Modeling and analysis of disassembly systems using continuous Petri nets

In this paper we focused our attention on a particular hybrid PN model called FOHPN, that is based on the fluidification of discrete PNs, and whose main feature is that the instantaneous firing speed of continuous transitions keeps constant during each macroperiod. In the first part of the paper we discuss in detail the advantages of fluidification, and provide a brief survey of the most important formalisms within the hybrid PN framework. Finally, we showed how FOHPNs can be efficiently used to model SC, and how interesting optimization problems can be solved via numerical simulation, by simply solving on-line a certain number of LPPs.

Hybrid Petri Nets (PN), combining T-timed discrete PN and continuous PN, are convenient for the modelling and the performance analysis of fluid systems or manufacturing systems such as batch or high speed production systems. For instance, the continuous process can be modelled by a continuous PN while the state of machines, up or down, can be represented by a discrete PN. The aim of the paper is to characterise the timed dynamic behaviour of continuous PN with constant speed. More precisely, the final values of the instantaneous firing speeds of continuous neutral weighted marked graph, supposed live, are determined independently of the initial marking and without using the timed evolution. Finally an application to a flow system is given.

Continuous Petri Nets (continuous-PN) have been introduced to avoid the explosion of the number of reachable states in a classical Petri Net, when this net contains a great number of tokens. This is the case of production systems, particularly a flexible manufacturing system. In a continuous-PN, the marking of a place is represented by a real number and with each transition is associated a maximum firing speed. Two kinds of modelling of manufacturing systems by continuous-PN are presented in this paper. The first one gives good results when the system is saturated (many parts). The second one works well even if the system is not saturated.

Most verification techniques for highly populated discrete systems suffer from the state explosion problem. The "fluidification" of discrete systems is a classical relaxation technique that aims to avoid the state explosion problem. Continuous Petri nets are the result of fluidifying traditional discrete Petri nets. In continuous Petri nets the firing of a transition is not constrained to the naturals but to the non-negative reals. Unfortunately, some important properties, as liveness, may not be preserved when the discrete net model is fluidified. Therefore, a thorough study of the properties of continuous Petri nets is required. This paper focuses on the study of deadlock-freeness in the framework of mono-T-semiflow continuous Petri nets, i.e., conservative nets with a single repetitive sequence (T-semiflow). The study is developed both on untimed and timed systems. Topological necessary conditions are extracted for this property. Moreover, a bridge relating deadlock-freeness conditions for untimed and timed systems is established

This paper deals with a "digital twin" (DT) approach for processing, reprocessing, and scrapping (P/R/S) technology running on a modular production system (MPS) assisted by a mobile cyber-physical robotic system (MCPRS). The main hardware architecture consists of four line-shaped workstations (WSs), a wheeled mobile robot (WMR) equipped with a robotic manipulator (RM) and a mobile visual servoing system (MVSS) mounted on the end effector. The system architecture integrates a hierarchical control system where each of the four WSs, in the MPS, is controlled by a Programable Logic Controller (PLC), all connected via Profibus DP to a central PLC. In addition to the connection via Profibus of the four PLCs, related to the WSs, to the main PLC, there are also the connections of other devices to the local networks, LAN Profinet and LAN Ethernet. There are the connections to the Internet, Cloud and Virtual Private Network (VPN) via WAN Ethernet by open platform communication unified architecture (OPC-UA). The overall system follows a DT approach that enables task planning through augmented reality (AR) and uses virtual reality (VR) for visualization through Synchronized Hybrid Petri Net (SHPN) simulation. Timed Petri Nets (TPNs) are used to control the processes within the MPS's workstations. Continuous Petri Nets (CPNs) handle the movement of the MCPRS. Task planning in AR enables users to interact with the system in real time using AR technology to visualize and plan tasks. SHPN in VR is a combination of TPNs and CPNs used in the virtual representation of the system to synchronize tasks between the MPS and MCPRS. The workpiece (WP) visits stations successively as it is moved along the line for processing. If the processed WP does not pass the quality test, it is taken from the last WS and is transported, by MCPRS, to the first WS where it will be considered for reprocessing or scrapping.

