After reviewing the development of active noise control principles, we analyzed the elements of the active noise control system in ducts. On the basis of this analysis, we created a model of these elements. Especially, we brought a model of the loudspeaker in the z-domain, suitable for description of systems containing analog and digital parts. Such model enabled us to analyze work and convergence of the adaptive signal processing algorithms applied to active noise control. As an example, we analyzed performance of FXLMS algorithm on simplified model of active noise control system in ventilation duct, and have shown a strong influence of the loudspeaker's transfer function on the power spectrum of the error signal.