A New Approach to Solve the Mutual Exclusion Constraints Problem for Discrete Event Systems with Disturbances – Application to a Manufacturing Workshop

This paper is dedicated to solving the control issue of a class of discrete event systems with disturbances and subject to Mutual Exclusion Constraints. More precisely, a new analytical approach for designing control laws is suggested to guarantee the satisfaction of these constraints in Timed Event Graph Networks (NTEGs) with some uncontrollable input transitions. This later can be a robot breakdown, a machine supply shortfall, or any other type of machine breakdown or stoppage. For this, Min-Plus linear models represent the dynamic behavior of the disturbed timed event graph, and marking specifications are described by inequalities in Min-Plus algebra. Sufficient conditions to compute feasible control laws are identified according to the initial marking of the considered Petri net. The calculated laws are feedback gains that are represented by monitor places preventing the system from possible violations. To demonstrate the effectiveness and the applicability of the proposed control mechanisms, a case study of a disturbed disassembly system is discussed.