In this paper, position control of servomotors is addressed. A radial basis function neural network is employed to identify the unknown nonlinear function of the plant model, and then a robust adaptive law is developed to train the parameters of the neural network, which does not require any preliminary off-line weight learning. Moreover, base on the identified model, we propose a new dynamic sliding mode control (DSMC) for a general class of nonaffine nonlinear systems by defining a new adaptive proportional-integral sliding surface and employing a linear state feedback. The main property of proposed controller is that it does not need an upper bound for the uncertainty and identified model; moreover, the switching gain increases and decreases according to the system circumstance by employing an adaptive procedure. Then, chattering is removed completely by using the DSMC with a small switching gain.

References

References
1.
Young
,
K. D.
,
Utkin
,
V. I.
, and
Ozguner
,
U.
, 1999, “
A Control Engineer’s Guide to Sliding Mode Control
,”
IEEE Trans. Control Syst. Technol.
,
7
(
3
), pp.
328
342
.
2.
Slotine
,
J. -J. E. E.
, and
Li
,
W.
,
Applied Nonlinear Control
(
Prentice-Hall
, 1991).
3.
Perruquetti
,
W.
, and
Pierre-Barbot
,
J.
,
Sliding Mode Control in Engineering
(
Marcel Dekker
, 2002).
4.
Gao
,
W.
, and
Hung
,
J. C.
, 1993, “
Variable Structure Control of Nonlinear Systems: A New Approach
,”
IEEE Trans. Ind. Electron.
,
40
(
1
), pp.
45
55
.
5.
Su
,
J.-P.
, and
Wang
,
C.-C.
, 2002, “
Complementary Sliding Control of Non-Linear Systems
,
Int. J. Control
,
75
(
5
), pp.
360
368
.
6.
Bartolini
,
G.
, and
Pydynowski
,
P.
, 1996, “
An Improved, Chattering Free, VSC Scheme for Uncertain Dynamical Systems
,”
IEEE Trans. Autom. Control
,
41
(
8
), pp.
1220
1226
.
7.
Bartolini
,
G.
,
Ferrara
,
A.
,
Usai
,
E.
, and
Utkin
,
V. I.
, 2000, “
On Multi-Input Chattering-Free Second-Order Sliding Mode Control
,”
IEEE Trans. Autom. Control
,
45
(
9
), pp.
1711
1717
.
8.
Asada
,
H.
, and
Slotine
,
J. -J. E. E.
,
Robot Analysis and Control
(
Wiley
,
New York
, 1986).
9.
Chen
,
M.-S.
,
Hwang
,
Y.-R.
, and
Tomizuka
,
M.
, 2000, “
A State-Dependent Boundary Layer Design for Sliding Mode Control
,”
IEEE Trans. Autom. Control
,
47
(
10
), pp.
1677
1681
.
10.
Chen
,
M.-S.
,
Chen
,
C.-H.
, and
Yang
,
F.-Y.
, 2007, “
An LTR-Observer-Based Dynamic Sliding Mode Control for Chattering Reduction
,”
Automatica
,
453
, pp.
1111
1116
.
11.
Emelyanov
,
S. V.
,
Korovin
,
S. K.
, and
Levant
,
A.
, 1993, “
Higher-Order Sliding Modes in Control Systems
,”
Diff. Eq.
,
29
, pp.
1627
1647
.
12.
Levant
,
A.
, 1993, “
Sliding Order and Sliding Accuracy in Sliding Mode Control
,”
Int. J. Control
,
58
, pp.
1247
1263
.
13.
Bartolini
,
G.
,
Ferrara
,
A.
, and
Usai
,
E.
, 1998, “
Chattering Avoidance by Second-Order Sliding Mode Control
,”
IEEE Trans. Autom. Control
,
43
(
2
), pp.
241
246
.
14.
Oh
,
S.
, and
Khalil
,
H.
, 1997, “
Nonlinear Output Feedback Tracking Using High-Gain Observer and Variable Structure Control
,”
Automatica
,
33
, pp.
1845
1856
.
15.
Levant
,
A.
, 1998, “
Robust Exact Differentiation via Sliding Mode Techniques
,”
Automatica
,
34
, pp.
379
384
.
16.
Boiko
,
I.
, and
Fridman
,
L.
, 2005, “
Analysis of Chattering in Continuous Sliding-Mode Controllers
,”
IEEE Trans. Autom. Control
,
50
(
9
), pp.
1442
1446
.
17.
Boiko
,
I.
,
Fridman
,
L.
, and
Iriarte
,
R.
