Active vibration control of an axially moving string by wave cancellation is presented. The control problem is formulated in the frequency domain. An exact, closed-form expression for the transfer function of the controlled system, consisting of the flexible structure, a feedback control law and the dynamics of the sensing and actuation devices, is derived. It is shown that all vibration modes can be stabilized and that the controlled system has no resonance. Moreover, the designed controller is applicable to the control of the string transverse vibration under various kinds of loading and constraint conditions. Results for the response of the controlled string under different excitations are presented and discussed along with the wave propagation and cancellation characteristics.

Issue Section:
Research Papers
Topics:
String, Vibration control, Waves, Vibration, Control equipment, Dynamics (Mechanics), Excitation, Feedback, Flexible structures, Resonance, Transfer functions, Wave propagation
1.
Archibald
F. R.
, and
Emslie
A. G.
,
1958
, “
The Vibration of A String having a Uniform Motion Along Its Length
,”
ASME Journal of Applied Mechanics
, Vol.
25
, No.
3
, pp.
347
–
348
.
2.
Balas
M. J.
,
1978
, “
Feedback Control of Flexible System
,”
IEEE Automatic Control
, Vol.
AC-23
, No.
4
, pp.
673
–
679
.
3.
Butkovskiy, A. G., 1983, Structural Theory of Distributed Systems, Ellis Horwood Limited.
4.
Chung
C. H.
, and
Tan
C. A.
,
1993
, “
Transfer Function Formulation of Constrained Distributed Parameter Systems, Part II: Applications
,” ASME
Journal of Applied Mechanics
, Vol.
60
, No.
4
, Dec, pp.
1012
–
1019
.
5.
Fujii
H.
, and
Ohtsuka
T.
, and
Murayama
T.
,
1992
, “
Wave-Absorbing Control for Flexible Structures with Non-Collocated Sensors and Actuators
,”
Journal of Guidance. Control, and Dynamics
, Vol.
15
, March, pp.
431
–
439
.
6.
Kuehnle, A. U., 1989, “Control of Longitudinal Waves in a Rod with Voigt Damping,” Proceedings of American Control Conference, Pittsburgh, PA, pp. 200–205.
7.
Mace
B. R.
,
1987
, “
Active Control of Flexural Vibrations
,”
Journal of Sound and Vibration
, Vol.
114
, No.
2
, pp.
253
–
270
.
8.
Mote
C. D.
,
1965
, “
A Study of Band Saw Vibrations
,”
Journal of Franklin Institute
, Vol.
279
, pp.
430
–
444
.
9.
Mote
C. D.
,
1972
, “
Dynamic Stability of Axially Moving Materials
,”
Shock and Vibration Digest
, Vol.
4
, No.
4
, pp.
2
–
11
.
1.
Tan
C. A.
, and
Chung
C. H.
,
1993
, “
Transfer Function Formulation of Constrained Distributed Parameter Systems, Part 1: Theory
,”
ASME Journal of Applied Mechanics
, Vol.
60
, No.
4
, Dec, pp.
1004
–
1011
;
2.
also ASME 13th Biennial Conference on Mechanical Vibration and Noise, DE-Vol. 34, pp. 241–252.
1.
Tanaka
N.
, and
Kikushima
Y.
,
1992
, “
Active Wave Control of a Flexible Beam
,”
JSME International Journal
, Series III, Vol.
35
, No.
2
, pp.
236
–
244
.
2.
Ulsoy
A. G.
,
1984
, “
Vibration Control in Rotating or Translating Elastic Systems
,”
ASME Journal of Dynamic Systems. Measurement, and Control
, Vol.
106
, No.
1
, pp.
6
–
14
.
3.
von Flotow
A. H.
,
1986
, “
Traveling Wave Control for Large Space-craft Structures
,”
Journal of Guidance, Control, and Dynamics
, Vol.
9
, No.
4
, pp.
462
–
468
.
4.
von Flotow
A. H.
, and
Scha¨fer
B.
,
1986
, “
Wave-Absorbing Controller for a Flexible Beam
,”
Journal of Guidance, Control, and Dynamics
, Vol.
9
, No.
6
, pp.
673
–
680
.
5.
Wickert
J. A.
, and
Mote
C. D.
,
1988
, “
Current Research on the Vibration and Stability of Axially Moving Materials
,”
Shock and Vibration Digest
, Vol.
20
, No.
5
, pp.
3
–
13
.
6.
Yang
B.
,
1992
, “
Noncolocated Control of a Damped String Using Time Delay
,”
ASME Journal of Dynamic Systems, Measurement, and Control
, Vol.
114
, No.
4
, December, pp.
736
–
740
.
7.
Yang
B.
, and
Mote
C. D.
,
1991
a, “
Active Vibration Control of the Axially Moving String in the s-Domain
,”
ASME Journal of Applied Mechanics
, Vol.
58
, No.
1
, March, pp.
189
–
196
.
8.
Yang
B.
, and
Mote
C. D.
,
1991
b, “
Controllability and Observability of Distributed Gyroscopic Systems
,”
ASME Journal of Dynamic Systems, Measurement, and Control
, Vol.
113
, No.
1
, March, pp.
11
–
17
.
9.
Yang
B.
, and
Tan
C. A.
,
1992
, “
Transfer Functions of One-Dimensional Distributed Parameter System
,”
ASME Journal of Applied Mechanics
, Vol.
59
, December, pp.
1009
–
1014
.
10.
Yang
B.
, and
Mote
C. D.
,
1992
, “
On Time Delay in Noncolocated Control of Flexible Mechanical System
,”
ASME Journal of Dynamic Systems. Measurement, and Control
, Vol.
114
, No.
3
, September, pp.
409
–
415
.
This content is only available via PDF.
Copyright © 1995
 by The American Society of Mechanical Engineers
You do not currently have access to this content.