Abstract: The control system is constituted by a succession of elongate parallel control elements, made of elastomer, which extend in directions transverse to the direction of the path of the fibres to be controlled and which each have a work face and an opposite face provided with at least one longitudinal fixing rib engaged in a longitudinal slit of a tubular support part and terminated by a retention head in the said tubular support part, the drawing device including means for guiding, driving and orientating all the aforesaid tubular support parts, to ensure the displacement of the said control elements for the fibres while abutting against the other control system of the drawing device.