Two different methods are introduced for the determination of optimal active control inputs and passive shunting parameters in the PZT-based smart structure vibration and sound pressure control problems. The first method makes use of the dynamic vibration absorber principle; the second method uses the receptance of the open circuit structure-PZT system for determination of active control laws and parameters of optimal passive shunting. The advantages of each method are discussed. Using both methods, optimal passive electrical shunting parameters and active control input voltage values are determined for minimization of the vibration level and near field sound pressure at a particular point located above the plate. Additionally, at moderate to higher forcing levels the hysteretic non-linearity inherent in the PZT affects the dynamic response of the system. Calculated optimal passive shunting values under the linear system assumption become less than optimal. For high forcing levels, nonlinearity effects are accounted for in calculation of optimal values for passive shunting by using a discretized Ishlinskii-type hysteresis model of the PZT dielectric behavior.