CONSTRAINT FILTERED-X AND FILTERED-U LEAST-MEAN-SQUARE ALGORITHMS FORTHE ACTIVE CONTROL OF NOISE IN DUCTS

In the active control of noise in ducts, it is common practice to loca te an error microphone far from the control source to avoid the near-f ield effects by evanescent waves. Such a distance between the control source and the error microphone makes a certain level of time delay in evitable and, hence, may yield undesirable effects on the convergence properties of control algorithms such as filtered-x and filtered-u lea st-mean-square (LMS). This paper discusses the dependence of the conve rgence rate on the acoustic error path in these popular algorithms and introduces new algorithms ''constraint filtered-x and constraint filt ered-u LMS,'' which increase the convergence region regardless of the time delay in the acoustic error path. In the algorithms, coefficients of the controller are adapted using modified residuals that are defin ed in such a way that the control process become stationary. Performan ces of the new LMS algorithms are presented in comparison with those b y the conventional algorithms based on computer simulations.