Output feedback control of discrete processes under time constraint: application to cluster tools

Practical control of timed behaviours in industrial applications is difficult. One of the few efficient modelling approaches to deal with time constraints on discrete event systems is to use timed event graph (TEG), a subclass of Petri nets. The dynamic behaviour of these graphs is represented by a linear equations system over the max-plus algebra. Up to date, these models were assumed to be fully observable. In this paper, it is demonstrated that if a TEG is strongly connected, one can derive a realisable output feedback control. In other words, the control law depends solely on the control itself and the system’s outputs, considered to be the only observable events. The satisfaction of a set of constraints is addressed in the case of a single input model (i.e. having only one input transition) and the procedure to derive a realisable output feedback control law is provided. Finally, the present control method is applied to a dual-armed cluster tool, a well-known industrial practical application.