This work investigates and compares the potential of adaptive feedforward and feedback methods for a hybrid active/passive radiation control using smart foam. The radiating structure is a vibrating plate mounted in a rigid baffle in an anechoic chamber. The smart foam, designed to reduce sound by the action of the passive absorption of the foam (which is effective at higher frequencies) and the active input of an embedded PVDF element driven by an oscillating electrical input (which is effective at lower frequencies), is positioned on the plate. The first test consists of using a single-input single-output (SISO) adaptive feedforward LMS controller to minimize the error sensor signal provided by a microphone in the close proximity of the active element under narrow-band excitation and broadband random excitation. For feedforward control, two different reference signals are considered: the voltage sent to the piezoceramic actuator driving the plate (disturbance) and the signal from an accelerometer directly mounted on the plate (more realistic in practice). In the latter case, the effect of the smart foam on the reference signal (or acceleration level) can be taken into account (feedback removal). An adaptive feedback controller is also implemented to avoid the use of a reference signal. In this case, a reference signal is obtained from the error signal using the internal model approach. The results from these three different control methods are compared in terms of the sound attenuation achieved. For broadband excitation, a feedforward adaptive control with an external reference is shown to be more efficient for this arrangement than a feedback adaptive control.