The concept of postponed event in timed discrete event systems and its PLC implementation

Supervisory Control Theory (SCT) is one of the most important frameworks for establishing formal discrete event control systems. Despite some difficulties, the programmable logic controller (PLC) implementation of supervisory controllers obtained from SCT for untimed systems is well established within the literature. However, there is no general and easy to use method for obtaining supervisory controllers with time delay functions. In order to address this need, in this paper the concept of postponed event is proposed for introducing the time delay functions within untimed automata. Postponed event pe is defined as the shifted version of an event e on the time axis by a deterministic time delay value. Postponed event is a general, easy to use and practical method for PLC implementation of supervisory controllers with time delay functions. Supervisory controllers can be obtained as in untimed systems by using SCT framework with the assumption that postponed events are taken into account as if they are normal (untimed) events. Then they are refined at the implementation stage by the assignment of time delay values to respective events. The implementation of postponed events can be realized by using on delay timers, off delay timers or pulse timers of PLCs. The applicability of the proposed method is demonstrated by means of an example.