The paper presents a terminal sliding mode controller for a certain class of disturbed nonlinear dynamical systems. The class of such systems is described by nonlinear second-order differential equations with an unknown and bounded disturbance. A sliding surface is defined by the system state and the desired trajectory. The control law is designed to force the trajectory of the system from any initial condition to the sliding surface within a finite time. The trajectory of the system after reaching the sliding surface remains on it. A computer simulation is included as an example to verify the approach and to demonstrate its effectiveness.

References

References
1.
Edward
,
C.
, and
Spurgeon
,
S.
,
1998
,
Sliding Mode Control: Theory and Applications
,
Taylor and Francis
,
London
.
2.
Liu
,
J.
, and
Wang
,
X.
,
2011
,
Advanced Sliding Mode Control for Mechanical Systems
,
Springer, Heidelberg
,
Dordrecht, London, New York
.
3.
Bandyopadhyay
,
B.
,
Deepak
,
F.
, and
Kim
,
K.
,
2010
,
Sliding Mode Control Using Novel Sliding Surfaces
,
Springer-Verlag
,
Berlin, Heidelberg
.
4.
Liu
,
J.
, and
Sun
,
F.
,
2007
, “
A Novel Dynamic Terminal Sliding Mode Control of Uncertain Nonlinear Systems
,”
J. Control Theory Appl.
,
5
(
2
), pp.
189
193
.
5.
Man
,
Z.
, and
Yu
,
X.
,
1997
, “
Terminal Sliding Mode Control of Mimo Linear Systems
,”
IEEE Trans. Circuits Syst.
,
44
(
11
), pp.
1065
1070
.
6.
Mobayen
,
S.
,
Majd
,
V.
, and
Sojoodi
,
M.
,
2012
, “
An LMI-Based Composite Nonlinear Feedback Terminal Sliding-Mode Controller Design for Disturbed Mimo Systems
,”
Math. Comput. Simul.
,
85
(
11
), pp.
1
10
.
7.
Zhihong
,
M.
,
Paplinski
,
A.
, and
Wu
,
H.
,
1994
, “
A Robust Mimo Terminal Sliding Mode Control Scheme for Rigid Robotic Manipulators
,”
IEEE Trans. Autom. Control
,
39
(
12
), pp.
2464
2469
.
8.
Mezghani
,
N.
,
Romdhane
,
B.
, and
Damak
,
T.
,
2010
, “
Terminal Sliding Mode Feedback Linearization Control
,”
Int. J. Sci. Tech. Autom. Control Comput. Eng.
,
4
(
1
), pp.
1174
1187
.
9.
Wu
,
Y.
,
Yu
,
X.
, and
Man
,
Z.
,
1998
, “
Terminal Sliding Mode Control Design for Uncertain Dynamic Systems
,”
Syst. Control Lett.
,
34
(
5
), pp.
281
287
.
10.
Xiang
,
W.
, and
Huangpu
,
Y.
,
2010
, “
Second-Order Terminal Sliding Mode Controller for a Class of Chaotic Systems With Unmatched Uncertainties
,”
Commun. Nonlinear Sci. Numer. Simul.
,
15
(
6
), pp.
3241
3247
.
11.
Li
,
J.
,
Gao
,
F.
,
Wang
,
G.
,
Wang
,
M.
,
Zhu
,
W.
, and
Li
,
Q.
,
2013
, “
Nonsingular Terminal Sliding Mode Control Based on Novel Reaching Law for Nonlinear Uncertain System
,”
Appl. Mech. Mater.
,
347–350
, pp.
302
306
.
12.
Yang
,
L.
, and
Yang
,
J.
,
2011
, “
Nonsingular Fast Terminal Sliding-Mode Control for Nonlinear Dynamical Systems
,”
Int. J. Robust Nonlinear Control
,
21
(
16
), pp.
1865
1879
.
13.
Yu
,
X.
, and
Zhihong
,
M.
,
2002
, “
Fast Terminal Sliding-Mode Control Design for Nonlinear Dynamical Systems
,”
IEEE Trans. Circuits Syst.
,
49
(
2
), pp.
261
264
.
14.
Tao
,
C.
, and
Taur
,
J.
,
2004
, “
Adaptive Fuzzy Terminal Sliding Mode Controller for Linear Systems With Mismatched Time-Varying Uncertainties
,”
IEEE Trans. Syst., Man, Cybernetics, Part B
,
34
(
1
), pp.
255
262
.
15.
Mon
,
Y.
,
2013
, “
Terminal Sliding Mode Fuzzy-PDC Control for Nonlinear Systems
,”
Int. J. Sci. Technol. Res.
,
2
(
4
), pp.
218
221
.
16.
Mitkowski
,
W.
, and
Skruch
,
P.
,
2013
, “
Fractional-Order Models of the Supercapacitors in the Form of RC Ladder Networks
,”
Bull. Pol. Acad. Sci.: Tech. Sci.
,
61
(
3
), pp.
100
106
.
17.
Wang
,
Y.
,
Luo
,
G.
,
Gu
,
L.
, and
Li
,
X.
,
2015
, “
Fractional-Order Nonsingular Terminal Sliding Mode Control of Hydraulic Manipulators Using Time Delay Estimation
,”
J. Vib. Control
.
18.
Feng
,
Y.
,
Yu
,
X.
, and
Zheng
,
Z.
,
2006
, “
Second-Order Terminal Sliding Mode Control of Input-Delay Systems
,”
Asian J. Control
,
8
(
1
), pp.
12
20
.
19.
Rasvan
,
V.
,
2011
, “
Stability and Sliding Modes for a Class of Nonlinear Time Delay Systems
,”
Math. Bohemica
,
136
(
2
), pp.
155
164
.
20.
Yu
,
S.
,
Yu
,
X.
,
Shirinzadeh
,
B.
, and
Man
,
Z.
,
2005
, “
Continuous Finite-Time Control for Robotic Manipulators With Terminal Sliding Mode
,”
Automatica
,
41
(
11
), pp.
1957
1964
.
21.
Feng
,
Y.
,
Yu
,
X.
, and
Man
,
Z.
,
2002
, “
Non-Singular Terminal Sliding Mode Control of Rigid Manipulators
,”
Automatica
,
38
(
12
), pp.
2159
2167
.
22.
Skruch
,
P.
,
2010
, “
Feedback Stabilization of a Class of Nonlinear Second-Order Systems
,”
Nonlinear Dyn.
,
59
(
2
), pp.
681
692
.
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