Bode integral constraints, collocation, and spillover in active noise and vibration control

With the success of feedforward techniques for active noise control, feedback control researchers have begun to explore the relationship between these two control paradigms. The goal of this paper is to further investigate this relationship by means of the classical Bode integral constraint on achievable performance. This constraint provides insight into the phenomenon of spillover which we define as disturbance amplification by the closed-loop system relative to the open-loop transfer function gain. Specifically, it is shown that a particular feedforward controller called the zero spillover controller avoids spillover by producing perfect disturbance cancellation at every frequency. The analysis suggests that spillover can be avoided only if the control speaker and the disturbance source are noncollocated and the performance microphone and the measurement microphone are noncollocated. For realizability, we derive the approximate zero spillover controller which is shown to be an optimal feedback controller for an LQG problem with suitable cross weighting. Finally, the results are illustrated by means of structural and acoustic examples.