Bode integral constraints 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 the present paper is to further investigate this relationship by means of the classical Bode integral constraint on achievable performance. These results provide insight into the phenomenon of spillover which has been widely discussed in the vibration control literature. Specifically, it is shown that a particular feedforward controller called the zero spillover controller avoids spillover by producing perfect disturbance cancellation at every frequency. 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 weights. Finally, the results are illustrated by means of illustrative mechanical and acoustic examples