Is. Kim et al., CONSTRAINT FILTERED-X AND FILTERED-U LEAST-MEAN-SQUARE ALGORITHMS FORTHE ACTIVE CONTROL OF NOISE IN DUCTS, The Journal of the Acoustical Society of America, 95(6), 1994, pp. 3379-3389
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.