Abstract

As a new strategy for magnetic levitation envisioned in the 1990s, the Inductrack system with Halbach arrays of permanent magnets has been intensively researched. The previous investigations discovered that an uncontrolled Inductrack system may be unstable even if the vehicle travels well below its operating speed and that instability can be persistent near and beyond the operating speed. It is therefore necessary to stabilize the system for safety and reliability. With strong nonlinearities and complicated electromagneto-mechanical coupling, however, the transient response of such a dynamic system is difficult to predict with fidelity. Because of this, model-based feedback control of Inductrack systems has not been well addressed. In this paper, by taking advantage of a recently available two degrees-of-freedom transient model, a new feedback control method for Inductrack systems is proposed. In the control system development, active Halbach arrays are used as an actuator, and a feedback control law, which combines a properly tuned proportional-integral-derivative controller and a nonlinear force-current mapping function, is created. The proposed control law is validated in numerical examples, where the transient motion of an Inductrack vehicle traveling at constant speeds is considered. As shown in the simulation, the control law efficiently stabilizes the Inductrack system in a wide range of operating speed, and in the meantime, it renders a smooth system output (real-time levitation gap) with fast convergence to any prescribed reference step input (desired levitation gap).

References

1.
Lee
,
H. W.
,
Kim
,
K. C.
, and
Lee
,
J.
,
2006
, “
Review of Maglev Train Technologies
,”
IEEE Trans. Magnetics
,
42
(
7
), pp.
1917
1925
.10.1109/TMAG.2006.875842
2.
Post
,
R. F.
, and
Ryutov
,
D. D.
,
1996
, “
The Inductrack Concept: A New Approach to Magnetic Levitation
,” Lawrence Livermore National Laboratory, Livermore, CA, LLNL Report No. UCRL-ID-124115.
3.
Post
,
R. F.
, and
Ryutov
,
D. D.
,
2000
, “
The Inductrack: A Simpler Approach to Magnetic Levitation
,”
IEEE Trans. Appl. Superconduct.
,
10
(
1
), pp.
901
904
.10.1109/77.828377
4.
Post
,
R. F.
, and
Ryutov
,
D. D.
,
2000
, “
The Inductrack Approach to Magnetic Levitation
,”
Proceedings of the 16th International Conference on Magnetically Levitated Systems and Linear Drives
, Rio de Janeiro, Brazil, June 6–11, pp.
6
11
.
5.
Halbach
,
K.
,
1981
, “
Physical and Optical Properties of Rare Earth Cobalt Magnets
,”
Nucl. Instrum. Methods Phys. Res.
,
187
(
1
), pp.
109
117
.10.1016/0029-554X(81)90477-8
6.
Post
,
R. F.
,
2000
, “
Maglev: A New Approach
,”
Sci. Am.
,
282
(
1
), pp.
82
87
.10.1038/scientificamerican0100-82
7.
Bermudez
,
J. L.
,
Zanolli
,
S.
,
Sandtner
,
J.
,
Bleuler
,
H.
, and
Benabderrahmane
,
C.
,
2000
, “
Preliminary Experiments on an Eddy Currents Bearing
,”
Proceedings of the Seventh International Symposium on Magnetic Bearings
, Zurich, Switzerland, Aug. 23–25, pp.
135
140
.http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.456.804&rep=rep1&type=pdf
8.
Gurol
,
S.
,
Baldi
,
B.
, and
Post
,
R. F.
,
2002
, “
Overview of the General Atomics Low Speed Urban Maglev Technology Development Program
,”
Proceedings of the 17th International Conference on Magnetically Levitated Systems and Linear Drives
, Lusanne, Switzerland, Sept. 3–5, Paper No. PP03103.
9.
Kratz
,
R.
, and
Post
,
R. F.
,
2002
, “
A Null-Current Electro-Dynamic Levitation System
,”
IEEE Trans. Appl. Superconduct.
,
12
(
1
), pp.
930
932
.10.1109/TASC.2002.1018551
10.
Tung
,
L. S.
,
Post
,
R. F.
, and
Martinez-Frias
,
J.
,
2001
, “
Final Progress Report for the NASA Inductrack Model Rocket Launcher at the Lawrence Livermore National Laboratory
,” Lawrence Livermore National Laboratory, Livermore, CA, LLNL Report No. UCRL-ID-144455.
