This paper presents a variable structure control design methodology for multi-input uncertain dynamic systems using only plant output information. Static output feedback is utilized in the design of the switching surface using a Linear Matrix Inequality approach recently proposed in the literature. A novel LMI based optimization approach is subsequently employed in the construction of the control law to guarantee that a sliding motion takes place. The efficacy of the algorithms is demonstrated on a nontrivial design example—an aircraft system representation which includes the flexible modes of the airframe. [S0022-0434(00)00204-5]

Issue Section:
Technical Papers
Keywords:
feedback, variable structure systems, multivariable control systems, uncertain systems, control system synthesis, matrix algebra, optimisation, aircraft control
Topics:
Aircraft, Control equipment, Design, Feedback, Linear matrix inequalities, Optimization
1.
El-Khazali, R., and DeCarlo, R., 1992, “Variable structure output feedback control,” Proceedings of the American Control Conference, pp. 871–875.
2.
Z˙ak
,
S.
, and
Hui
,
S.
,
1993
, “
Output feedback in variable structure controllers and state estimators for uncertain/nonlinear dynamic systems
,”
Proc. IEE, Part D
, Vol.
140
, pp.
41
–
50
.
3.
Hui
,
S.
, and
Z˙ak
,
S.
,
1993
, “
Robust output feedback stabilisation of uncertain dynamic systems with bounded controllers
,”
Int. J. Robust Nonlinear Control
,
3
, pp.
115
–
132
.
4.
Edwards
,
C.
, and
Spurgeon
,
S.
,
1995
, “
Sliding mode stabilisation of uncertain systems using only output information
,”
Int. J. Control
,
62
, pp.
1129
–
1144
.
5.
Heck
,
B.
,
Yallapragada
,
S.
, and
Fan
,
M.
,
1995
, “
Numerical methods to design the reaching phase of output feedback variable structure control
,”
Automatica
,
31
, pp.
275
–
279
.
6.
Edwards
,
C.
, and
Spurgeon
,
S.
,
2000
, “
On the limitations of some variable structure output feedback controller designs
,”
Automatica
,
36
, pp.
743
–
748
.
7.
Arzelier, D., Angulo, M., and Bernussou, J., 1997, “Sliding surface design by quadratic stabilization and pole placement,” Proceedings of the European Control Conference.
8.
Benton
,
R.
, and
Smith
,
D.
,
1998
, “
Static output feedback stabilization with prescribed degree of stability
,”
IEEE Trans. Autom. Control
,
AC-43
, pp.
1493
–
1496
.
9.
Iwasaki
,
T.
, and
Skelton
,
R.
,
1994
, “
Linear quadratic optimal control with static output feedback
,”
Syst. Control Lett.
,
23
, pp.
421
–
430
.
10.
Iwasaki
,
T.
, and
Skelton
,
R.
,
1995
, “
Parametrization of all stabilizing controller via quadratic Lyapunov functions
,”
J. Optim. Theory Appl.
,
77
, pp.
291
–
307
.
11.
Gahinet, P., Nemirovski, A., Laub, A., and Chilali, M., 1995, LMI Control Toolbox, Users’s Guide, The Math Works, Inc.
12.
Syrmos
,
V.
,
Abdallah
,
C.
,
Dorato
,
P.
, and
Grigoriadis
,
K.
,
1997
, “
Static output feedback-a survey
,”
Automatica
,
33
, pp.
125
–
137
.
13.
Ghaoui
,
L. E.
,
Oustry
,
F.
, and
AitRami
,
M.
,
1997
, “
A cone complementary linearization algorithm for static output-feedback and related problems
,”
IEEE Trans. Autom. Control
,
42
, pp.
1171
–
1176
.
14.
Chilali
,
M.
, and
Gahinet
,
P.
,
1996
, “
H∞ design with pole placement constraints: an LMI approach
,”
IEEE Trans. Autom. Control
,
AC-41
, pp.
358
–
367
.
15.
Kaynes, I., and Fry, D., 1983, “The initial design of active control systems for a flexible aircraft,” AGARD Conference Proceedings No. 354.
Copyright © 2000
 by ASME
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