Noise reduction in ducts achievable by point control

Noise control in a one-dimensional duct is analyzed. This problem is of practical interest and is also simple enough that a complete theoretical analysis is possible. It is shown that the optimal controller lends to an unstable closed loop. The noise reduction level achievable with a stable closed loop is calculated for arbitrary choices of sensor and actuator locations. This enables the best placement of sensors and actuators to be determined. A Iso, the analysis indicates that a "spatial waterbed" effect exists in some configurations of active noise control; i.e., that noise levels are increased for points outside of the region over which the design is done.