Control of the vibrating structures is desirable in various engineering applications for preventing fatigue and failure. It can be achieved by passive means using dynamic absorbers or by active means using sensors and actuators. In some cases, it is also not practical to apply a desirable control force in those locations at which the dynamics of the structure are to be controlled. In recent years, dynamic absorption schemes are investigated in which control strategies that absorb a steady state motion of a desired location in the structure have been developed. Such a vibration control strategy is termed as zero assignment. Unlike conventional full-state feedback control, which requires all the states of the system to be measured, zero assignment requires least numbers of sensors and actuators (depending on the number of dynamic absorption points) for estimating the control gains and, hence, it may provide economical engineering solution. However, while applying control strategy by active zero assignment, small time delay from the sensors and actuators in the feedback loop is unavoidable and they influence the control gains as well as the stability of the system. In this paper, we have developed vibration control strategy by active zero assignment and obtained closed form control gains for systems with and without time delays by using truncated and full Taylor series expansion. Some examples related to conservative and nonconservative systems as well as realistic distributed parameter systems are presented to demonstrate the active dynamic absorption and the effects of time delay on control gains. The effect of delay in the stability of the controlled system is also summarized.

1.
Den Hartog
,
J. P.
, 1984,
Mechanical Vibration
, 4th ed.,
Dover
,
New York
.
2.
Alkhatib
,
R.
, and
Golnaraghi
,
M.
, 2003, “
Active Structural Vibration Control: A Review
,”
Shock Vib.
1070-9622,
35
(
5
), pp.
367
383
.
3.
Ram
,
Y. M.
, and
Elhay
,
S.
, 1996, “
The Theory of a Multi Degree of Freedom Dynamic Absorber
,”
J. Sound Vib.
0022-460X,
195
, pp.
607
615
.
4.
Mottershead
,
J. E.
, and
Lallement
,
G.
, 1999, “
Vibration Nodes, and the Cancellation of Poles and Zeros by Unit Rank Modifications to Structures
,”
J. Sound Vib.
0022-460X,
222
(
5
), pp.
833
851
.
5.
Singh
,
K. V.
, and
Ram
,
Y. M.
, 2000, “
Dynamic Absorption by Passive and Active Control
,”
ASME J. Vibr. Acoust.
0739-3717,
122
, pp.
429
433
.
6.
Mottershead
,
J. E.
, 2001, “
Structural Modification for the Assignment of Zeros Using Measured Receptances
,”
ASME J. Appl. Mech.
0021-8936,
68
(
5
), pp.
791
798
.
7.
Mottershead
,
J. E.
,
Mares
,
C.
, and
Friswell
,
M. I.
, 2001, “
An Inverse Method for the Assignment of Vibration Nodes
,”
Mech. Syst. Signal Process.
0888-3270,
15
(
1
), pp.
87
100
.
8.
Ram
,
Y. M.
, 2002, “
Nodal Control of a Vibrating Rod
,”
Mech. Syst. Signal Process.
0888-3270,
16
, pp.
69
81
.
9.
Singh
,
A. N.
,
Singh
,
K. V.
,
Ram
,
Y. M.
, and
Pang
,
S.
, 2003, “
Zero Assignment in Continuous Systems
,”
Proceedings of the ASME International Mechanical Engineering Congress and R&D Exposition (IMECE) Conference
, Washington, Vol.
2
, pp.
1065
1071
.
10.
Singh
,
A. N.
, and
Ram
,
Y. M.
, 2003, “
Dynamic Absorption in a Vibrating Beam
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
0954-4062,
217
, pp.
187
197
.
11.
Diekmann
,
O.
,
van Gils
,
S. A.
,
Lunel
,
S. M. V.
, and
Walther
,
H.-O.
, 1995,
Delay Equations, Functional, Complex and Nonlinear Analysis
,
Springer-Verlag
,
New York
.
12.
Gu
,
K.
,
Kharitonov
,
V. L.
, and
Chen
,
J.
, 2003,
Stability of Time-Delay Systems
,
Birkhauser
,
Boston
.
13.
Hu
,
H. Y.
, and
Wang
,
Z. H.
, 2002,
Dynamics of Controlled Mechanical Systems With Delayed Feedback
,
Springer
,
New York
.
14.
Stepan
,
G.
, 1989,
Retarded Dynamical Systems: Stability and Characteristic Functions
,
Longman Scientific and Technical
,
Essex
.
15.
Watanabe
,
K.
,
Nobuyama
,
E.
, and
Kojima
,
K.
, 1996, “
Recent Advances in Control of Time-Delay Systems a Tutorial Review
,”
35th IEEE CDC ’96 (Conference on Decision and Control)
, Kobe, Japan, pp.
2083
2089
.
16.
Richard
,
J. -P.
, 2003, “
Time-Delay Systems: An Overview of Some Recent Advances and Open Problems
,”
Automatica
0005-1098,
39
(
10
), pp.
1667
1694
.
17.
Datta
,
B. N.
, 2003,
Numerical Methods for Linear Control Systems Design and Analysis
,
Elsevier Academic Press
,
Boston
.
18.
Ram
Y. M.
, and
Singh
K. V.
, 2008, “
Active Absorption of Viscously Damped System With Time Delay
,”
ASME J. Appl. Mech.
0021-8936,
75
(
5
), p.
051005
.
19.
Mottershead
,
J. E.
, and
Ram
,
Y. M.
, 2006, “
Inverse Eigenvalue Problems in Vibration Absorption: Passive Modification and Active Control
,”
Mech. Syst. and Signal Process.
0888-3270,
20
(
1
), pp.
5
44
.
20.
Datta
,
B. N.
,
Ram
,
Y.
, and
Elhay
,
S.
, 1997, “
Orthogonality and Partial Pole Assignment for the Symmetric Definite Quadratic Pencil
,”
Linear Algebra Appl.
,
257
, pp.
29
48
.
21.
Datta
,
B. N.
, and
Sarkissian
,
D.
, 2001, “
Theory and Computations of Some Inverse Eigenvalue Problems for the Quadratic Pencil
,”
Contemp. Math.
0271-4132,
280
, pp.
221
239
.
22.
Datta
,
B. N.
,
Ram
,
Y. M.
, and
Sarkissian
,
D. R.
, 2002, “
Spectrum Modification in Gyroscopic Systems
,”
Z. Angew. Math. Mech.
0044-2267,
82
, pp.
191
200
.
23.
Datta
,
B. N.
, and
Sarkissian
,
D. R.
, 2002, “
Feedback Control in Distributed Parameter Gyroscopic Systems: A Solution of the Partial Eigenvalue Assignment Problem
,”
Mech. Syst. Signal Process.
0888-3270,
16
(
1
), pp.
3
17
.
24.
Holt
,
D. A.
, and
Singh
,
K. V.
, 2009, “
Active/Passive Vibration Control of Continuous Systems by Zero Assignments
,”
Proceedings of the International Modal Analysis Conference, IMAC XXVII, A Conference and Exposition on Structural Dynamics
, Orlando, FL, Feb. 9–12.
You do not currently have access to this content.