Analysis of perfect noise cancelling controllers

Presents results to show that perfect noise cancellation can be achieved in acoustic ducts with causal and stable controllers. These results are derived under general conditions without imposing any configuration constraints, like unidirectional sensors, on the controllers. The analysis is applicable to many acoustic noise control applications such as active noise suppression in air-conditioning ducts. The analysis considers both, open-end and closed-end, boundary conditions as well as finite and semi-infinite length duct configurations. The implementation issues for an `ideal´ noise canceling controller are discussed. The practical difficulties posed in otherwise ideally suited infinite-dimensional controllers are outlined. Implications of colocation and non-colocation of actuating speaker and sensing microphone are discussed. A mathematical analysis is given to demonstrate that the control system designed based on perfect cancellation technique is highly sensitive to the imperfections in the practical implementation of the theoretical infinite-dimensional controllers