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A new sliding mode control (SMC) algorithm for the thirdorder uncertain, nonlinear and timevarying dynamic system subject to acceleration constraint is proposed. The algorithm employs a timevarying switching plane. At the initial time t=t_{0}, the plane passes through the point determined by the system initial conditions in the error state space. Afterwards, the plane moves with a constant velocity to the origin of the state space. In order to select the switching plane parameters, the integral of the absolute error is minimised. Two types of the acceleration constraints are considered. First, a conventional constraint expressed by an inequality is analysed and then an elastic (or stretchable) constraint represented by a penalty function is taken into account. In the second case, we assume that the threshold value of the system acceleration is known and exceeding this value is undesirable, however possible if justified by essential improvement of the system performance. In both cases, the switching plane is chosen in such a way that the reaching phase is eliminated, insensitivity of the system to the external disturbance and the model uncertainty is guaranteed from the very beginning of the proposed control action and fast, monotonic error convergence to zero is achieved.
References


1)

R.S. DeCarlo ,
S. Żak ,
G. Mathews
.
Variable structure control of nonlinear multivariable systems: a tutorial.
Proc. IEEE
,
3 ,
212 
232

2)

J.Y. Hung ,
W. Gao ,
J.C. Hung
.
Variable structure control: a survey.
IEEE Trans. Ind. Electron.
,
1 ,
2 
22

3)

J.J.E. Slotine ,
W. Li
.
(1991)
Applied nonlinear control.

4)

V. Utkin
.
Variable structure systems with sliding modes.
IEEE Trans. Autom. Control
,
2 ,
212 
222

5)

S.B. Choi ,
C.C. Cheong ,
D.W. Park
.
Moving switching surfaces for robust control of secondorder variable structure systems.
Int. J. Control
,
1 ,
229 
245

6)

S.B. Choi ,
D.W. Park
.
Moving sliding surfaces for fast tracking control of secondorder dynamic systems.
Trans. ASME J. Dyn. Syst. Meas. Control
,
1 ,
154 
158

7)

S.B. Choi ,
D.W. Park ,
S. Jayasuriya
.
A timevarying sliding surface for fast and robust tracking control of secondorder uncertain systems.
Automatica
,
7 ,
899 
904

8)

A. Bartoszewicz
.
A comment on “A timevarying sliding surface for fast and robust tracking control of secondorder uncertain systems”.
Automatica
,
12 ,
1893 
1895

9)

A. Bartoszewicz
.
Timevarying sliding modes for secondorder systems.
IEE Proc., Control Theory Appl.
,
5 ,
455 
462

10)

S. Tokat ,
I. Eksin ,
M. Gűzelkaya
.
A new design method for sliding mode controllers using a linear timevarying sliding surface.
IMechE
,
455 
466

11)

S. Tokat ,
I. Eksin ,
M. Guzelkaya
.
New approaches for online tuning of the linear sliding surface slope in sliding mode controllers.
Turkish J. Electr. Eng. Comput. Sci.
,
1 ,
45 
59

12)

S. Tokat ,
I. Eksin ,
M. Gűzelkaya ,
Turan Sőylemez
.
Design of a sliding mode controller with a nonlinear timevarying sliding surface.
Trans. Inst. Meas. Control
,
2 ,
145 
162

13)

Temeltas, H.: `A fuzzy adaptation technique for sliding mode controllers', Proc. IEEE Int. Symp. Industrial Electronics, 1998, Pretoria, South Africa, p. 110–115.

14)

Q. Ha ,
D. Rye ,
H. DurrantWhyte
.
Fuzzy moving sliding mode control with application to robotic manipulators.
Automatica
,
607 
616

15)

N. Yagiz ,
Y. Hacioglu
.
Fuzzy sliding modes with moving surface for the robust control of a planar robot.
J. Vib. Control
,
903 
922

16)

F. Betin ,
D. Pinchon ,
G. Capolino
.
A timevarying sliding surface for robust position control of a DC motor drive.
IEEE Trans. Ind. Electron.
,
2 ,
462 
473

17)

Sivert, A., Faqir, A., Nahidmobarakeh, B., Betin, F., Capolino, G.A.: `Moving switching surfaces for high precision control of electrical drives', Proc. IEEE Int. Conf. Industrial Technology, 2004, p. 175–180.

18)

Wai, R.J., Yu, S.L., Su, K.H.: `Development of adaptive fuzzy control for electrical servodrive via total sliding mode technique', IEEE Int. Conf. Fuzzy Systems, 2004, 2, p. 807–812.

19)

D.W. Park ,
S.B. Choi
.
Moving sliding surfaces for highorder variable structure systems.
Int. J. Control
,
960 
970
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