Abstract

For the reduction of unbalanced vibrations in a multi-input and multi-output flexible rotor system with electromagnetic actuators (EAs), conventional adaptive feedforward controllers (AFFCs) are very sensitive for changes in rotor spin frequencies. Although frequency updating is used in these controllers, a small variation in the rotor spin frequency can completely reduce their effectiveness. An adaptive notch filter is used in this research for the frequency estimation. By using this external frequency estimation, the performance of the conventional AFFCs can be enhanced. During changes in the rotor spin frequency, fundamental harmonics of the flexible rotor are also excited. Their amplitude is much higher compared to steady-state unbalanced vibrations, which can accelerate the wear and tear of components of EAs. By using feedback controllers, the amplitude of these fundamental harmonics can be reduced significantly. In real rotors with flexible bearing supports, any looseness of bolts and presence of transverse cracks can change system parameters significantly. Multiple harmonics are generated corresponding to even single spinning speed of the rotor. Robust stability as well as performance can be achieved in the presence of uncertainty and rotor crack nonlinearities using feedback controllers designed by mu-synthesis. By using the multiharmonic hybrid control, the higher harmonics can be compensated efficiently in case of a crack in rotor systems. The fast Fourier transform of the control signal can indicate the presence of a transverse crack in an online manner. In this way, active vibration control as well as rotor crack fault detection can be done simultaneously.

References

References
1.
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
.10.1109/87.531924
2.
Itou
,
M.
,
Matsushita
,
O.
,
Okubo
,
H.
, and
Fujiwara
,
H.
,
2000
, “
Unbalance Vibration Control for High Order Bending Critical Speeds of Flexible Rotor Supported by Active Magnetic Bearings
,”
Proceedings of the Eighth International Symposium on Transport Phenomena and Dynamics of Rotating Mach ISROMAC-8,
Honolulu, HI
, Mar. 26–30, pp.
922
928
.
3.
Shin
,
K.-K.
, and
Ni
,
J.
,
2001
, “
Adaptive Control of Active Balancing Systems for Speed-Varying Rotors Using Feedforward Gain Adaptation Technique
,”
ASME J. Dyn. Syst., Meas., Control
,
123
(
3
), pp.
346
352
.10.1115/1.1388015
4.
Knospe
,
C. R.
,
Hope
,
R. W.
,
Fedigan
,
S. J.
, and
Williams
,
R. D.
,
1993
, “
Adaptive on-Line Balancing Using Digital Control
,”
Proceedings MAG '93, Magnetic Bearings, Magnetic Drives and Dry Gas Seals Conference and Exhibition
,
Alexandria, VA
, July 29–30, pp.
156
164
.
5.
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
.10.1016/0957-4158(95)00015-W
6.
Knospe
,
C. R.
,
Hope
,
R. W.
,
Tamer
,
S. M.
, and
Fedigan
,
S. J.
,
1996
, “
Robustness of Adaptive Unbalance Control of Rotors With Magnetic Bearings
,”
Modal Anal.
,
2
(
1
), pp.
33
52
.10.1177/107754639600200103
7.
Knospe
,
C. R.
,
Tamer
,
S. M.
, and
Fedigan
,
S. J.
,
1997
, “
Robustness of Adaptive Rotor Vibration Control to Structured Uncertainty
,”
ASME J. Dyn. Syst., Meas., Control
,
119
(
2
), pp.
243
250
.10.1115/1.2801240
8.
DeSmidt
,
H. A.
,
Wang
,
K. W.
, and
Smith
,
E. C.
,
2008
, “
Multiharmonic Adaptive Vibration Control of Misaligned Driveline Via Active Magnetic Bearings
,”
ASME J. Dyn. Syst., Meas., Control
,
130
(
4
), p.
041006
.10.1115/1.2907382
9.
Ye
,
Y.
,
Zhou
,
K.
,
Zhang
,
B.
,
Wang
,
D.
, and
Wang
,
J.
,
2006
, “
High-Performance Repetitive Control of PWM DC-AC Converters With Real-Time Phase-Lead FIR Filter
,”
IEEE Trans. Circuits Syst. II: Express Briefs
,
53
(
8
), pp.
768
772
.10.1109/TCSII.2006.875383
10.
Hornik
,
T.
, and
Zhong
,
Q. C.
,
2011
, “
A Current-Control Strategy for Voltage-Source Inverters in Microgrids Based on H-Infinity and Repetitive Control
,”
IEEE Trans. Power Electron.
,
26
(
3
), pp.
