This work aims at reconstructing Petri net models for biological systems from experimental time-series data X'. The reconstructed models shall reproduce the experimentally observed dynamic behavior in a simulation. For that, we consider Petri nets with priority relations among the transitions and control-arcs, to obtain additional activation rules for transitions to control the dynamic behavior. The contribution of this paper is to present an integrative reconstruction method, taking both concepts, priority relations and control-arcs, into account. Our approach is based on previous works for special cases and shows how these known steps have to be modified and combined to generate the desired integrative models, called X'-deterministic extended Petri nets.