Feedback control to guarantee marking constraints in timed event graphs including disturbances: Application to disassembly systems

Abstract

This paper addresses the control problem of Timed Event Graphs (TEGs) with disturbance transitions, which are subject to marking constraints. In these graphical models, disturbances are uncontrollable input transitions and constraints correspond to the maximum limits of tokens in some places which must not be exceeded. An analytical methodology based on the use of Min-Plus formalisms to synthesize feedback control laws that guarantee the concerned constraints is established. For this, Min-Plus linear models describe the dynamic behavior of the TEGs, and marking constraints are represented by inequalities in Min-Plus algebra. Sufficient conditions are defined to verify the existence of feedback control laws guaranteeing constraint satisfaction in disturbed TEGs. To verify the effectiveness of these proposed theoretical approaches, a real case study of a disturbed disassembly system with limited stocks of components is processed.