This study deals with sliding-mode nonlinear observers for a flux-controlled active magnetic bearing (AMB) operated with zero-bias flux. The Lyapunov sliding-mode observer (LSMO) feedback designs are performed for the nonlinear AMB dynamics due to control voltage saturation. The nonlinear observers are designed to estimate the magnetic flux and rotor mass velocity. The observer designs are incorporated in equivalence implementation of the nonlinear state-feedback controller. The main design tools such as sliding-mode control, Lyapunov-based control are used in this framework. The proposed observers are verified by means of numerical simulations, and stability and effectiveness of the proposed observer-based feedback designs are shown.

References

1.
Maslen
,
E. H.
,
2000
, “
Magnetic Bearings—Graduate Seminar Notes
,” Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA.
2.
Bahr
,
F.
,
Melzer
,
M.
,
Makarov
,
D.
,
Karnaushenko
,
D.
,
Schmidt
,
O. G.
, and
Hofmann
,
W.
,
2012
, “
Flux Based Control of AMBs Using Integrated Ultra-Thin Flexible Bismuth Hall Sensors
,”
13th International Symposium on Magnetic Bearings
, Arlington, VA, Aug. 6–9, pp.
1
15
.
3.
Lin
,
Z.
, and
Knospe
,
C.
,
2000
, “
A Saturated High Gain Control for a Benchmark Experiment
,”
American Control Conference
, Chicago, IL, June 28–30, pp.
2644
2648
.
4.
Tsiotras
,
P.
, and
Arcak
,
M.
,
2002
, “
Low-Bias Control of AMB Subject to Voltage Saturation: State-Feedback and Observer Designs
,” 41st
IEEE
Conference on Decision and Control
, Las Vegas, NV, Dec. 10–13, pp.
2474
2479
.
5.
Maslen
,
E. H.
,
2006
, “
Self-Sensing for Active Magnetic Bearings: Overview and Status
,”
Tenth International Symposium on Magnetic Bearings
, Martigny, Switzerland, Aug. 21–23, pp.
13
19
.
6.
Peng
,
C.
,
Fang
,
J.
, and
Xu
,
X.
,
2015
, “
Mismatched Disturbance Rejection Control for Voltage-Controlled Active Magnetic Bearing Via State-Space Disturbance Observer
,”
IEEE Trans. Power Electron.
,
30
(
5
), pp.
2753
2762
.
7.
Itkis
,
U.
,
1967
,
Control Systems of Variable Structure
,
Wiley
,
New York
.
8.
Utkin
,
V. I.
,
1977
, “
Variable Structure Systems With Sliding Modes
,”
IEEE Trans. Autom. Control
,
22
(
2
), pp.
212
222
.
9.
Spurgeon
,
S. K.
,
2008
, “
Sliding Mode Observers: A Survey
,”
Int. J. Syst. Sci.
,
39
(
8
), pp.
741
764
.
10.
Baloh
,
M.
,
Gang
,
T.
, and
Allaire
,
P.
,
2000
, “
Modeling and Control of a Magnetic Bearing Actuated Beam
,”
American Control Conference
, Chicago, IL, June 28–30, pp.
1602
1606
.
11.
Rundell
,
A. E.
,
Drakunov
,
S. V.
, and
DeCarlo
,
R. A.
,
1996
, “
A Sliding Mode Observer and Controller for Stabilization of Rotational Motion of a Vertical Shaft Magnetic Bearing
,”
IEEE Trans. Control Syst. Technol.
,
4
(
5
), pp.
598
608
.
12.
Nguyen
,
Q. D.
, and
Ueno
,
S.
,
2010
, “
Improvement of Sensorless Speed Control for Nonsalient Type Axial Gap Self-Bearing Motor Using Sliding Mode Observer
,”
IEEE
International Conference on Industrial Technology (ICIT)
, Vina del Mar, Chile, Mar. 14–17, pp.
373
378
.
13.
Shi
,
J.
,
Yan
,
Y.
,
Yu
,
S.
, and
Yu
,
X.
,
2012
, “
Dynamic Output Feedback Sliding Mode Control for Magnetic Bearing System Stabilization
,”
Tenth World Congress on Intelligent Control and Automation
, Beijing, China, July 6–8, pp.
1547
1552
.
14.
Whittle
,
E.
,
Noshadi
,
A.
,
Shi
,
J.
, and
Kalam
,
A.
,
2015
, “
Experimental Study on Servo Linear Quadratic Gaussian and Observer-Based Sliding Mode Control for Active Magnetic Bearing System
,”
Power Engineering Conference
(
AUPEC
), Australasian Universities, Wollongong, Australia, Sept. 27–30, pp. 1–6.
