A modern control theory formulation of Active Structural Acoustic Control (ASAC) of simple structures radiating acoustic energy into light or heavy fluid mediums is discussed in this dissertation. ASAC of a baffled, simply-supported plate subject to mechanical disturbances is investigated. For the case of light fluid loading, a finite element modelling approach is used to extend previous ASAC design methods. Vibration and acoustic controllers are designed for the plate. Comparison of the controller performance shows distinct advantages of the ASAC method for minimizing radiated acoustic power. A novel approach to the modelling of the heavy fluid-loaded plate is developed here. Augmenting structural and acoustic dynamics using state vector formalism allows the design of both vibration and ASAC controllers for the fluid-loaded plate. This modern control approach to active structural acoustic control is unique in its ability to suppress both persistent and transient disturbances on a plate in a heavy fluid. Numerical simulations of the open-loop and closed-loop plate response are provided to support the theoretical developments. / Ph. D.