It is shown that brushless direct current (DC) motors (BLDCMs), which have found many useful applications in motion control areas, display chaotic behaviors. To avoid undesirable inherent oscillations of such DC motors, a control strategy should be adopted in the applications. So, the control problem of applied chaotic power systems is taken into account in this paper. Some important aspects of the design and implementation are considered to reach a suitable controller for the applications. In this regard, it is assumed that the system is fluctuated by unknown uncertainties and environmental noises. Additionally, a part of the system dynamics is supposed to be unknown in advance and the effects of nonlinear input saturation are fully taken into account. Then, a one input nonsmooth adaptive sliding mode controller is realized to handle the aforementioned issues. The proposed controller does not require any knowledge about the bounds of the system uncertainties and external fluctuations as well as about the parameters of the input saturation. The finite time convergence and robustness of the driven control scheme are mathematically proved and numerically illustrated using matlab simulations for DC motors.

References

References
1.
Wang
,
L.
,
Fan
,
J.
,
Wang
,
Z.
,
Zhan
,
B.
, and
Li
,
J.
,
2015
, “
Dynamic Analysis and Control of a Permanent Magnet Synchronous Motor With External Perturbation
,”
ASME J. Dyn. Syst. Meas. Control
,
138
(
1
), p.
011003
.
2.
Patil
,
O.
, and
Gandhi
,
P.
,
2014
, “
On the Dynamics and Multiple Equilibria of an Inverted Flexible Pendulum With Tip Mass on a Cart
,”
ASME J. Dyn. Syst. Meas. Control
,
136
(
4
), p.
041017
.
3.
Aghababa
,
M. P.
,
2012
, “
Design of an Adaptive Finite-Time Controller for Synchronization of Two Identical/Different Non-Autonomous Chaotic Flywheel Governor Systems
,”
Chin. Phys. B
,
21
(
3
), p.
030502
.
4.
Zhang
,
Z.
,
2015
, “
Empirical Study on the Dissipative Structure Model of Manufacturing Systems Based on Entropy Approach
,”
ASME J. Dyn. Syst. Meas. Control
,
137
(
4
), p.
041003
.
5.
Gan
,
Q.
, and
Li
,
Y.
,
2013
, “
Exponential Synchronization of Stochastic Reaction-Diffusion Fuzzy Cohen-Grossberg Neural Networks With Time-Varying Delays Via Periodically Intermittent Control
,”
ASME J. Dyn. Syst. Meas. Control
,
135
(
6
), p.
061009
.
6.
Shiravani
,
F.
, and
Shafiei
,
M. H.
,
2017
, “
Robust Output Regulation Via Sliding Mode Control and Disturbance Observer: Application in a Forced Van Der Pol Chaotic Oscillator
,”
ASME J. Dyn. Syst. Meas. Control
,
139
(
9
), p.
091015
.
7.
Leite
,
D.
,
Palhares
,
R. M.
,
Campos
,
V. C. S.
, and
Gomide
,
F.
,
2015
, “
Evolving Granular Fuzzy Model-Based Control of Nonlinear Dynamic Systems
,”
IEEE Trans. Fuzzy Syst.
,
23
(
4
), pp.
923
938
.
8.
Aghababa
,
M. P.
,
2017
, “
Stabilization of a Class of Fractional-Order Chaotic Systems Using a Non-Smooth Control Methodology
,”
Nonlinear Dyn.
,
89
(
2
), pp.
1357
1370
.
9.
Rakkiyappan
,
R.
,
Lakshmanan
,
S.
, and
Lim
,
C. P.
,
2016
, “
Asymptotical Synchronization of Lur'e Systems Using Network Reliable Control
,”
ASME J. Dyn. Syst. Meas. Control
,
139
(
1
), p.
011004
.
10.
Lam
,
H. K.
, and
Li
,
H.
,
2014
, “
Synchronization of Chaotic Systems Using Sampled-Data Polynomial Controller
,”
ASME J. Dyn. Syst. Meas. Control
,
136
(
3
), p.
031006
.
11.
Lee
,
H.
, and
Utkin
,
V. I.
,
2007
, “
Chattering Suppression Methods in Sliding Mode Control Systems
,”
Annu. Rev. Control
,
31
(
2
), pp.
