This article proposes a fully forward on-the-fly algorithm to synthesise safety/reachability controllers for real time systems. Given a time Petri net (TPN) with controllable and uncontrollable transitions and a safety/reachability property, the control consists of limiting the firing intervals of controllable transitions to satisfy the property of interest. This algorithm, based on the state class graph method, computes on-the-fly the reachable state classes of the TPN while collecting progressively firing subintervals to be avoided so that to satisfy the property. It does not need to compute controllable predecessors and then split state classes as it is the case for other approaches based on exploration of state space of the system (backward and forward approaches). Moreover, in the category of state-dependent controllers based on the restriction of firing intervals, the algorithm, proposed here, synthesises maximally permissive controllers.