A lumping method via an inverse modal analysis approach is proposed in this paper for creating a lumped parameter model for a structure with distributed parameters. On the basis of the lumped parameter model, the formulation of an optimal controller in physical state space is presented and, furthermore, the design of a reduced-order controller is described. The method is demonstrated and verified by the vibration and noise control experiments carried out on a clamped plate. Several modes of the plate with high sound radiating efficiencies are well controlled by using three sensors and one actuator, based on a 9 degree-of-freedom (DOF) lumped parameter model of the plate.

1.
Nelson, P. A., and Elliott, S. J., 1992, Active Control of Sound, Academic, London.
2.
Baumann
,
W. T.
,
Ho
,
F. S.
, and
Robertshaw
,
H. H.
,
1992
, “
Active structural acoustic control of broadband disturbances
,”
J. Acoust. Soc. Am.
,
92
, pp.
1998
2005
.
3.
Thomas
,
D. R.
, and
Nelson
,
P. A.
,
1995
, “
Feedback control of sound radiation from a plate excited by a turbulent boundary layer
,”
J. Acoust. Soc. Am.
,
98
, pp.
2651
2662
.
4.
Fuller, C. R., Elliott, S. J., and Nelson, P. A., 1996, Active Control of Vibration, Academic, London.
5.
Meirovitch, L., 1990, Dynamics and Control of Structures, Wiley, New York.
6.
Bai
,
M. R.
, and
Shieh
,
C.
,
1985
, “
Active noise cancellation by using the linear quadratic Gaussian independent modal space control
,”
J. Acoust. Soc. Am.
,
97
, pp.
2664
2674
.
7.
Kosut
,
R. L.
,
1970
, “
Suboptimal control of linear time-invariant systems subject to control structure constraints
,”
IEEE Trans. Autom. Control
,
AC-15
, pp.
557
563
.
8.
Seto
,
K.
, and
Mitsuta
,
S.
,
1994
, “
A new method for making a reduced-order model of flexible structures using unobservability and uncontrollability and its application in vibration control
,”
JSME Int. J., Series C
,
37
, pp.
444
449
.
9.
Balas
,
M. J.
,
1978
, “
Feedback control of flexible structures
,”
IEEE Trans. Autom. Control
,
AC-23
, pp.
673
679
.
10.
Ren, M. Z., Doi, F., Seto, K., and Gadate, Y., 1996, “The influence of phase-lag on active structure-borne sound control of flexible plate,” Proceedings of 3rd International Conference on Motion and Vibration Control (MOVIC), Japan, pp. 365–370.
You do not currently have access to this content.