Nordmann
, R.
, and Allaire
, P. E.
, 2000, “Implementation Results of Mu-Synthesis Control for an Energy Storage Flywheel Test Rig
,” The Eight International Symposium on Magnetic Bearings (ISMB-8)
, Zurich, Switzerland.30.
Cole
, M. O. T.
, Keogh
, P. S.
, and Burrows
, C. R.
, 1998, “Vibration Control of a Flexible Rotor Magnetic Bearing System Subject to Direct Forcing and Base Motion Disturbances
,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
, 212
(7
), pp. 535
–546
.31.
Duchemin
, M.
, Berlioz
, A.
, and Ferraris
, G.
, 2006, “Dynamic Behavior and Stability of a Rotor Under Base Excitation
,” ASME J. Vibr. Acoust.
, 128
(5
), pp. 576
–585
.32.
Marx
, S.
, and Nataraj
, C.
, 2007, “Suppression of Base Excitation of Rotors on Magnetic Bearings
,” Int. J. Rotating Mach.
, 2007
, p. 91276
. 0002-782033.
Shiau
, T. N.
, Kuo
, C. P.
, and Hwang
, J. R.
, 1997, “Multi-Objective Optimization of a Flexible Rotor in Magnetic Bearings With Critical Speeds and Control Current Constraints
,” ASME J. Eng. Gas Turbines Power
, 119
(1
), pp. 186
–195
.34.
El-Shafei
, A.
, and Yakoub
, R. Y. K.
, 2002, “Optimum Design of Squeeze Film Dampers Supporting Multiple-Mode Rotors
,” ASME J. Eng. Gas Turbines Power
, 124
(4
), pp. 992
–1002
.35.
Choi
, B. K.
, and Yang
, B. S.
, 2001, “Multiobjective Optimum Design of Rotor-Bearing Systems With Dynamic Constraints Using Immune-Genetic Algorithm
,” ASME J. Eng. Gas Turbines Power
, 123
(1
), pp. 78
–81
.36.
Shi
, J.
, Zmood
, R.
, and Qin
, L.
, 2002, “The Indirect Adaptive Feed-Forward Control in Magnetic Bearing Systems for Minimizing Selected Vibration Performance Measures
,” The Eight International Symposium on Magnetic Bearings (ISMB-8)
, Mito, Japan.37.
Keogh
, P. S.
, Sahinkaya
, M. N.
, Burrows
, C. R.
, and Prabhakar
, S.
, 2006, “Wavelet Based Adaptation of H∞ Control in Flexible Rotor/Magnetic Bearing System
,” IFToMM Seventh International Conference on Rotor Dynamics
, Vienna, Austria.38.
Poznyak
, A.
, Bejarano
, F. J.
, and Fridman
, L.
, 2007, “Numerical Method for Weights Adjustment in Minimax Multi-Model LQ-Control
,” Opt. Control Appl. Methods
, 28
(4
), pp. 289
–300
.39.
Stuckman
, B. E.
, and Stuckman
, P. L.
, 1993, “Finding the Best Optimal-Control Using Global Search
,” Comput. Electr. Eng.
, 19
(1
), pp. 9
–18
.40.
Kamali
, K.
, Jiang
, L. J.
, Yen
, J.
, and Wang
, K. W.
, 2007, “Using Q-Learning and Genetic Algorithms to Improve the Efficiency of Weight Adjustments for Optimal Control and Design Problems
,” ASME J. Comput. Inf. Sci. Eng.
, 7
(4
), pp. 302
–308
.41.
Bryson
, A. E.
, and Ho
, Y. C.
, 1975, Applied Optimal Control: Optimization, Estimation, and Control
, Hemisphere
, Washington, DC
.42.
Larsonneur
, R.
, and Herzog
, R.
, 1994, “Feedforward Compensation of Unbalance: New Results and Application Experiences
,” IUTAM Symposium on the Active Control of Vibration
, Bath, UK, pp. 45
–52
.43.
Sahinkaya
, M. N.
, Cole
, M. O. T.
, and Burrows
, C. R.
, 2002, “On the Use of Schroeder Phased Harmonic Sequences for the Multi-Frequency Vibration Control of Flexible Rotor/Magnetic Bearing Systems
,” The Eight International Symposium on Magnetic Bearings (ISMB-8)
, Mito, Japan, pp. 217
–222
.44.
Abulrub
, A. H. G.
, Sahinkaya
, M. N.
, Burrows
, C. R.
, and Keogh
, P. S.
, 2009, “Performance Assessment of a Multi-Frequency Controller Applied to a Flexible Rotor Magnetic Bearing System—Contact Dynamics
,” Motion and Vibration Control
, H.
Ulbrich
and L.
Ginzinger
, eds., Springer
, Dordrecht, The Netherlands
, pp. 11
–20
.45.
Burrows
, C. R.
, Sahinkaya
, M. N.
, and Clements
, S.
, 1988, “Electromagnetic Control of Oil-Film Supported Rotors Using Sparse Measurements
,” Trans. ASME, J. Vib., Acoust., Stress, Reliab. Des.
, 110
(3
), pp. 295
–299
.Copyright © 2011
by American Society of Mechanical Engineers
You do not currently have access to this content.