943
952
.10.1109/TPEL.2010.2089471
11.
Navarro-López
,
E. M.
,
Cortés
,
D.
, and
Castro
,
C.
,
2009
, “
Design of Practical Sliding-Mode Controllers With Constant Switching Frequency for Power Converters
,”
Electric Power Syst. Res.
,
79
(
5
), pp.
796
802
.10.1016/j.epsr.2008.10.018
12.
Arahal
,
M. R.
,
Barrero
,
F.
,
Toral
,
S.
,
Duran
,
M.
, and
Gregor
,
R.
,
2009
, “
Multi-Phase Current Control Using Finite-State Model-Predictive Control
,”
Control Eng. Pract.
,
17
(
5
), pp.
579
587
.10.1016/j.conengprac.2008.10.005
13.
Townsend
,
C. D.
,
Summers
,
T. J.
, and
Betz
,
R. E.
,
2012
, “
Multigoal Heuristic Model Predictive Control Technique Applied to a Cascaded H-Bridge StatCom
,”
IEEE Trans. Power Electron.
,
27
(
3
), pp.
1191
1200
.10.1109/TPEL.2011.2165854
14.
Fang
,
J.
,
Xu
,
X.
,
Tang
,
J.
, and
Liu
,
H.
,
2013
, “
Adaptive Complete Suppression of Imbalance Vibration in AMB Systems Using Gain Phase Modifier
,”
J. Sound Vib.
,
332
(
24
), pp.
6203
6215
.10.1016/j.jsv.2013.07.004
15.
Shi
,
J.
,
Zmood
,
R.
, and
Qin
,
L.
,
2004
, “Synchronous Disturbance Attenuation in Magnetic Bearing Systems Using Adaptive Compensating Signals,”
Control Eng. Practice
, 12(3), pp.
283
290
.10.1016/S0967-0661(03)00095-9
16.
Gao
,
H.
,
2011
, “
Real-Time Feed-Forward Force Compensation for Active Magnetic Bearings System Based on H∞ Controller
,”
Chin. J. Mech. Eng.
,
24
(
01
), pp.
58
66
.10.3901/CJME.2011.01.058
17.
Wei
,
T.
,
2012
, “
Autobalancing for Magnetically Suspended High-Speed Rotors Based on Lead Feedforward Compensation for Displacement Stiffness Force
,”
J. Mech. Eng.
,
48
(
16
), pp.
184
191
.10.3901/JME.2012.16.184
18.
Kai-Yew
,
L.
,
Coppola
,
V. T.
, and
Bernstein
,
D. S.
,
1996
, “
Adaptive Autocentering Control for an Active Magnetic Bearing Supporting a Rotor With Unknown Mass Imbalance
,”
IEEE Trans. Control Syst. Technol.
,
4
(
5
), pp.
587
597
.10.1109/87.531925
19.
Chen
,
Q.
,
Liu
,
G.
, and
Zheng
,
S.
,
2015
, “
Suppression of Imbalance Vibration for AMBs Controlled Driveline System Using Double-Loop Structure
,”
J. Sound Vib.
,
337
, pp.
1
13
.10.1016/j.jsv.2014.09.042
20.
Liu
,
B.
,
Fang
,
J.
,
Liu
,
G.
, and
Fan
,
Y.
,
2010
, “
Unbalance Vibration Control and Experiment Research of Magnetically Suspended Flywheels
,”
Jixie Gongcheng Xuebao (Chin. J. Mech. Eng.)
,
46
(
12
), pp.
188
194
.10.3901/JME.2010.12.188
21.
Shafai
,
B.
,
Beale
,
S.
,
Larocca
,
P.
, and
Cusson
,
E.
,
1994
, “
Magnetic Bearing Control Systems and Adaptive Forced Balancing
,”
IEEE Control Syst.
,
14
(
2
), pp.
4
13
.10.1109/37.272775
22.
Chen
,
S. Y.
, and
Lin
,
F. J.
,
2011
, “
Robust Nonsingular Terminal Sliding-Mode Control for Nonlinear Magnetic Bearing System
,”
IEEE Trans. Control Syst. Technol.
,
19
(
3
), pp.
636
643
.10.1109/TCST.2010.2050484
23.
Lin
,
F. J.
,
Chen
,
S. Y.
, and
Huang
,
M. S.
,
2011
, “
Intelligent Double Integral Sliding-Mode Control for Five-Degree-of-Freedom Active Magnetic Bearing System
,”
IET Control Theory Appl.