179
188
.
12.
Bhat
,
S. P.
, and
Bernstein
,
D. S.
,
2000
, “
Finite-Time Stability of Continuous Autonomous Systems
,”
SIAM J. Control Optim.
,
38
(
3
), pp.
751
766
.
13.
Wang
,
Y.
,
Gu
,
L.
,
Xu
,
Y.
, and
Cao
,
X.
,
2016
, “
Practical Tracking Control of Robot Manipulators With Continuous Fractional-Order Nonsingular Terminal Sliding Mode
,”
IEEE Trans. Ind. Electron.
,
63
(
10
), pp.
6194
6204
.
14.
Yau
,
H.-T.
, and
Chen
,
C.-L.
,
2007
, “
Chaos Control of Lorenz Systems Using Adaptive Controller With Input Saturation
,”
Chaos, Solitons Fractals
,
34
(
5
), pp.
1567
1574
.
15.
Navid
,
V.
,
Khooban
,
M. H.
,
Khayatian
,
A.
, and
Blaabjerg
,
F.
,
2017
, “
Design of Robust Double-Fuzzy-Summation Nonparallel Distributed Compensation Controller for Chaotic Power Systems
,”
ASME J. Dyn. Syst. Meas. Control
,
140
(
3
), p.
031004
.
16.
Hu
,
Q.
,
Jiang
,
B.
, and
Zhang
,
Y.
,
2015
, “
Output Feedback Attitude Tracking for Spacecraft Under Control Saturation and Disturbance
,”
ASME J. Dyn. Syst. Meas. Control
,
138
(
1
), p.
011006
.
17.
He
,
W.
,
He
,
X.
, and
Ge
,
S. S.
,
2016
, “
Vibration Control of Flexible Marine Riser Systems With Input Saturation
,”
IEEE/ASME Trans. Mechatronics
,
21
(1), pp.
254
265
.
18.
Hu
,
Q.
,
Zhang
,
J.
, and
Friswell
,
M. I.
,
2015
, “
Finite-Time Coordinated Attitude Control for Spacecraft Formation Flying Under Input Saturation
,”
ASME J. Dyn. Syst. Meas. Control
,
137
(
6
), p.
061012
.
19.
Aghababa
,
M. P.
, and
Aghababa
,
H. P.
,
2012
, “
Chaos Suppression of a Class of Unknown Uncertain Chaotic Systems Via Single Input
,”
Commun. Nonlinear Sci. Numer. Simul.
,
17
(
9
), pp.
3533
3538
.
20.
Lu
,
S.-M.
,
2016
, “
A Review of High-Efficiency Motors: Specification, Policy, and Technology
,”
Renewable Sustainable Energy Rev.
,
59
, pp.
1
12
.
21.
Hemati
,
N.
,
1994
, “
Strange Attractors in Brushless DC Motors
,”
IEEE Trans. Circuits Syst. I: Fundam. Theory Appl.
,
41
(
1
), pp.
40
45
.
22.
Gao
,
Y.
, and
Chau
,
K. T.
,
2003
, “
Design of Permanent-Magnets to Avoid Chaos in PM Synchronous Machines
,”
IEEE Trans. Magn.
,
39
(
5
), pp.
2995
2997
.
23.
Sira-Ramirez
,
H.
,
Zurita-Bustamante
,
E. W.
, and
Luviano
,
A.
,
2017
, “
Robust Flat Filtering Control of a Nonlinear Manipulator-Direct Current Motor System
,”
ASME J. Dyn. Syst. Meas. Control
,
140
(
2
), p.
021009
.
24.
Campos
,
R. F.
,
Couto
,
E.
,
Oliveira
,
J.
, and
Nied
,
A.
,
2017
, “
On-Line Parameter Identification of an Induction Motor With Closed-Loop Speed Control Using the Least Square Method
,”
ASME J. Dyn. Syst. Meas. Control
,
139
(
7
), p.
071010
.
25.
Zhou
,
L.
, and
Trumper
,
D. L.
,
2017
, “
Reluctance Force Magnetic Suspension Characteristics and Control for Cylindrical Rotor Bearingless Motors
,”
ASME J. Dyn. Syst. Meas. Control
,
139
(
3
), p.
