Control performance and robustness of an active noise control system for uncertain primary sound fields

In this work, the control performance and robustness of an active noise control system subjected to uncertain primary sound fields are investigated. For this purpose, the performance index, residual potential energy in a desired quiet zone, is derived as a function of sound field variables, quiet zone variables, and control system variables. In the presence of uncertainty, typical measures of the robustness and performance of a control system, maximum, minimum, mean, and variance of the performance index are derived theoretically. In addition, based on the least-squares orthogonality principle, the condition for implementing the best-oriented control system, which is robust and can maximize the control performance by using a given number of control sources and sensors, is investigated. Finally, numerical simulations are carried out to illustrate and verify the proposed theory.