In this work, a numerical effort is presented for modelling and control of structure-acoustics coupled systems. Modelling of sound transmission through a panel-cavity-panel system is presented. An approximate series solution is assumed and the solution is obtained using Galarkin's method. The system to be modelled is consisting of a rectangular cavity with two flexible panels, one at the top of the cavity while the other at the bottom and four other fixed boundaries. PZT pair patches are considered to be bonded to the top panel, and each pair is assumed to produce a pure moment actuation when an electric drive signal is used to excite them. The flexible panel is exposed to an external pressure excitation due to a planar wave generated by a sound source mounted above the cavity. Displacements at the mid points are calculated for the upper and lower panels. The developed model is controlled using the optimal LQR control law. The numerically obtained time responses from the compensated model are found to be acceptable compared to the uncompensated ones. It is found that the actuation of the upper panel can decrease the vibration of the lower one rather than decreasing the acoustic pressure inside the cavity.