A Digital Twin (DT) of an Industrial Production System (IPS) can be seen as a digital replica of the industrial system (referred hereafter as the Physical Twin - PT) designed to support the decisions of a stakeholder. The DT concept has gained a strong interest in both the scientific and the industrial communities. Nevertheless, the large diversity of definitions and propositions that can be found in the literature demonstrates the lack of maturity on this subject. In particular, an aspect is sparsely tackled: the information flows existing inside the DT, with the synchronisation issues associated. This paper proposes a conceptual architecture with a strong information system orientation in order to tackle this issue and illustrates the concepts with an implementation on pedagogical production system.