15.
Tsiotras
,
P.
,
Wilson
,
B.
, and
Bartlett
,
R.
,
2000
, “
Control of a Zero-Bias Magnetic Bearing Using Control Lyapunov Functions
,” 39th
IEEE
Conference on Decision and Control
, Sydney, Australia, Dec. 12–15, pp.
4048
4053
.
16.
Jastrzebski
,
R. P.
,
Smirnov
,
A.
,
Mystkowski
,
A.
, and
Pyrhönen
,
O.
,
2014
, “
Cascaded Position-Flux Controller for AMB System Operating at Zero Bias
,”
Energies
,
7
(
6
), pp.
3561
3575
.
17.
Mystkowski
,
A.
,
Pawluszewicz
,
E.
, and
Dragašius
,
E.
,
2015
, “
Robust Nonlinear Position-Flux Zero-Bias Control for Uncertain AMB System
,”
Int. J. Control
,
88
(
8
), pp.
1619
1629
.
18.
Mystkowski
,
A.
, and
Pawluszewicz
,
E.
,
2015
, “
Remarks on Some Robust Nonlinear Observer and State-Feedback Zero-Bias Control of AMB
,”
IEEE
16th International Carpathian Control Conference
, Szilvásvárad, Hungary, May 27–30, pp.
328
333
.
19.
Tsiotras
,
P.
, and
Wilson
,
B. C.
,
2003
, “
Zero– and Low–Bias Control Designs for Active Magnetic Bearings
,”
IEEE Trans. Control Syst. Technol.
,
11
(
6
), pp.
889
904
.
20.
Sontag
,
E. D.
,
1983
, “
A Lyapunov-Like Characterization of Asymptotic Controllability
,”
SIAM J. Control Optim.
,
21
(
3
), pp.
462
471
.
21.
Mazenc
,
F.
,
Queiroz
,
M. S.
,
Malisoff
,
M.
, and
Gao
,
F.
,
2006
, “
Further Results on Active Magnetic Bearing Control With Input Saturation
,”
IEEE Trans. Control Syst. Technol.
,
14
(
5
), pp.
914
919
.
22.
Lu
,
B.
, and
Wu
,
F.
,
2004
, “
Control Design of Switched LPV Systems Using Multiple Parameter-Dependent Lyapunov Functions
,”
American Control Conference
, Boston, MA, June 30–July 2, pp.
3875
3880
.
23.
Schweitzer
,
G.
, and
Maslen
,
E. H.
,
2009
,
Magnetic Bearings: Theory, Design, and Application to Rotating Machinery
,
Springer
,
Berlin
.
24.
Slotine
,
J. J. E.
,
Hedrick
,
J. K.
, and
Misawa
,
E. A.
,
1987
, “
On Sliding Observers for Nonlinear Systems
,”
ASME J. Dyn. Syst., Meas., Control
,
109
(
3
), pp.
245
252
.
25.
Fichtenholz
,
G. M.
,
1987
,
Differential- und Integralrechnung 3
, 11th ed.,
Deutscher Verlag der Wissenschaften
,
Berlin
(Translated From the Russian by Boll L. and Groger K.).
26.
Arcak
,
M.
, and
Kokotović
,
P.
,
2001
, “
Observer-Based Control of Systems With Slope-Restricted Nonlinearities
,”
IEEE Trans. Autom. Control
,
46
(
7
), pp.
1146
1150
.
27.
Torres
,
M.
,
Sira-Ramirez
,
H.
, and
Escobar
,
G.
,
1999
, “
Sliding Mode Nonlinear Control of Magnetic Bearings
,”
IEEE
International Conference on Control Applications
, Kohala Coast-Island, HI, Aug. 22–27, pp.
743
748
.
28.
Mystkowski
,
A.
, and
Pawluszewicz
,
E.
,
2017
, “
Nonlinear Position-Flux Zero-Bias Control for AMB System With Disturbance
,”
Appl. Comput. Electromagn. Soc. J.
,
32
(
8
), pp.
650
656
.http://www.aces-society.org/search.php?vol=32&no=8&type=2
29.
Mystkowski
,
A.
,
2010
, “
Sensitivity and Stability Analysis of Mu-Synthesis AMB Flexible Rotor
,”
Solid State Phenom.
,
164
, pp.
313
318
.
30.
Mystkowski
,
A.
,
2010
, “
μ–Synthesis Control of Flexible Modes of AMB Rotor
,”
Acta Mech. Autom.
,
4
(
5
), pp.
83
90
.http://yadda.icm.edu.pl/baztech/element/bwmeta1.element.baztech-article-BPB2-0048-0014?printView=true
You do not currently have access to this content.