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

Practical control of timed behaviors in industrial applications is difficult. One of the few efficient modeling approaches to deal with time constraints on discrete event systems (DES) is to use Timed Event Graph (TEG), a sub-class of Petri Nets. The dynamic behavior 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 realizable 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 realizable 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.