Chaotic motion and chaos control of a permanent magnet synchronous motor (PMSM) are studied in this paper. The dynamics of chaotic PMSM with load vibration perturbation is presented and its complex dynamic characteristics are analyzed by using bifurcation diagrams, Lyapunov exponents, and phase portraits. Furthermore, an adaptive neural sliding mode control is addressed to suppress chaos oscillations for the PMSM. The neural network approximation is applied in the controller to emulate of the load perturbation. Simulation results show that the proposed control scheme can eliminate the chaos and make the system achieve stable states even with the existence of unknown load vibration disturbance.

References

1.
Chan
,
C. C.
, and
Chau
,
K. T.
,
1997
, “
An Overview of Power Electronics in Electric Vehicles
,”
IEEE Trans. Ind. Electron.
,
44
(
1
), pp.
3
13
.
2.
Cho
,
Y.
,
Lee
,
K. B.
,
Song
,
J. H.
, and
Lee
,
Y. I.
,
2015
, “
Torque-Ripple Minimization and Fast Dynamic Scheme for Torque Predictive Control of Permanent-Magnet Synchronous Motors
,”
IEEE Trans. Power Electron.
,
30
(
4
), pp.
2182
2190
.
3.
Ananthamoorthy
,
N. P.
, and
Baskaran
,
K.
,
2015
, “
High Performance Hybrid Fuzzy PID Controller for Permanent Magnet Synchronous Motor Drive With Minimum Rule Base
,”
J. Vib. Control
,
21
(
1
), pp.
181
194
.
4.
Jung
,
J. W.
,
Leu
,
V. Q.
,
Do
,
T. D.
,
Kim
,
E. K.
, and
Choi
,
H. H.
,
2014
, “
Adaptive PID Speed Control Design for Permanent Magnet Synchronous Motor Drives
,”
IEEE Trans. Power Electron.
,
30
(
2
), pp.
900
908
.
5.
Deane
,
J. H.
, and
Hamill
,
D. C.
,
1990
, “
Instability, Subharmonics, and Chaos in Power Electronic Systems
,”
IEEE Trans. Power Electron.
,
5
(
3
), pp.
260
268
.
6.
Jing
,
Z.
,
Yu
,
C.
, and
Chen
,
G.
,
2004
, “
Complex Dynamics in a Permanent-Magnet Synchronous Motor Model
,”
Chaos, Solitons Fractals
,
22
(
4
), pp.
831
848
.
7.
Meng
,
Z.
,
Sun
,
C.
,
An
,
Y.
,
Cao
,
J.
, and
Gao
,
P.
,
2007
, “
Chaos Anti-Control of Permanent Magnet Synchronous Motor Based on Model Matching
,”
IEEE International Conference on Electrical Machines and Systems
, pp.
1748
1752
.
8.
Hemati
,
N.
,
1994
, “
Strange Attractors in Brushless DC Motors
,”
IEEE Trans. Circuits Syst. I: Fundam. Theory Appl.
,
41
(
1
), pp.
40
45
.
9.
Li
,
Z.
,
Zhang
,
B.
,
Tian
,
L.
,
Mao
,
Z.
, and
Pong
,
M. H.
,
1999
, “
Strange Attractors in Permanent-Magnet Synchronous Motors
,”
IEEE International Conference on Power Electronics and Drive Systems
, Vol.
1
, pp.
150
155
.
10.
Li
,
Z.
,
Park
,
J. B.
,
Joo
,
Y. H.
,
Zhang
,
B.
, and
Chen
,
G.
,
2002
, “
Bifurcations and Chaos in a Permanent-Magnet Synchronous Motor
,”
IEEE Trans. Circuits Syst. I: Fundam. Theory Appl.
,
49
(
3
), pp.
383
387
.
11.
Hu
,
J.
,
Liu
,
L.
, and
Ma
,
D. W.
,
2014
, “
Robust Nonlinear Feedback Control of a Chaotic Permanent-Magnet Synchronous Motor With a Load Torque Disturbance
,”
J. Korean Phys. Soc.
,
65
(
12
), pp.
2132
2139
.
12.
Gao
,
Y.
, and
Chau
,
K. T.
,
2004
, “
Hopf Bifurcation and Chaos in Synchronous Reluctance Motor Drives
,”
IEEE Trans. Energy Convers.
,
19
(
2
), pp.
296
302
.
13.
Ataei
,
M.
,
Kiyoumarsi
,
A.
, and
Ghorbani
,
B.
