This study is concerned with the problem of active structural acoustic control (ASAC) of radiation from elastically supported plates under multiple-frequency excitation. The control is achieved by use of piezoelectric (PZT) actuators. An optimization procedure is developed to find the optimal locations of actuators with which the radiated sound power from the plate is minimized. Also, the optimization of the piezoelectric actuator locations has been conducted for the active control of sound radiation from plates under heavy fluid loading. In this dissertation, two types of approaches have been developed to optimally design the error sensors. One is to design the sensors which can provide information about the radiated sound power. The other is based on the sufficient conditions developed in this work for the error criteria in the linear quadratic optimal control theory. For the second approach, an optimization procedure has been developed to determine the optimal locations of microphone sensors in the sound field or the optimal dimensions and locations of polyvinylidene fluoride (PVDF) structural sensors applied directly to the plates. Moreover, a series of parametric studies have been conducted to evaluate the sensitivity of the control performance of the optimally designed actuator and sensor systems to the changes in important system parameters, such as the disturbance frequency, the plate support conditions and so on. The results demonstrate that for a plate under a multiple-frequency excitation, if the disturbance has an equal force amplitude for various frequencies, the optimization of the actuator location can be performed at the highest frequency component only. Through the use of a small number of carefully located error sensors, it is possible to achieve global sound attenuation. The optimization procedure provides not only a technique for control system design in practice, but also knowledge about the potential of active structural acoustic control. / Ph. D.