An integrated control method for designing non-blocking supervisors using Petri nets

Mi Zhao

doi:10.1177/1687814017700829

Abstract

This article presents an efficient integrated approach on designing a non-blocking supervisor for the most general classes of Petri nets, called G-systems that allow multiple resource acquisitions. This work mainly focuses on developing a deadlock prevention policy with a polynomial computational complexity. First, an extraction algorithm of liveness requirement constraints is presented according to the concept of resource partial orders. By considering the different resource requirements of various processes, monitors are added for the uncontrolled G-system on the basis of those precise linear inequality constraints. Afterward, we explore an iterative control policy by utilizing the traditional mathematical programming method, which can ensure the liveness of the resultant controlled system. Comparing with the existing deadlock control policies reported in the literature, the proposed method can achieve a non-blocking controlled G-system with simple structure and high computational efficiency. Finally, a...

Highlights

Nowadays, deadlocks can cause the part or the whole stoppage in highly automated manufacturing systems, even leading to catastrophic results
Section ‘‘Deadlock control policy based on MIP method’’ develops an iterative control method for G-systems by combining the MIP-based deadlock detection method with the results provided in section ‘‘linear inequality constraints (LICs) extraction method for G-systems.’’ A typical G-system example is illustrated in section ‘‘The application of the proposed policy’’ to validate the results in sections ‘‘LICs extraction method for G-systems’’ and ‘‘Deadlock control policy based on MIP method,’’ and some comparison and discussion among different deadlock control policies for G-systems are made subsequently
When an uncontrolled G-system (NS, MS0, MSF ) is considered, the set of precise constraints on liveness specifications can be derived according to Algorithm 1, which is usually transformed into the set of generalized mutual exclusion constraints (GMECs)

Summary

Introduction

Deadlocks can cause the part or the whole stoppage in highly automated manufacturing systems, even leading to catastrophic results. When an uncontrolled G-system (NS, MS0 , MSF ) is considered, the set of precise constraints on liveness specifications can be derived according to Algorithm 1, which is usually transformed into the set of GMECs. each monitor is added to achieve the constraint from Algorithm 2, and minimally restricts the permissive behavior of the controlled G-system (N c, M0c, MFc ), which indicates that it prevents only transition firings that yield forbidden markings. From Algorithm 1, it is worth noting that the number of LICs set is no more than that of resource places, that is, jCj jPRj. Based on MIP-based detection method in Algorithm 2, we need at most jCj iterative steps to obtain a live controlled system. The imposing constraints is of size O(jPAj + jPRj) at worst. }

A G-system example

Discussion

Conclusion

Subsystem