Influence of model parameter variability on the directivity filters of compact loudspeaker arrays

2845 Sound directivity control is made possible by a compact array of independently driven loudspeakers. Recently, a control system for such a multi-channel source based on its acoustic radiation modes has been proposed. These modes form an orthogonal set of velocity patterns on the source surface, and emerge from the eigendecomposition of a free-field radiation operator that depends on frequency. Since the diaphragm velocities are driven by electrical signals, each directivity filter is a set of voltages yielding a radiation mode. Moreover, these filters must take into account the acoustic coupling between the transducers if they interact inside a hollow cabinet. Usually, nominally identical drivers are distributed over a spherical frame in the shape of a Platonic solid, which leads to frequency-independent radiation modes. Furthermore, if the individual drivers possess identical electromechanical features, the directivity filters are frequency independent too. However, the electromechanical parameters of commercial loudspeakers might present a significant deviation from their nominal values due to their manufacturing process. This work discusses the effects of electromechanical parameter variability on the frequency independence of the directivity filters of Platonic solid loudspeakers. As an example, a dodecahedral loudspeaker array, whose parameters of the individual drivers are experimentally characterized, is investigated.