The active control of acoustic pressure in a 2-D cavity with a flexible boundary (a beam) is considered. Specifically, this control is implemented via piezoceramic patches on the beam which produce pure bending moments. The incorporation of the feedback control in this manner leads to a system with an unbounded input term. Approximation methods in the context of an LQR state space formulation are discussed and numerical results demonstrating the effectiveness of this approach in computing feedback controls for noise reduction are presented.