Two methods for reducing controller dimensionality in acoustics applications

The author examines the finite-dimensional linear problem where local control affects a remote, unmeasurable variable, under the assumption that the mapping from the local space to the remote space is rank-deficient. Such is the case in the acoustic radiating and scattering problems when transducers are located on the radiating body, but control of the far field is desired. Drawing upon the acoustics problem for motivation, it is shown that the rank-deficient mapping allows for control of only a subspace of the local space, and two frequency-domain methods are presented to construct filters acting on the transducer arrays: each reduces the controller dimension so that only the propagating subspace is controlled. The constructions are of interest because the filters can be made frequency-independent, and can thus be easily implemented in fast digital hardware