, 1994, “
Analysis of Chattering in Continuous Sliding Mode Control
,”
IEEE Trans. Autom. Control
,
39
(
12
), pp.
2465
2469
.
18.
Man
,
Z.
,
Poplinsky
,
A. P.
, and
Wu
,
H. R.
, 2005, “
A Robust Terminal Sliding-Mode Control Scheme for Rigid Robot Manipulators
,”
American Control Conference
,
Portland
,
OR
, pp.
2439
2444
.
19.
Tanaka
,
K.
, and
Wang
,
H. O.
,
Fuzzy Control Systems Design and Analysis
(
John Wiley
,
Canada
, 2001).
20.
Bose
,
B. K.
,
Power Electronics and AC Drives
(
Prentice-Hall
,
Englewood Cliffs, NJ
, 1986).
21.
Novotny
,
D. W.
, and
Lipo
,
T. A.
,
Vector Control and Dynamics of AC Drives
(
Oxford University Press
,
New York
, 1996).
22.
Lin
,
C.-M.
, and
Hsu
,
C.-F.
, 2004, “
Adaptive Fuzzy Sliding-Mode Control for Induction Servomotor System
,”
IEEE Trans. Energy Convers.
,
19
(
2
), pp.
362
368
.
23.
Lee
,
H.
, and
Utkin
,
V.-I.
, 2007, “
Chattering Suppression Methods in Sliding Mode Control Systems
,”
Annu. Rev. Control
,
31
, pp.
179
188
.
24.
Narendra
,
K. S.
, and
Parthasarathy
,
K.
, 1990, “
Identification and Control of Dynamic Systems Using Neural Networks
,”
IEEE Trans. Neural Netw.
,
1
(
1
), pp.
4
27
.
25.
Levin
,
A. U.
, and
Narendra
,
K. S.
, 1996, “
Control of Nonlinear Dynamical Systems Using Neural Networks–Part II: Observability, Identification, and Control
,”
IEEE Trans. Neural Netw.
,
7
(
1
), pp.
30
42
.
26.
Hunt
,
K. J.
,
Sbarbaro
,
D.
,
Zbikowski
,
R.
, and
Gawthrop
,
P. J.
, 1992, “
Neural Networks for Control System-A Survey
,”
Automatica
,
28
(
6
), pp.
1083
1112
.
27.
Lewis
,
F. L.
,
Lu
,
K.
, and
Yesildirek
,
A.
, 1995, “
Neural Net Robot Controller With Guarantee Tracking Performance
,”
IEEE Trans. Neural Netw.
,
6
(
3
), pp.
703
715
.
28.
Khalil
,
H. K.
,
Nonlinear Systems
(
Prentice-Hall
,
Englewood Cliffs, NJ
, 1996).
29.
Narendra
,
K. S.
, and
Parthasarathy
,
K.
, 1987, “
A New Adaptive Law for Robust Adaptation Without Persistent Excitation
,”
IEEE Trans. Autom. Control
,
32
, pp.
134
145
.
30.
Edvards
,
C.
, and
Spurgeon
,
S.
,
Sliding Mode Control: Theory and Applications
(
Taylor & Francis
, 1998).
31.
Zhihong
,
M.
, and
Glumineau
,
X. H. Y.
, 1997, “
Terminal Sliding Mode Control of MIMO Linear Systems
,”
IEEE Trans. Circuits Syst.
,
44
(
11
), pp.
1065
1070
.
32.
Levant
,
A.
, 2001, “
Universal SISO Sliding-Mode Controllers With Finite Time Convergence
,”
IEEE Trans. Autom. Control
,
49
, pp.
1447
1451
.
33.
Levant
,
A.
, 2005, “
Homogeneity Approach to High-Order Sliding Mode Design
,”
Automatica
,
41
, pp.
823
830
.
34.
Hirschorn
,
R. M.
, 2001, “
Singular Sliding-Mode Control
,”
IEEE Trans. Autom. Control
,
46
(
2
), pp.
469
472
.
35.
Cavallo
,
A.
,
Maria
,
G. D.
, and
Nistri
,
P.
, 1999, “
Robust Control Design With Integral Action and Limited Rate Control
,”
IEEE Trans. Autom. Control
,
44
(
8
), pp.
1569
1572
.
36.
Cavallo
,
A.
, and
Natale
,
C.
, 2003, “
Output Feedback Control Based on a High-Order Sliding Manifold Approach
,”
IEEE Trans. Autom. Control
,
48
(
3
), pp.
469
472
.
You do not currently have access to this content.