11.
Post
,
R. F.
,
1998
, “
Inductrack Demonstration Model
,” Lawrence Livermore National Laboratory, Livermore, CA, LLNL Report No. UCRL-ID-129664.
12.
Murai
,
T.
, and
Hasegawa
,
H.
,
2003
, “
Electromagnetic Analysis of Inductrack Magnetic Levitation
,”
Electr. Eng. Jpn.
,
142
(
1
), pp.
67
74
.10.1002/eej.10061
13.
Ham
,
C.
,
Ko
,
W.
, and
Han
,
Q.
,
2006
, “
Analysis and Optimization of a Maglev System Based on the Halbach Magnet Arrays
,”
J. Appl. Phys.
,
99
(
8
), p.
08P510
.10.1063/1.2162475
14.
Cho
,
H. W.
,
Han
,
H. S.
,
Bang
,
J. S.
,
Sung
,
H. K.
, and
Kim
,
B. H.
,
2009
, “
Characteristic Analysis of Electrodynamic Suspension Device With Permanent Magnet Halbach Array
,”
J. Appl. Phys.
,
105
(
7
), p.
07A314
.10.1063/1.3068425
15.
Flankl
,
M.
,
Wellerdieck
,
T.
,
Tuysuz
,
A.
, and
Kolar
,
J. W.
,
2018
, “
Scaling Laws for Electrodynamic Suspension in High-Speed Transportation
,”
IET Electric Power Appl.
,
12
(
3
), pp.
357
364
.10.1049/iet-epa.2017.0480
16.
Luo
,
C.
,
Zhang
,
K.
,
Duan
,
J.
, and
Jing
,
Y.
,
2020
, “
Study of Permanent Magnet Electrodynamic Suspension System With a Novel Halbach Array
,”
J. Elect. Eng. Technol.
,
15
(
2
), pp.
969
977
.10.1007/s42835-019-00342-3
17.
Sim
,
M. S.
, and
Ro
,
J. S.
,
2020
, “
Semi-Analytical Modeling and Analysis of Halbach Array
,”
Energies
,
13
(
5
), p.
1252
.10.3390/en13051252
18.
Han
,
Q.
,
2004
, “
Analysis and Modeling of the EDS Maglev System Based on the Halbach Permanent Magnet Array
,” Ph.D. dissertation,
University of Central Florida
,
Orlando, FL
.
19.
Kim
,
N. H.
, and
Ge
,
L.
,
2006
, “
Modeling of Electrodynamic Suspension Systems
,”
ASME
Paper No. DETC2006-99122.
10.1115/DETC2006-99122
20.
Kim
,
N. H.
, and
Ge
,
L.
,
2013
, “
Dynamic Modeling of Electromagnetic Suspension System
,”
J. Vib. Control
,
19
(
5
), pp.
729
741
.10.1177/1077546312438601
21.
Ko
,
W.
,
2007
, “
Modeling and Analysis of the EDS Maglev System With the Halbach Magnet Array
,” Ph.D. dissertation,
University of Central Florida
,
Orlando, FL
.
22.
Long
,
Z.
,
He
,
G.
, and
Xue
,
S.
,
2011
, “
Study of EDS & EMS Hybrid Suspension System With Permanent-Magnet Halbach Array
,”
IEEE Trans. Magnetics
,
47
(
12
), pp.
4717
4724
.10.1109/TMAG.2011.2159237
23.
Buth
,
B.
, and
Lu
,
B.
,
2012
, “
Dynamic Analysis of Vehicle-Guideway Interaction in a Maglev Cargo Transportation System
,”
ASME
Paper No. IMECE2012-85552.10.1115/IMECE2012-85552
24.
Pradhan
,
R.
, and
Katyayan
,
A.
,
2018
, “
Vehicle Dynamics of Permanent-Magnet Levitation Based Hyperloop Capsules
,”
ASME
Paper No. DSCC2018-9130.10.1115/DSCC2018-9130
25.
Storset
,
O. F.
, and
Paden
,
B. E.
,
2005
, “
Discrete Track Electrodynamic Maglev Part I: Modelling
,”
IEEE Transactions on Magnetics
.
26.
Storset
,
O. F.
, and
Paden
,
B. E.
,
2005
, “
Electrodynamic Magnetic Levitation With Discrete Track Part II: Periodic Track Model for Numerical Simulation and Lumped Parameter Model
,”
IEEE Transactions on Magnetics
.https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.472.2117&rep=rep1&type=pdf
27.
