Analysis of Effort Constraint Algorithm in Active Noise Control Systems
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Analysis of Effort Constraint Algorithm in Active Noise Control Systems F. Taringoo, J. Poshtan, and M. H. Kahaei Faculty of Electrical Engineering, Iran University of Science and Technology, Tehran 16846, Iran Received 11 February 2005; Revised 25 November 2005; Accepted 30 January 2006 Recommended for Publication by Shoji Makino In ANC systems, in case of loudspeakers saturation, the adaptive algorithm may diverge due to nonlinearity. The most common algorithm used in ANC systems is the FXLMS which is especially used for feed-forward ANC systems. According to its mathematical representation, its cost function is conventionally chosen independent of control signal magnitude, and hence the control signal may increase unlimitedly. In this paper, a modified cost function is proposed that takes into account the control signal power. Choosing an appropriate weight can prevent the system from becoming nonlinear. A region for this weight is obtained and the mean weight behavior of the algorithm using this cost function is achieved. In addition to the previous paper results, the linear range for the effort coefficient variation is obtained. Simulation and experimental results follow for confirmation. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.
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INTRODUCTION
Adaptive algorithms are widely used for feed-forward control systems, in which the mean-square error is minimized using the method of steepest descent, with no constraint on the magnitude of the control signals. In recent years, adaptive signal processing has been developed and applied to the expanding field of active noise control (ANC) [1]. ANC is achieved by introducing a canceling antinoise wave through an appropriate secondary source as shown in Figure 1. These secondary sources are interconnected through an electric system using a specific signal processing algorithm for the particular cancellation scheme [2]. In ANC systems the reference signal x(n) synthesizes with the same frequency component as primary noise [3]. The adaptive filter W(n) produces an antinoise signal which is amplified and transmitted into the acoustical system using a canceling loudspeaker to control the system. An error microphone located close to the loudspeaker receives both the primary and canceling signals to generate the error signal e(n). Most adaptive system analyses assume that nonlinear effects can be neglected, and hence model both the unknown system and the adaptive path as linear with memory. Linearity simplifies the mathematical problem and often permits a detailed system analysis in many important practical circumstances. However, more sophisticated models must be used when nonlinear effects are significant to the system
behavior (such as amplifier saturation). In real systems, loudspeakers are not perfectly linear, and are saturated when driven by large-amplitude signals [4]. In many practical applications of ANC systems, the total power that can be supplied by the control signal is limited. However, in FXLMS algorithm, no constraint on the control sig
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