Robustness Analysis of Automated Manufacturing Systems With Unreliable Resources Using Petri Nets

Abstract

This paper studies the maximally permissive robustness analysis of automated manufacturing systems (AMSs) with unreliable resources in the paradigm of Petri nets (PNs). Two types of robust markings, i.e., strongly robust markings and weakly robust markings, are defined in this paper. We propose robustness equivalence and non-robustness equivalence to characterize the markings that exhibit the same robustness and non-robustness, respectively. Reachability graph (or RG hereafter) is directly used to determine the robustness of markings; however, it is difficult to use in large-scale systems due to formidable computational difficulty. As an alternative, we present a reduced reachability graph (or R2G hereafter) based necessary and sufficient condition to check the robustness of markings, in terms of the liveness analysis of markings in R2G. We show that all safe markings of an R2G correspond to strongly robust markings of the corresponding RG, and deadlock markings as well as their bad markings and livelock markings as well as their bad markings of an R2G correspond to non-robust markings and weakly robust markings of the corresponding RG, respectively. Hence, the robustness of markings in an RG can be determined effectively and efficiently through the liveness analysis of markings in the corresponding R2G. Note to Practitioners—In practical manufacturing scenarios, it is urgent to analyze and control the automated manufacturing systems (AMSs) so as to ensure their continual production against any resource failure. If the failures of an AMS are not handled gracefully, the whole system may fall into a blocking. As a consequence, system production does not meet rapid manufacturing goals and objectives. In this paper, we focus on the maximally permissive robustness analysis of AMSs with unreliable resources in the paradigm of Petri nets. We define two types of robustness in terms of markings, i.e., strong robustness and weak robustness. From the viewpoint of reachability graph, we propose robustness equivalence and non-robustness equivalence among markings and present the procedures to check the robustness of markings. Furthermore, a set of necessary and sufficient conditions are established to provably ensure that the robustness of markings can be determined through liveness analysis in a reduced reachability graph. Therefore, the robustness of markings can be determined in a computationally efficient way.