In this paper, a multirate output feedback (MROF) based discrete-time sliding mode control for the stochastic system with slowly varying bounded uncertainty is proposed. The states are estimated by the multirate Kalman filter and are used for designing the stochastic sliding mode controller which guarantee the stability under the bounded uncertainty and the uncertain noise covariance. The proposed algorithm has advantage of computational and implementation simplicity as it requires only the past output and input information. The stochastic sliding band (SSB) is also calculated which is found to be wider as compared to the state feedback case. Finally, the design procedure for stochastic sliding mode controller is demonstrated with an illustrative example.

References

References
1.
Utkin
,
V. I.
,
1977
, “
Variable Structure Systems With Sliding Mode
,”
IEEE Trans. Autom. Control
,
22
(
2
), pp.
212
222
.
2.
Utkin
,
V. I.
,
1992
,
Sliding Modes in Control Optimization
,
Springer-Verlag
,
New York
.
3.
Hung
,
J. Y.
,
Gao
,
W.
, and
Hung
,
J. C.
,
1993
, “
Variable Structure Control: A Survey
,”
IEEE Trans. Ind. Electron.
,
40
(
1
), pp.
2
22
.
4.
Edwards
,
C.
, and
Spurgeon
,
S. K.
,
1998
,
Sliding Mode Control: Theory and Applications
,
Taylor and Francis
,
London, UK
.
5.
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
.
6.
Milosavljevic
,
C.
,
1985
, “
General Conditions for the Existence of Quasi Sliding Mode on the Switching Hyperplane in Discrete Variable Structure Systems
,”
Autom. Remote Control
,
46
, pp.
307
314
.
7.
Sarpturk
,
S. Z.
,
Istefanopulos
,
Y.
, and
Kaynak
,
O.
,
1987
, “
On the Stability of Discrete-Time Sliding Mode Control Systems
,”
IEEE Trans. Control Systems
,
32
(
10
), pp.
930
932
.
8.
Gao
,
W.
,
Wang
,
Y.
, and
Homaifa
,
A.
,
1995
, “
Discrete-Time Variable Structure Control System
,”
IEEE Trans. Ind. Electron.
,
42
(
2
), pp.
117
122
.
9.
Bartoszewicz
,
A.
,
1995
, “
A Comment on a ‘Time-Varying Sliding Surface for Fast and Robust Tracking Control of Second-Order Uncertain Systems'
,”
Automatica
,
31
(
12
), pp.
1893
1895
.
10.
Bartoszewicz
,
A.
,
1998
, “
Discrete-Time Quasi Sliding Mode Control Strategies
,”
IEEE Trans. Ind. Electron.
,
45
(
4
), pp.
633
637
.
11.
Bartoszewicz
,
A.
, and
Nowacka-Leverton
,
A.
,
2009
,
Time-Varying Sliding Modes for Second and Third Order Systems
,
Springer–Verlag
,
Berlin/Heidelberg
.
12.
Kranc
,
G. M.
,
1957
, “
Input-Output Analysis of Multi-Rate Feedback System
,”
IRE Trans. Autom. Control
,
3
(
1
), pp.
21
28
.
13.
Jury
,
E.
,
1967
, “
A Note on Multirate Sampled-Data Systems
,”
IRE Trans. Autom. Control
,
12
(
3
), pp.
319
320
.
14.
Hagiwara
,
T.
, and
Araki
,
M.
,
1988
, “
Design of a Stable State Feedback Controller Based on the Multi-Rate Sampling of Plant Output
,”
IEEE Trans. Autom. Control
,
33
(
9
), pp.
812
819
.
15.
Colaneri
,
P.
,
Scattolini
,
R.
, and
Schiavoni
,
N.
,
1990
, “
Stabilization of Multi-Rate Sampled-Data Linear Systems
,”
Automatica
,
26
(
2
), pp.
377
380
.
16.
Werner
,
H.
, and
Furuta
,
K.
,
1995
, “
Simultaneous Stabilization by Piecewise Constant Periodic Output Feedback
,”
Control Theory Adv. Technol.
,
10
(
4
), pp.
1763
1775
.
17.
Werner
,
H.
,
1998
, “
Multimodel Robust Control by Fast Output Sampling—An LMI Approach
,”
Automatica
,
34
(
12
), pp.
