In recent years, output feedback control has been the emphasis of many practical low authority controller design implementations. The focus on ''collocated'' output feedback control is probably a result of the well cited reference by Balas [1] devoted to direct rate-feedback control (DRFB). As noted by Balas, in the absence of transduction device dynamics and rigid body modes, direct rate-feedback control can be employed with unconditional stability. However, in the presence of additional dynamics due to transducers, amplifiers and signal conditioning circuitry, one is typically faced with stability-robustness issues and the task of choosing some frequency shaped compensator which will assure adequate disturbance rejection (typically at low frequencies) while also rejecting noise at high frequencies. Given that physical limitations impose finite stability margins, it proves beneficial to explore the concept of ''moving away from collocated output feedback control'' to enhance performance in the suppression of reverberant sound and vibration.
The dissipation of reverberant energy within a system can be enhanced by the proper location of transducers with respect to the physical system. For example, to dissipate energy from a reverberant, enclosed, sound field, both passive and active treatments are typically positioned in the corner of the enclosure to couple to all of the acoustic modes. As demonstrated by Clark and Cole [2], an ideal volumetric source and pressure sensor can be configured in a feedback control loop to dissipate energy from enclosed sound fields for such applications. However, a later study by Clark et al. [3] demonstrated that transduction device dynamics impose limitations on the ideal control system implementation. The work presented herein serves to further demonstrate that spatial compensation can be used to enhance control system performance by separating the transducers to further separate the zeros and poles of the system, specifically at lower frequencies. Once the ''collocated'' transducers are separated, the ''perfectly'' alternating poles and zeros characteristic of a drive point mobility are no longer perfectly alternating, since nodal lines of higher modes are inevitably crossed. However, the separation and spatial location of the transducer can be judiciously selected to enhance the performance (energy dissipation) of the closed loop system. The price to be paid is quite often a reduction in stability margins and bandwidth. One must take care, while separating the transducers, not to reduce the gain margin to a level such that the overall damping which can be added to the lower modes of the system is less than that of the original ''collocated'' system.
To provide an example, a reverberant acoustic field is studied experimentally. The effect of moving a microphone away from an acoustic loudspeaker placed in a rectangular