Robustness Analysis of Automated Manufacturing Systems With Uncontrollable Events Using Petri Nets

Abstract

In this paper, we address the robustness analysis problem of automated manufacturing systems with uncontrollable events in the paradigm of Petri nets (PNs). First, we formalize unreliable resource failures as the removal of all ingoing transitions of unreliable resource places (denoted by unreliable transitions hereafter). Second, we obtain a necessary and sufficient condition to check the robustness of markings, so called robustness controllability theorem (abbreviated as RCT hereafter) in the paradigm of reduced reachability graph (abbreviated as R2G hereafter). All markings involved in the R2G of a PN are equivalent to that of its reachability graph, except that all arcs associated to unreliable transitions are removed from R2G. Based on RCT, the robustness of all markings in an R2G can be determined. An example is proposed to illustrate the approach. Note to Practitioners—In reality, it is an urgent issue to analyze the behaviors of automated manufacturing systems (AMSs) so as to guarantee their stable operation against resource failures, e.g., the missing of a signal or the failure of a sensor. In this connection, different methods are proposed to deal with the robustness analysis and control problem of AMSs with unreliable resources. The objective is to avoid any deadlock in the AMSs or to ensure the liveness of the subsystems that require only reliable resources when there exist resource failures. Due to limited actuating and sensing abilities, AMSs may be partially controlled, i.e., there exist events whose firing may not be inhibited by an external action. However, fewer research works consider this practical situation when handling robustness analysis and control issue, which renders the existing approaches impracticable. In this paper, we solve the robustness analysis problem of AMSs with uncontrollable events by using Petri nets. A necessary and sufficient condition is proposed to check the robustness of markings, called robustness controllability theorem (abbreviated as RCT hereafter) in the paradigm of reduced reachability graph. With the aid of RCT, the robustness of all markings can be determined so as to guarantee the flexibility of AMSs.