Designing Liveness-Enforcing Supervisors for Manufacturing Systems by Using Maximally Good Step Graphs of Petri Nets

Abstract

Many deadlock control methods rely on reachability graphs of Petri nets (PN), thus suffering from state-space explosion issues. This paper proposes a novel approach to designing liveness-enforcing supervisors for PN by constructing its maximally good step graphs (MGSG), a class of partial order techniques in mitigating the aforementioned issues. Specifically, we first categorize the MGSG markings into allowed and unallowed ones. Then, we define good and risky transitions at allowed markings. Through the execution of risky transitions, the initial marking cannot be reachable from the allowed ones. Next, we design a maximal number of risky transitions (MNRT) problem to compute control places. In MNRT, all allowed markings and the firing of all good transitions are permitted, while risky transitions are forbidden. The objective is to maximize the prevention of risky transitions by using a single control place, which can be achieved by solving an integer linear programming problem. MNRT problems are recursively solved for unforbidden risky transitions until their resulting markings are prohibited. Finally, a controlled PN is generated and has been demonstrated to retain liveness. The experimental results show that our approach effectively reduces the number of control places and mitigates state-space explosion issues over its state-of-the-art peers. Note to Practitioners—Raw materials are handled in manufacturing systems through a series of well-coordinated processes. However, multiple processes competing for the same resources (like machines or robots) may result in an undesirable deadlock situation, where production slows down or entirely halts. A liveness-enforcing supervisor is designed to counter such a situation. As a mathematical tool, PN can be applied to model manufacturing systems. The supervisor design involves adding control places and directed arcs into PN to ensure its liveness, which implies that the systems can execute their tasks and never enter into deadlocks. In this work, we develop a deadlock control approach, which can generate a live and controlled PN without exploring a complete state space of PN. Experimental results show the effectiveness of our approach in reducing the number of control places and its practicability applied to large-scale systems, thus surpassing state-of-the-art methods.