In recent years, environmental noise has been attracting increasing attention due to its negative impact on people's physical and mental health. One of the promising solutions to mitigate noise is the application of smart structures, whose acoustic performance is actively controlled. In the present work, an Active Structural- Acoustic Control (ASAC) strategy is developed using a plate-cavity system in order to abate the interior noise in some locations of the cavity. The employed algorithm is the Filtered-x Normalized Least Mean Squares (FxNLMS), which is typically applied to Active Noise Cancellation (ANC) problems. The peculiarity of this work is that the control is applied directly to the vibration of the plate, similar to Active Vibration Control (AVC) strategies. The major innovation in this case is that, instead of evaluating the acoustic benefits due to a vibration reduction, here the sound field is controlled directly by closing the loop on the acoustic pressure. The algorithm has been implemented in Single-Input Single-Output (SISO) and Single-Reference Multiple-Output (SRMO) configurations, where the latter is a first step toward a multichannel architecture. In contrast with many existing applications, here the cross-effects between different actuators are considered in the implementation of the algorithm, thus improving the performance in the controlled positions. The experimental test bench adopted for validation is a plate-cavity system called Noise Box, which is made up of a single-layer glass panel and a reinforced concrete structure, designed to simulate the interior sound field of a vehicle cabin. The plate was instrumented with piezoelectric patches used as actuators, while condenser microphones were used as sensors. First, a numerical model of the system was created to develop the control logic. Then, an experimental campaign was carried out to validate the results.