Scott D. Sommerfeldt
John W. Parkins
Appl. Res. Lab. and Graduate Program in Acoustics, Penn State Univ., P.O. Box 30, State College, PA 16804
The use of multiple secondary sources and multiple error sensors can significantly improve global attenuation whether one employs a control method based on the squared pressure or energy density. A single source positioned close to a pressure node will be inefficient at exciting the corresponding mode, therefore the secondary modes will dominate the pressure field, and attenuation is unlikely at the related frequency. Increasing the number of secondary sources improves the probability that at least one source will not lie close to a pressure node, thereby mitigating this problem. Problems also arise when error sensors are close to nodes. Adding multiple error sensors increases the probability that the sensors will be able to observe the dominant modes, which will yield improved attenuation. Using a greater number of error sensors than secondary sources will yield a determined control system, with a unique optimal solution. If more sources are used than sensors, an underdetermined control system will result which can be uniquely solved by adding more constraints to the system, such as minimum effort. The performance of the energy density versus squared pressure control methods are compared as they relate to the use of multiple secondary sources and multiple error sensors.