Matrix Controller Design and Deadlock Analysis of Automated Manufacturing Systems. Part 2: Deadlock Avoidance Policy

Abstract

A matrix framework is offered that permits direct, fast design and reconfigures the rule-based controllers for automated manufacturing systems. The controller design is based on standard manufacturing techniques such as the bill of materials, task sequencing matrix, and resource requirement matrix that give the matrix equations. The result is a multiloop discrete event controller with outer loops for dispatching of shared resources. The equations of the closed-loop manufacturing system can be used to derive a Petri net for rigorous performance analysis. Combining the matrix controller state equation and the well-known Petri nets marking transition equation yields a complete dynamical description of a discrete event system. The matrix formulation allows a rigorous analysis of deadlock in terms of circular blockings, siphons, and the numbers of resources available. This allows efficient dispatching and routeing with deadlock avoidance. The matrix controller also allows both nonlinear activity level algorithms and logical discrete-event supervisory algorithms. Such a hybrid controller would potentially allow the optimisation of shared resource assignment and job sequencing between machines with fast and precise operation of each individual machine. A multiple-part-path re-entrant job shop is used to illustrate the concepts introduced.