[en] This paper presents the extension of a multiphysics software solution allowing to perform integrated simulation of multiphysics controlled systems. This enhancement relies on an innovative formulation of time integration schemes allowing to take into account simultaneously, in an integrated FEM-based approach, the non linear structural response of a system and the controller dynamics. Interest and feasibility of this unified approach is illustrated through the Modelling of the position control of a segment of the primary mirror of the E-ELT (European Extremely Large Telescope), a highly representative application of complex multiphysics controlled systems.