,
5
(
11
), pp.
1287
1303
.10.1049/iet-cta.2010.0237
24.
Gosiewski
,
Z.
, and
Mystkowski
,
A.
,
2008
, “
Robust Control of Active Magnetic Suspension: Analytical and Experimental Results
,”
Mech. Syst. Signal Process.
,
22
(
6
), pp.
1297
1303
.10.1016/j.ymssp.2007.08.005
25.
Jastrzebski
,
R. P.
,
Hynynen
,
K. M.
, and
Smirnov
,
A.
,
2010
, “
H∞ Control of Active Magnetic Suspension
,”
Mech. Syst. Signal Process.
,
24
(
4
), pp.
995
1006
.10.1016/j.ymssp.2009.10.008
26.
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
.10.1109/87.531915
27.
Schuhmann
,
T.
,
Hofmann
,
W.
, and
Werner
,
R.
,
2012
, “
Improving Operational Performance of Active Magnetic Bearings Using Kalman Filter and State Feedback Control
,”
IEEE Trans. Ind. Electron.
,
59
(
2
), pp.
821
829
.10.1109/TIE.2011.2161056
28.
Liu
,
B.
,
Fang
,
J.
, and
Liu
,
G.
,
2008
, “
Self-Tuning Control Based on RBF Neural Network Observer in Suppression of Imbalance Vibration of Magnetically Suspended Flywheels
,”
Proceedings of Second International Symposium on Systems and Control in Aerospace and Astronautics
, Shenzhen, China, Dec. 10–12, pp.
1
5
.
29.
Paul
,
M.
, and
Hofmnn
,
W.
,
1997
, “
Compensation for Unbalances at Magnetic Bearings
,”
Proceedings of the International Conference on Computational Intelligence, Theory and Applications
,
Germany
, pp.
501
509
.
30.
Ren
,
T.-J.
,
Chen
,
T.-C.
, and
Chen
,
C.-J.
,
2008
, “
Motion Control for a Two-Wheeled Vehicle Using a Self-Tuning PID Controller
,”
Control Eng. Pract.
,
16
(
3
), pp.
365
375
.10.1016/j.conengprac.2007.05.007
31.
Beltran-Carbajal
,
F.
,
Silva-Navarro
,
G.
, and
Arias-Montiel
,
M.
,
2013
, “
Active Unbalance Control of Rotor Systems Using on-Line Algebraic Identification Methods
,”
Asian J. Control
,
15
(
6
), pp.
1627
1637
.10.1002/asjc.744
32.
Sivrioglu
,
S.
, and
Saigo
,
M.
,
2005
, “
Adaptive Backstepping for Nonlinear Switching Control AMB System With Base Excitation
,” Proceedings of IEEE Conference on Control Applications (
CCA
), Toronto, ON, Canada, Aug. 28–31, pp.
651
656
.10.1109/CCA.2005.1507201
33.
Zheng
,
S.
, and
Feng
,
R.
,
2016
, “
Feedforward Compensation Control of Rotor Imbalance for High-Speed Magnetically Suspended Centrifugal Compressors Using a Novel Adaptive Notch Filter
,”
J. Sound Vib.
,
366
, pp.
1
14
.10.1016/j.jsv.2015.12.029
34.
Chen
,
Q.
,
Liu
,
G.
, and
Han
,
B.
,
2017
, “
Unbalance Vibration Suppression for AMBs System Using Adaptive Notch Filter
,”
Mech. Syst. Signal Process.
,
93
, pp.
136
150
.10.1016/j.ymssp.2017.02.009
35.
VahedforoughShafai
,
E.
, and
Beale
,
B. S.
,
2007
, “
Estimation and Rejection of Unknown Sinusoidal Disturbances Using a Generalized Adaptive Forced Balancing Method
,”
American Control Conference
, July 11–13, pp.
3529
3534
.10.1109/ACC.2007.4282833
36.
Rodriguez
,
P.
,
Luna
,
A.
,
Candela
,
I.
,
Mujal
,
R.
,
Teodorescu
,
R.
, and
Blaabjerg
,
F.
,
2011
, “
Multiresonant Frequency-Locked Loop for Grid Synchronization of Power Converters Under Distorted Grid Conditions
,”
IEEE Trans. Ind. Electron.
,
58
(
1
), pp.
127
138
.10.1109/TIE.2010.2042420
37.
Djurovi
,
I.
,
2007
, “
Estimation of the Sinusoidal Signal Frequency Based on the Marginal Median DFT
,”
IEEE Trans. Signal Process.
