In this paper, distributed parameter-dependent modeling and control approaches are proposed for flexible structures. The distributed model is motivated from distributed control design, which is advantageous in reducing control implementation cost and increasing control system reliability. This modeling approach mainly relies on a central finite difference scheme to capture the distributed nature of the flexible system. Based on the proposed distributed model, a sufficient synthesis condition for the design of a distributed output-feedback controller is presented using induced L2 norm as the performance criterion. The controller synthesis condition is formulated as linear matrix inequalities, which are convex optimization problems and can be solved efficiently using interior-point algorithms. The distributed controller inherits the same structure as the plant, which results in a localized control architecture and a simple implementation scheme. These modeling and control approaches are demonstrated on a non-uniform cantilever beam problem through simulation studies.

1.
Meirovitch
,
L.
, 1997,
Principles and Techniques of Vibrations
,
Prentice-Hall
, Upper Saddle River, NJ.
2.
Balas
,
M. J.
, 1978, “
Active Control of Flexible Systems
,”
J. Optim. Theory Appl.
0022-3239,
25
(
3
), pp.
415
436
.
3.
Shiffman
,
J. J.
, 1993, “
Lyapunov Functions and the Control of the Euler-Bernoulli beam
,”
Int. J. Control
0020-7179,
57
(
4
), pp.
971
990
.
4.
Balas
,
M. J.
, 1982, “
Trends in Large Space Structure Control Theory: Fondest Hopes, Wildest Dreams
,”
IEEE Trans. Autom. Control
0018-9286,
AC-27
, pp.
522
535
.
5.
Bruant
,
I.
,
Coffignal
,
G.
,
Lene
,
F.
, and
Verge
,
M.
, 2001, “
Active Control of Beam Structures with Piezoelectric Actuators and Sensors: Modeling and Simulation
,”
Smart Mater. Struct.
0964-1726,
10
, pp.
404
408
.
6.
Varadan
,
V. V.
,
Lim
,
Y.
, and
Varadan
,
V. K.
, 1996, “
Closed Loop Finite-element Modeling of Active/Passive Damping in Structural Vibration Control
,”
Smart Mater. Struct.
0964-1726,
5
, pp.
685
694
.
7.
Kim
,
J.
,
Varadan
,
V. V.
,
Varadan
,
V. K.
, and
Bao
,
X.
, 1996, “
Finite-element Modeling of a Smart Cantilever Plate and Comparison with Experiments
,”
Smart Mater. Struct.
0964-1726,
5
, pp.
165
170
.
8.
Bamieh
,
B.
, 1997, “
The Structure of Optimal Controllers of Spatially Invariant Distributed Parameter Systems
,”
Proc. IEEE Conf. Dec. Contr.
, pp.
1056
1061
.
9.
Bamieh
,
B.
,
Paganini
,
F.
, and
Dahleh
,
M.
, 2002, “
Distributed Control of Spatially-invariant Systems
,”
IEEE Trans. Autom. Control
0018-9286,
AC-47
(
7
), pp.
1091
1107
.
10.
D’Andrea
,
R.
, 1998, “
A Linear Matrix Inequality Approach to Decentralized Control of Distributed Parameter Systems
,”
Proc. Amer. Contr. Conf.
, pp.
1350
1354
.
11.
D’Andrea
,
R.
, and
Dullerud
,
G. E.
, 2003, “
Distributed Control of Spatially Interconnected Systems
,”
IEEE Trans. Autom. Control
0018-9286,
AC-48
(
9
), pp.
1478
1495
.
12.
Dullerud
,
G. E.
,
D’Andrea
,
R.
, and
Lall
,
S. G.
, 1998, “
Control of Spatially Varying Distributed Systems
,”
Proc. 37th IEEE Conf. Dec. Contr.
, pp.
1889
1893
.
13.
Wu
,
F.
, 2003, “
Distributed Control for Interconnected Linear Parameter-dependent Systems
,”
IEE Proc.: Control Theory Appl.
1350-2379,
150
(
5
), pp.
518
527
.
14.
Lupi
,
V. D.
,
Chun
,
H. M.
, and
Turner
,
J. D.
, 1992, “
Distributed Control and Simulation of a Bernoulli-Euler Beam
,” AIAA
J. Guid. Control Dyn.
0731-5090,
15
(
3
), pp.
727
734
.
15.
Zhou
,
K.
, and
Doyle
,
J. C.
, 1998,
Essentials of Robust Control
,
Prentice Hall
, Upper Saddle River, NJ.
16.
Popov
,
E. P.
, 1976,
Mechanics of Materials
,
Prentice Hall
, Upper Saddle River, NJ.,
2 Ed.
17.
Spector
,
V. A.
, and
Flashner
,
H.
, 1989, “
Flexible Manipulator Modeling for Control System Development
,” AIAA
J. Guid. Control Dyn.
0731-5090,
12
(
6
), pp.
943
945
.
18.
Yousefi-Koma
,
A.
, 1997, “
Active Vibration Control of Smart Structures using Piezoelements
,” Ph.D. dissertation, University of Michigan, MI.
19.
D’Andrea
,
R.
, 1999, “
Software for Modeling, Analysis and Control Design for Multidimensional Systems
,”
Proc. IEEE Int. Symp. Computer-Aided Contr. Syst. Design
, pp.
24
27
.
You do not currently have access to this content.