Analytical methods for controlling timed event graphs with disturbances and paths subject to marking constraints: application to a disassembly process

Abstract

This paper discusses the problem of marking constraints in a class of partially controllable timed Petri nets. Specifically, these are Timed Event Graphs (TEGs) which include disturbed input transitions and which are subject to token capacity constraints in some paths. Using the Min-Plus algebra formalism, formal approaches are proposed to design causal control laws to guarantee compliance with marking constraints in TEGs. Sufficient conditions are defined to show the existence and synthesis of these controllers. The developed methodologies are illustrated in a case study of a disassembly system with a limited stock of components.