A mathematical model of the transverse vibration of a plate to be used for
free and forced vibration control purposes is presented. For the analysis o
f plate flexural vibration, the eigenfunctions of a Poisson-Kirchoff plate
have been used as basis functions in a Galerkin formulation. Separation of
variables and a double Fourier expansion coupled with Navier's method are u
sed to find the optimal location of the sensors/actuators. A quadratic cont
rol objective is defined as a measure of system performance. The control ob
jective is composed of those error variables that are important to the desi
gn, and they are used to approximate the high-order plant system by a lower
order model. To guarantee that the error in the reduced model is smaller t
han the desired error, a minimum required number of modes in the plate mode
l has been derived analytically.