,
2010
, “
Control of Chaos in Permanent Magnet Synchronous Motor by Using Optimal Lyapunov Exponents Placement
,”
Phys. Lett. A
,
374
(
41
), pp.
4226
4230
.
14.
Zaher
,
A. A.
,
2008
, “
A Nonlinear Controller Design for Permanent Magnet Motors Using a Synchronization-Based Technique Inspired From the Lorenz System
,”
Chaos: Interdiscip. J. Nonlinear Sci.
,
18
(
1
), p.
013111
.
15.
Yu
,
J.
,
Chen
,
B.
,
Yu
,
H.
, and
Gao
,
J.
,
2011
, “
Adaptive Fuzzy Tracking Control for the Chaotic Permanent Magnet Synchronous Motor Drive System Via Backstepping
,”
Nonlinear Anal.: Real World Appl.
,
12
(
1
), pp.
671
681
.
16.
Choi
,
H. H.
,
2012
, “
Adaptive Control of a Chaotic Permanent Magnet Synchronous Motor
,”
Nonlinear Dyn.
,
69
(
3
), pp.
1311
1322
.
17.
Babaei
,
M.
,
Nazarzadeh
,
J.
, and
Faiz
,
J.
,
2008
, “
Nonlinear Feedback Control of Chaos in Synchronous Reluctance Motor Drive Systems
,”
IEEE
International Conference on Industrial Technology
, Chengdu, China, Apr. 21–24, pp.
1
5
.
18.
Chang
,
S. C.
,
2010
, “
Synchronization and Controlling Chaos in a Permanent Magnet Synchronous Motor
,”
J. Vib. Control
,
16
(
12
), pp.
1881
1894
.
19.
Hao
,
J. H.
,
Wang
,
X. W.
, and
Zhang
,
H.
,
2014
, “
Chaotic Robust Control of Permanent Magnet Synchronous Motor System Under Uncertain Factors
,”
Acta Phys. Sin.
,
63
(
22
), p.
220203
.
20.
Wang
,
J.
,
Chen
,
X.
, and
Fu
,
J.
,
2014
, “
Adaptive Finite-Time Control of Chaos in Permanent Magnet Synchronous Motor With Uncertain Parameters
,”
Nonlinear Dyn.
,
78
(
2
), pp.
1321
1328
.
21.
Prior
,
G.
, and
Krstic
,
M.
,
2015
, “
A Control Lyapunov Approach to Finite Control Set Model Predictive Control for Permanent Magnet Synchronous Motors
,”
ASME J. Dyn. Syst. Meas. Control
,
137
(
1
), p.
011001
.
22.
Zribi
,
M.
,
Oteafy
,
A.
, and
Smaoui
,
N.
,
2009
, “
Controlling Chaos in the Permanent Magnet Synchronous Motor
,”
Chaos, Solitons Fractals
,
41
(
3
), pp.
1266
1276
.
23.
Yu
,
J.
,
Yu
,
H.
,
Chen
,
B.
,
Gao
,
J.
, and
Qin
,
Y.
,
2012
, “
Direct Adaptive Neural Control of Chaos in the Permanent Magnet Synchronous Motor
,”
Nonlinear Dyn.
,
70
(
3
), pp.
1879
1887
.
24.
Bao
,
B. C.
,
2013
,
An Introduction to Chaotic Circuits
,
Science Press
,
Beijing
.
25.
Hilborn
,
R. C.
,
1994
,
Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers
,
Oxford University
,
London
.
26.
Ramasubramanian
,
K.
, and
Sriram
,
M. S.
,
2000
, “
A Comparative Study of Computation of Lyapunov Spectra With Different Algorithms
,”
Phys. D
,
139
(
1
), pp.
72
86
.
27.
Chandrasekar
,
A.
,
Rakkiyappan
,
R.
,
Cao
,
J.
, and
Lakshmanan
,
S.
,
2014
, “
Synchronization of Memristor-Based Recurrent Neural Networks With Two Delay Components Based on Second-Order Reciprocally Convex Approach
,”
Neural Networks
,
57
, pp.
79
93
.
28.
Ku
,
C. C.
, and
Lee
,
K. Y.
,
1995
, “
Diagonal Recurrent Neural Networks for Dynamic Systems Control
,”
IEEE Trans. Neural Networks
,
6
(
1
), pp.
144
156
.
29.
Zheng
,
J. F.
,
Feng
,
Y.
, and
Lu
,
Y. L.
,
2009
, “
High-Order Terminal Sliding-Mode Control for Permanent Magnet Synchronous Motor
,”
Control Theory Appl.
,
26
(
6
), pp.
697
700
.
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