A model for a 2D acoustic cavity with a flexible boundary (a beam) controlled via piezoceramic patches producing bending moments in the beam is considered. The associated control problem for this fluid/structure interaction system to reduce the acoustic pressure in the cavity involves unbounded control inputs. Approximation methods in the context of an LQR state space formulation are discussed, and numerical results are presented to demonstrate the effectiveness of this approach in computing feedback controls for noise reduction.