## 3 Overall Architecture of DMPN
### The Operational Principle of Monitoring and Control Networks  
The principle of DMPN is quite different from that of hierarchical Petri nets. A hierarchical Petri net mainly deals with readability. Because a complex process is reflected in the Petri net, there is more state space, which makes the network structure more complex and difficult to understand. For researchers who do not need to pay attention to specific processes, these accurately described processes become redundant, and the method of hierarchical decomposition can be used to solve this problem. Additionally, hierarchical Petri net can decompose some complex workflows into subnets, and complex processes in subnets can continue to be decomposed into subnets. For people who want to understand the differing complexities of the network, they can choose network-level selectively. On the other hand, DMPN does not function in this way. Actually, it solves the real-time mapping problem between Petri net processes and device entities. For Petri net, it is more used for post-analysis. If the network satisfies the transition firing conditions, it can generate tokens in the post-set. However, for engineering practice, the transition firing conditions satisfied by Petri net are only the most important conditions, and there are some conditions or emergencies that cannot be easily added to the network, such as missing materials, machine damage or network disconnection. Therefore, the on-site situation cannot always run according to the established logic of a Petri net. Conversely, in DMPN, the monitoring network is a network that can represent the status of the scene in real time. The transition time, which is different from the traditional Petri net, is calculated later. Further, the control network is a copy of the monitoring network and mainly uses the subnet information, composed of the conflict places and its pre-sets and post-sets, to complete the control function, and the bearing function determines the direction of the branches of the Petri net. The monitoring network \(\Sigma_{mnt}\) and the control network \(\Sigma_{ct}\) are two parts of DMPN: neither part can be omitted. A Petri net is mainly a description of the process; however, there is no clear description of how the Petri net reflects and influences the field devices mathematically. As described, mapping the field devices is the main reason for the functional distinction. In the industrial field, monitoring tasks and control devices usually belong to different departments, and the behavior of control and decision making have a greater impact on the whole process. Wrong operations and decisions may bring huge losses to enterprises. Therefore, in the whole process, it is not conducive to personnel responsible to describe feedback-based monitoring behavior and operational behavior with significant impact on one network when it is not in line with the actual situation. In order not to break its original rules and definitions and to embody the original advantages of Petri net in the CPS architecture, \(\Sigma_{ct}\) is established on the basis of \(\Sigma_{mnt}\). After that, \(\Sigma_{ct}\) is equivalent to the power source of \(\Sigma_{mnt}\), while \(\Sigma_{mnt}\) mainly receives on-site data for reflecting the presentation and operates according to the conventional Petri net rules. The double networks work together to realize the function of virtual-reality mapping. Further, in the latter case description, it can also be reflected that \(\Sigma_{ct}\) is separated, and \(\Sigma_{mnt}\) can better describe the product production process. There is cooperation with scripts to write double-net control logic in the HMI of Dview. In the physical layer, there are objects such as field devices, which correspond to the machine agents in the PAG gateway, thus completing the virtual-reality mapping. In the cyber layer, there is monitoring network and a control network, which are, respectively, responsible for displaying the running status of field equipment and controlling it.