031003
.
26.
Jung
,
J.-W.
,
Leu
,
V. Q.
,
Do
,
T. D.
,
Kim
,
E.-K.
, and
Choi
,
H. H.
,
2015
, “
Adaptive PID Speed Control Design for Permanent Magnet Synchronous Motor Drives
,”
IEEE Trans. Power Electron.
,
30
(
2
), pp.
900
908
.
27.
Premkumar
,
K.
, and
Manikandan
,
B. V.
,
2015
, “
Speed Control of Brushless DC Motor Using Bat Algorithm Optimized Adaptive Neuro-Fuzzy Inference System
,”
Appl. Soft Comput.
,
32
, pp.
403
419
.
28.
Premkumar
,
K.
, and
Manikandan
,
B. V.
,
2015
, “
Fuzzy PID Supervised Online ANFIS Based Speed Controller for Brushless DC Motor
,”
Neurocomputing
,
157
, pp.
76
90
.
29.
Linares-Flores
,
J.
,
García-Rodríguez
,
C.
,
Sira-Ramírez
,
H.
, and
Ramírez-Cárdenas
,
O. D.
,
2015
, “
Robust Backstepping Tracking Controller for Low-Speed PMSM Positioning System: Design, Analysis, and Implementation
,”
IEEE Trans. Ind. Inf.
,
11
(
5
), pp.
1130
1141
.
30.
Xia
,
C.
,
Jiang
,
G.
,
Chen
,
W.
, and
Shi
,
T.
,
2016
, “
Switching-Gain Adaptation Current Control for Brushless DC Motors
,”
IEEE Trans. Ind. Electron.
,
63
(4), pp.
2044
2052
.
31.
Chen
,
Q.
,
Ren
,
X.
, and
Na
,
J.
,
2015
, “
Robust Finite-Time Chaos Synchronization of Uncertain Permanent Magnet Synchronous Motors
,”
ISA Trans.
,
58
, pp.
262
269
.
32.
Prior
,
G.
, and
Krstic
,
M.
,
2014
, “
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
.
33.
Chun
,
T.-W.
,
Tran
,
Q.-V.
,
Lee
,
H.-H.
, and
Kim
,
H.-G.
,
2014
, “
Sensorless Control of BLDC Motor Drive for an Automotive Fuel Pump Using a Hysteresis Comparator
,”
IEEE Trans. Power Electron.
,
29
, pp.
1382
1391
.
34.
Faustner
,
D.
,
Kemmetmüller
,
W.
, and
Kugi
,
A.
,
2016
, “
Flatness-Based Torque Control of Saturated Surface-Mounted Permanent Magnet Synchronous Machines
,”
IEEE Trans. Control Syst. Technol.
,
24
(
4
), pp.
1201
1213
.
35.
Xu
,
W.
,
Jiang
,
Y.
, and
Mu
,
C.
,
2016
, “
Novel Composite Sliding Mode Control for PMSM Drive System Based on Disturbance Observer
,”
IEEE Trans. Appl. Supercond.
,
26
(7), p.
0612905
.
36.
Curran
,
P. F.
, and
Chua
,
L. O.
,
1997
, “
Absolute Stability Theory and the Synchronization Problem
,”
Int. J. Bifurcat. Chaos
,
7
(6), pp.
1357
1382
.
37.
Utkin
,
V. I.
,
1992
,
Sliding Modes in Control Optimization
,
Springer Verlag
,
Berlin
.
38.
Vincent
,
U. E.
, and
Guo
,
R.
,
2011
, “
Finite-Time Synchronization for a Class of Chaotic and Hyperchaotic Systems Via Adaptive Feedback Controller
,”
Phys. Lett. A
,
375
(
24
), pp.
2322
2326
.
39.
Wang
,
F.
,
Zhang
,
X.
,
Chen
,
B.
,
Lin
,
C.
,
Li
,
X.
, and
Zhang
,
J.
,
2017
, “
Adaptive Finite-Time Tracking Control of Switched Nonlinear Systems
,”
Inf. Sci.
,
421
, pp.
126
135
.
You do not currently have access to this content.