Study of the acoustic feedback problem of active noise control by using the l1 and l2 vector space optimization approaches

This study attempts to explore the acoustic feedback problem that is frequently encountered in feedforward active noise control (ANC) structure from the standpoint of control theories. The analysis is carried out on the basis of the Youla’s parametrization and the l1-norm and l2-norm vector space optimization. The ANC problem is formulated as a model matching procedure and is solved via linear programming in the dual vector space. These methods alleviate the problems caused by the nonminimum phase (NMP) zeros of the cancellation path. The ANC algorithms are implemented by using a digital signal processor. Various types of noises were chosen for validating the developed algorithms. The proposed methods are also compared with the well-known filtered-u least-mean square (FULMS) method. The experimental results show that the acoustic feedback problem significantly degrades the performance and stability of the ANC system regardless which method is used. Insights into the difficulties due to acoustic feedback are addressed along the line of control theories.