Constraint filtered-x and filtered-u least-mean-square algorithms for the active control of noise in ducts

Abstract

In the active control of noise in ducts, it is common practice to locate an error microphone far from the control source to avoid the near-field effects by evanescent waves. Such a distance between the control source and the error microphone makes a certain level of time delay inevitable and, hence, may yield undesirable effects on the convergence properties of control algorithms such as filtered-x and filtered-u least-mean-square (LMS). This paper discusses the dependence of the convergence rate on the acoustic error path in these popular algorithms and introduces new algorithms "constraint filtered-x and constraint filtered-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 defined in such a way that the control process become stationary. Performances of the new LMS algorithms are presented in comparison with those by the conventional algorithms based on computer simulations.

On-Line Fundamental Frequency Tracking Method for Harmonic Signal and Application to Anc

“…Because the number of the dominant frequency components in range of the interested bandwidth 70}160 Hz is four, we estimated four frequencies (p"4) and the fundamental frequency from them, and generated the reference signal which includes "ve frequency components (l"5) to be ACTIVE CONTROL OF HARMONIC NOISE WITH REFERENCE GENERATOR reduced. The estimated fundamental frequency was 15.3 Hz and the mode order was m I " [5,6,7,9] and m ?I " [5,6,7,8,9]. The frequency estimation was converged after 2850 step.…”

“…Because the number of the dominant frequency components in range of the bandwidth 10}450 Hz is 2, we estimated two frequencies (p"2) and the fundamental frequency from them, and generated the reference signal which included nine frequency components (l"9) to be reduced. The mode order was m I " [4,8] where both initial values were 0.85. As shown in Figure 12, the proposed method has good tracking capability.…”

“…We used a constrained ,ltered-x LMS algorithm [8] as the feedforward control algorithm. In this simulation, we assumed that we know the exact model of the cancellation path.…”

A New Infinite Impulse Response Filter-Based Adaptive Algorithm for Active Noise Control

“…(2) As shown in Appendix A, Efx 2 ðnÞg ¼ 0 if and only if Efe 2 ðnÞg ¼ 0: So when the coefficient vector is reaching the optimal value such that the primary dðnÞ is perfectly cancelled [5,2], both MSEs reach their global minimum.…”

Experiments on resonant vibration suppression of a piezoelectric flexible clamped–clamped plate using filtered-U least mean square algorithm

“…He used the algorithm for active noise control. Two new kinds of constraints FXLMS and FULMS control algorithms were developed to increase the convergence region of the system (Kim et al, 1994). Kim et al (2011) implemented an improved FULMS algorithm to suppress noise of a short acoustic duct.…”