[en] This paper concerns the modeling and the integrated numerical simulation of a flexible mechanism subject to the action of a digital control system. A general method is proposed, based on the formalism of flexible multibody systems (MBS) using the Finite Element Method (FEM). Nonlinear effects in the mechanical structure or in the control system can be taken into account. The numerical simulation tool is applied to design an active control system in a hot-dip galvanizing line, which aims at reducing the vibrations of the steel strip.