1625
1630
.
18.
Janardhanan
,
S.
, and
Bandyopadhyay
,
B.
,
2006
, “
Output Feedback Sliding Mode Control for Uncertain Systems Using Fast Output Sampling Technique
,”
IEEE Trans. Ind. Electron.
,
53
(
5
), pp.
1677
1682
.
19.
Janardhanan
,
S.
, and
Bandyopadhyay
,
B.
,
2007
, “
Multirate Output Feedback Based Robust Quasi-Sliding Mode Control of Discrete-Time Systems
,”
IEEE Trans. Autom. Control
,
52
(
3
), pp.
499
503
.
20.
Mehta
,
A.
, and
Bandyopadhyay
,
B.
,
2006
, “
Multirate Output Feedback Based Frequency Shaped Sliding Mode Control
,”
IEEE International Conference on Industrial Technology
(ICIT2006)
, pp.
2658
2662
.
21.
Mehta
,
A.
, and
Bandyopadhyay
,
B.
,
2009
, “
Frequency Shaped Sliding Mode Control Using Output Sampled Measurements
,”
IEEE Trans. Ind. Electron.
,
56
(
1
), pp.
28
35
.
22.
Mehta
,
A.
, and
Bandyopadhyay
,
B.
,
2010
, “
The Design and Implementation of Output Feedback Based Frequency Shaped Sliding Mode Controller for the Smart Structure
,”
2010 IEEE Symposium on Industrial Electronics
(ISIE2010)
, Bari, Italy, July 4–7, pp.
353
358
.
23.
Mehta
,
A.
, and
Bandyopadhyay
,
B.
,
2015
,
Frequency Shaped and Observer Based Discrete-Time Sliding Mode Control
,
Springer
,
Heidelberg, Germany
.
24.
Shah
,
D.
, and
Mehta
,
A.
,
2015
, “
Output Feedback Discrete-Time Networked Sliding Mode Control
,”
International Workshop on Recent Advances in Sliding Modes
(RASM2015)
, Istanbul, Turkey, Apr. 9–11, pp.
1
7
.
25.
Yaz
,
E.
, and
Azemi
,
A.
,
1993
, “
Sliding Mode Observer for Nonlinear Models With Unbounded Noise and Measurement Uncertainties
,”
Dyn. Control
,
3
(
3
), pp.
217
235
.
26.
Yaz
,
E.
, and
Azemi
,
A.
,
1993
, “
Variable Structure Observer With a Boundary Layer for Correlated Noise/Disturbance Models and Disturbance Minimization
,”
Int. J. Control
,
57
(
5
), pp.
1191
1206
.
27.
Zeng
,
F.
,
Cheng
,
M.
, and
Gao
,
W.-B.
,
1994
, “
Variable Structure Control of Stochastic System
,”
Syst. Control Lett.
,
22
(
3
), pp.
209
222
.
28.
Er
,
M. J.
, and
Anderson
,
B. D. O.
,
1992
, “
Performance Study of Multi-Rate Output Controllers Under Noise Disturbance
,”
Int. J. Control
,
56
(
3
), pp.
531
545
.
29.
Drazenovic
,
B.
,
1969
, “
The Invariance Conditions in Variable Structure Systems
,”
Automatica
,
5
(
3
), pp.
287
295
.
30.
Kwakernaak
,
H.
, and
Sivan
,
R.
,
1972
,
Linear Optimal Control Systems
,
Wiley Interscience
,
New York
.
31.
Sangsuk-Iam
,
S.
, and
Bullock
,
T. E.
,
1990
, “
Analysis of Discrete-time Kalman Filtering Under Incorrect Noise Covariances
,”
IEEE Trans. Autom. Control
,
35
(
12
), pp.
531
545
.
32.
Su
,
W. C.
,
Drakuunov
,
S. V.
, and
Ozguner
,
U.
,
2000
, “
An O(T2) Boundary Layer in Sliding Mode for Sampled-Data Systems
,”
IEEE Trans. Autom. Control
,
45
(
3
), pp.
482
485
.
33.
Kennedy
,
W. J.
, and
Gentle
,
J. F.
,
1980
,
Statistical Computing
,
Dekker
,
New York
.
You do not currently have access to this content.