The critical nature of hard real-time embedded systems leads to an increased usage of Model Based Design to generate a correct-by-construction code from a formal specification. If Model Based Design is widely used at application level, most of the low level code, like the device drivers, remains written by hand. Timed Automata are an appropriate formalism to model real time embedded systems but are not easy to use in practice for two reasons i) both hardware and software timings are difficult to obtain, ii) a complex infrastructure is needed for their implementation. This paper introduces an extension of untimed automata with logical time. The new semantics introduces two new types of actions: delayed action which are possibly avoidable, and ineluctable action which will happen eventually. The controller synthesis problem is adapted to this new semantics. This paper focuses specifically on the reachability problem and gives an algorithm to generate a controller.