A new robust state and parameter estimation strategy called the Variable Structure Filter (VSF) has recently been proposed and used for state and parameter estimation. A very common problem of linear stochastic systems is to design a combined robust control and estimation strategy, given system and noise uncertainties. Variable Structure Control (VSC) and its special form of Sliding Mode Control (SMC) show superb robustness. This paper proposes a new strategy involving the Sliding Mode Control and the Variable Structure Filter. Both the estimator and controller are based on the concepts of Variable Structure Systems (VSS). In the presence of bounded parametric uncertainties and noise, a robust stability is guaranteed. Further more, the combined strategy can be used to achieve high regulation rates or short settling times. The object of this paper is to introduce this combined VSF and SMC strategy and to demonstrate its application to a third order model of a high precision hydrostatic system, referred to as the Electrohydraulic Actuator System (EHA).

Volume Subject Area:
Fluid Power Systems and Technology
Topics:
Actuators, Control equipment, Filters, Sliding mode control, Noise (Sound), Parameter estimation, Uncertainty, Variable structure systems, Design, Hydrostatics, Robust control, Robustness, Stability, Stochastic systems
1.
Utkin
V I
,
1977
, “
Variable structure system with sliding modes
.”
IEEE Transactions on Automatic Control
,
AC-22
, pp.
212
–
222
.
2.
Letizia
Corradini M.
and
Leo
T.
and
Orlando
G.
,
2002
, “
Experimental Testing of a Discrete-time Sliding Mode Controller for Trajectory Tracking of A Wheeled Mobile Robot in the Presence of Skidding Effects
,”
J. of Robotic systems
19
(
4
), pp.
177
–
188
.
3.
Zinober
A. S. I
,
El-Ghezawi
O. M. E.
and
Billings
S. A.
,
1982
, “
Multivariable-Structure Adaptative Model-following Control Systems
,”
Proceedings of IEEE
,
129
, pp.
6
–
12
.
4.
Slotine
J.-J. E.
,
Hedrick
J. K.
and
Misawa
E. A.
,
1987
, “
On Sliding Observers for Nonlinear Systems
,”
J. of Dynamic Systems, Measurement and Control
,
109
, pp.
245
–
252
5.
Decarlo
R. A.
,
Zak
S. H.
and
Matthews
G. P.
,
1988
, “
Variable Structure Control of Nonlinear Multivariable Systems: A Tutorial
,”
Proceedings of the IEEE
,
76
, No.
3
,
212
–
232
.
6.
Furuta
K.
,
1990
, “
Sliding Mode Control of A Discrete System
,”
System & Control Letters
,
14
, pp.
145
–
152
.
7.
Misawa
E. A.
,
1997
, “
Discrete-Time Sliding Mode Control for Nonlinear Systems With Unmatched Uncertainties and Uncertain Control Vector
,”
ASME Journal of Dynamic Systems, Measurement, and Control
,
119
, pp.
503
–
512
.
8.
Utkin, V. I., 1992, “Sliding Modes in Control Optimization,” Springer-Verlag Berlin.
9.
Walcott
B. L.
and
Zak
S. H.
,
1987
, “
State Observation of Nonlinear Uncertain Dynamical Systems
,”
IEEE Transaction on Automatic Control
,
32
, pp.
166
–
170
.
10.
Habibi
S. R.
and
Burton
R.
,
2003
, “
The Variable Structure Filter
”
ASME Journal of Dynamic Systems, Measurement and Control
,
125
, pp.
287
–
293
.
11.
Sabanovic, A. and Fridman, L. and Spurgeon, S., 2004, “Variable Structure Systems: From Principles to Implementation,” The Institution of Electrical Engineers, London.
12.
S.V. Emelyanov, 1967, “Variable Structure Control Systems,” Moscow: Nauka (in Russian).
13.
Utkin, V. I., 1978, “Sliding Mode and Their Application in Variable Structure Systems,” English translation, Mir Publication, Moscow.
14.
Sarpturk
S. Z.
and
Istefanopulos
Y.
and
Kaynak
O.
,
1987
, “
The Stability of Discrete-time Sliding Mode Control Systems
IEEE Transactions on Automatic Control
, Vol.
32
, pp.
930
–
932
.
15.
Slotine
J.-J. E
and
Sastry
S. S
,
1983
, “
Tracking Control of Nonlinear Systems Using Sliding Surfaces, with Application to Robot Manipulators
,”
International Journal of Control
,
38
, pp.
465
–
492
.
16.
V. Utkin and J. Guldner and J. Shi, 1999, “Sliding Mode Control in Electromechanical Systems,” Taylor & Francis London.
17.
Slotine
J.-J. E.
,
1984
, “
Sliding Controller design for nonlinear Systems
,”
International Journal of Control
,
40
, pp.
421
–
434
.
18.
Itkis, Y., 1976, “Control Systems of Variable Structure,” New York: Wiley.
19.
Misawa
E. A.
,
1997
, “
Discrete-Time Sliding Mode Control: The Linear Case
,”
ASME Journal of Dynamic Systems, Measurement, and Control
,
119
, pp.
819
–
821
20.
Campbell, S.L. and Meyer, C.D. Jr, 1991, “Generalized Inverses of Linear Transformations,” New York: Dover.
21.
Habibi
S. R.
and
Singh
G.
,
2000
, “
Derivation of Design Requirements for Optimization of A High Performance Hydrostatic Actuation System
,”
International Journal of Fluid Power
,
2
, pp.
11
–
27
.
22.
Zinober, A. S. I.(Ed.), 1994, “Variable Structure and Lyapunov Control,” Springer-Verlag London Limited.
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