The objective is to use active control to suppress the acoustic energy that is radiated to the far field from a structure that has been excited by a short-duration pulse. The problem is constrained by the assumption that the far-field pressure cannot be directly measured. Therefore, a method is developed for estimating the total radiated energy from measurements on the structure. Using this estimate as a cost function, a feedback controller is designed using linear quadratic regulator theory to minimize the cost. Computer simulations of a clamped-clamped beam show that there is appreciable difference in the total radiated energy between a system with a controller designed to suppress vibrations of the structure and a system with a controller that takes into account the coupling of these vibrations to the surrounding fluid. The results of this work provide a framework for a general, model-based method for actively suppressing transient structural acoustic radiation that can also be applied to steady, narrow, or broadband disturbances.