,
55
(
5
), pp.
2043
2051
.10.1109/TSP.2007.893211
38.
Vazquez
,
J. R.
, and
Salmeron
,
P.
,
2003
, “
Active Power Filter Control Using Neural Network Technologies
,”
IEE Proc. Electric Power Appl.
,
150
(
2
), pp.
139
145
.10.1049/ip-epa:20030009
39.
Mojiri
,
M.
, and
Bakhshai
,
A. R.
,
2004
, “
An Adaptive Notch Filter for Frequency Estimation of a Periodic Signal
,”
IEEE Trans. Autom. Control
,
49
(
2
), pp.
314
318
.10.1109/TAC.2003.821414
40.
Yazdani
,
D.
,
Mojiri
,
M.
,
Bakhshai
,
A.
, and
JoÓs
,
G.
,
2009
, “
A Fast and Accurate Synchronization Technique for Extraction of Symmetrical Components
,”
IEEE Trans. Power Electron.
,
24
(
3
), pp.
674
684
.10.1109/TPEL.2008.2010321
41.
Chu
,
Z.
,
Ding
,
M.
,
Du
,
S.
, and
Feng
,
X.
,
2011
, “
Exponential Stability, Semistability, and Boundedness of a Multi-ANF System
,”
IEEE Trans. Circuits Syst. I: Regular Papers
,
58
(
2
), pp.
326
335
.10.1109/TCSI.2010.2071790
42.
Kumar Vashisht
,
R.
, and
Peng
,
Q.
,
2018
, “
Nonlinear Dynamic Modeling of the Cracked Rotor Ball Bearing System With Emphasis on Damage Detection Capabilities
,”
ASME J. Vib. Acoust.
,
140
(
4
), p.
041018
.10.1115/1.4039404
43.
Gu
,
D. W.
,
Petkov
,
P. H.
, and
Konstantinov
,
M. M.
,
2005
, “
Robust Control Design With MATLAB
,”
Springer
,
London
.
44.
Sawicki
,
J. T.
,
Friswell
,
M. I.
,
Kulesza
,
Z.
,
Wroblewski
,
A.
, and
Lekki
,
J. D.
,
2011
, “
Detecting Cracked Rotors Using Auxiliary Harmonic Excitation
,”
J. Sound Vib.
,
330
(
7
), pp.
1365
1381
.10.1016/j.jsv.2010.10.006
45.
Kulesza
,
Z.
,
2014
, “
Dynamic Behavior of Cracked Rotor Subjected to Multisine Excitation
,”
J. Sound Vib.
,
333
(
5
), pp.
1369
1378
.10.1016/j.jsv.2013.10.031
46.
McCormack
,
A. S.
,
Godfrey
,
K. R.
, and
Flower
,
J. O.
,
1994
, “
The Detection of and Compensation for Nonlinear Effects Using Periodic Input Signals
,”
International Conference on Control—Control'94
, Vol. 291, Coventry, UK, Mar. 21–24, pp.
297
302
.
47.
Schoukens
,
J.
,
Pintelon
,
R.
,
Rolain
,
Y.
, and
Dobrowiecki
,
T.
,
2001
, “
Frequency Response Function Measurements in the Presence of Nonlinear Distortions
,”
Automatica
,
37
(
6
), pp.
939
946
.10.1016/S0005-1098(01)00037-1
48.
Shimada
,
Y.
,
Nishimura
,
Y.
,
Usagawa
,
T.
, and
Ebata
,
M.
,
1999
, “Active Control for Periodic Noise with Variable Fundamental. An Extended DXHS Algorithm with Frequency Tracking Ability,” J. Acoust. Soc. Japan, 20(4), pp.
301
312
.
49.
Yoon
,
J.-M.
,
Bahn
,
W.
,
Kim
,
T.-I.
,
Han
,
J.-S.
,
Lee
,
S.-H.
, and
Cho
,
D.-I. D.
,
2017
, “
Discrete Derivative Method for Adaptive Notch Filter-Based Frequency Estimators
,”
Int. J. Control Autom. Syst.
,
15
(
2
), pp.
668
679
.10.1007/s12555-016-0030-x
50.
Manngård
,
M.
, and
Böling
,
J. M.
,
2017
, “
Online Frequency Estimation With Applications to Engine and Generator Sets
,”
Mech. Syst. Signal Process.
,
91
, pp.
233
249
.10.1016/j.ymssp.2016.12.043
You do not currently have access to this content.