Optimal acoustic error sensing for global active control in a harmonically excited enclosure

The performance of an active control system in global control of enclosed sound fields depends largely on the localization of the error sensors, among other factors. In this paper a modified cost function is proposed in order to guarantee the maximum attenuation that can be produced by a set of secondary sources in the case of an harmonically excited sound field. The cost function is modified in order to drive the error signal to the value corresponding to the optimally attenuated sound field, instead of minimizing the squared pressure. To evaluate the performance of the proposed control system, its robustness against unstructured error is also investigated using a set of intensive calculations. Following this approach, the sensors can be located anywhere and the optimal attenuation is reached using an equal number of error sensors and secondary sources. The results also suggest that the greater the number of error sensors than secondary sources the more robust the control system is. This behavior holds for both the usual strategy of minimizing the squared pressure and the approach presented in this paper. However, the latter strategy is more robust than the traditional approach of minimizing the squared pressures and its robustness does not depend on the location of the error sensors. Thus, as a main conclusion, the use of the new cost function leads to a guaranteed efficiency and a more robust control system and gives absolute freedom in selecting the location of the error sensors.