KortüM
,
W.
, and
Utzt
,
A.
,
1984
, “
Control Law Design and Dynamic Evaluations for a Maglev Vehicle With a Combined Lift and Guidance Suspension System
,”
ASME J. Dyn. Syst., Meas. Control
,
106
(
4
), pp.
286
292
.10.1115/1.3140687
28.
Zhai
,
M.
,
Long
,
Z.
, and
Li
,
X.
,
2019
, “
Fault-Tolerant Control of Magnetic Levitation System Based on State Observer in High Speed Maglev Train
,”
IEEE Access
,
7
, pp.
31624
31633
.10.1109/ACCESS.2019.2898108
29.
Sun
,
Y. G.
,
Xie
,
S.
,
Xu
,
J. Q.
, and
Lin
,
G. B.
,
2020
, “
A Robust Levitation Control of Maglev Vehicles Subject to Time Delay and Disturbances: Design and Hardware Experimentation
,”
Appl. Sci.
,
10
(
3
), p.
1179
.10.3390/app10031179
30.
Brunelli
,
B.
,
Casadei
,
D.
,
Serra
,
G.
, and
Tani
,
A.
,
1996
, “
Active Damping Control for Electrodynamic Suspension Systems Without Mechanical Transducers
,”
IEEE Trans. Magnetics
,
32
(
5
), pp.
5055
5057
.10.1109/20.539488
31.
Kaloust
,
J.
,
Ham
,
C.
,
Siehling
,
J.
,
Jongekryg
,
E.
, and
Han
,
Q.
,
2004
, “
Nonlinear Robust Control Design for Levitation and Propulsion of a Maglev System
,”
IEE Proc. Control Theory Appl.
,
151
(
4
), pp.
460
464
.10.1049/ip-cta:20040547
32.
De Boeij
,
J.
,
Steinbuch
,
M.
, and
Gutiérrez
,
H.
,
2006
, “
Real-Time Control of the 3-DOF Sled Dynamics of a Null-Flux Maglev System With a Passive Sled
,”
Proceedings of IEEE International Symposium on Industrial Electronics
, Montreal, Quebec, July 9–12, pp.
2549
2555
.
33.
Wang
,
R.
, and
Yang
,
B.
,
2019
, “
A Transient Model of Inductrack Dynamic Systems
,”
ASME
Paper No. DETC2019-97166.10.1115/DETC2019-97166
34.
Wang
,
R.
, and
Yang
,
B.
,
2020
, “
Transient Response of Inductrack Systems for Maglev Transport: Part I—A New Transient Model
,”
ASME J. Vib. Acoust.
,
142
(
3
), p. 031005.10.1115/1.4046131
35.
Wang
,
R.
, and
Yang
,
B.
,
2020
, “
Transient Response of Inductrack Systems for Maglev Transport: Part II—Solution and Dynamic Analysis
,”
ASME J. Vib. Acoust.
,
142
(
3
), p.
031006
.10.1115/1.4046132
36.
Yamada
,
T.
,
Iwamoto
,
M.
, and
Ito
,
T.
,
1974
, “
Magnetic Damping Force in Inductive Magnetic Levitation System for High‐Speed Trains
,”
Electr. Eng. Jpn.
,
94
(
1
), pp.
80
84
.10.1002/eej.4390940112
37.
Wang
,
R.
,
Yang
,
B.
, and
Gao
,
H.
,
2020
, “
Transient Vibration and Feedback Control of an Inductrack Maglev System
,”
ASME
Paper No. IMECE2020-23061.10.1115/IMECE2020-23061
38.
Ham
,
C.
,
Ko
,
W.
,
Lin
,
K. C.
, and
Joo
,
Y.
,
2013
, “
Study of a Hybrid Magnet Array for an Electrodynamic Maglev Control
,”
J. Magnetics
,
18
(
3
), pp.
370
374
.10.4283/JMAG.2013.18.3.370
39.
Griffiths
,
D. J.
, and
Heald
,
M. A.
,
1991
, “
Time‐Dependent Generalizations of the Biot–Savart and Coulomb Laws
,”
Am. J. Phys.
,
59
(
2
), pp.
111
117
.10.1119/1.16589
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