The coverability problem for Petri nets plays a central role in the verification of concurrent shared-memory programs. However, its high EXPSPACE-complete complexity poses a challenge when encountered in real-world instances. In this paper, we develop a new approach to this problem which is primarily based on applying forward coverability in continuous Petri nets as a pruning criterion inside a backward coverability framework. A cornerstone of our approach is the efficient encoding of a recently developed polynomial-time algorithm for reachability in continuous Petri nets into SMT. We demonstrate the effectiveness of our approach on standard benchmarks from the literature, which shows that our approach decides significantly more instances than any existing tool and is in addition often much faster, in particular on large instances.

Supply chains have been more serious for environmental issues for not only the reduction of CO2 emission but also for material starvation. To enhance a closed loop supply chain for assembled product, a disassembly system is required. At end-of-life, the assembly products at recycling organization should be disassembled environmentally and economically for not only low carbonization but also of material circulation. This recycling and reusing of product enables to reduce CO2 release because the virgin materials which release CO2 volumes caused by production and logistics can be saved by the usage of the recovered materials. Parts with higher recycling and CO2 saving rates ought to be chosen and physically disassembled, but the manual disassembly brings a higher cost, rather than discarding the parts. Therefore, material recovery value is also to be considered for parts selection during the assembly operation. Parts information like material recovery value, CO2 release, weight, precedence relationships are required for environmental and economic parts selection. This study proposes a CAD based approach for environmental and economic parts selection for disassembly using solid works sustainability. It considers higher CO2 saving rate, higher recycling rate and higher material recovery value as environmental and economic criteria for parts selection.

On fluidification of Petri Nets: from discrete to hybrid and continuous models

In this paper, we study performance evaluation of workflow-based information systems. Because of state space explosion, analysis by stochastic models, such as stochastic Petri nets and queuing models, is not suitable for workflow systems in which a large number of flow instances run concurrently. We use fluid-flow approximation technique to overcome this difficulty. In the proposed method, GSPN (Generalized Stochastic Petri Nets) models representing workflows are approximated by a class of timed continuous Petri nets, called routing timed continuous Petri nets (RTCPN). In RTCPN models, each discrete set is approximated by a continuous region on a real-valued vector space, and variance in probability distribution is replaced with a real-valued interval. Next we derive piecewise linear systems from RTCPN models, and use interval methods to compute guaranteed enclosures for state variables. As a case study, we solve an optimal resource assignment problem for a paper review process.

Continuous Petri nets aim to avoid the state explosion problem of classical discrete Petri nets by relaxing the integrality constraint of the firing of transitions. Although the resulting formalism can successfully model a number of features of dynamic systems, its use in complex real systems can be hindered by the limited number of possible dynamics and by the difficulty in accommodating uncertain parameters. The modeling formalism of Flexible Nets can overcome these difficulties by significantly extending the modeling and analysis possibilities of continuous Petri nets. The modeling capabilities of Flexible Nets will be presented together with their analysis possibilities in both the transient and steady state.

This work is concerned with duality of controllability and observability of Timed continuous Petri nets (TCPNs). Based on the duality definition presented in [4] for (discrete) Petri nets, a procedure for computing a dual system of a given TCPN, in a particular configuration, is provided in this work. Furthermore, it is demonstrated that the rank of the controllability matrix of a TCPN and the rank of the observability matrix of its dual are related in a precise manner. The analysis here presented can be used to translate previous results of observability analysis to controllability and vice versa.

A class of Petri nets, called extended Petri nets, with multiple types of places, multiple classes of tokens and multiple arcs is proposed. It is utilized for the hierarchical modeling of flexible manufacturing systems, ensuring a priori that the extended Petri net system model obtained is live, bounded, consistent and error free. The proposed method views the operation of the flexible manufacturing system as a process that is decomposed into operations with specified precedence relations. For each operation the required resources are identified, and on the basis of these requirements the overall system is decomposed into a set of finite subsystems. The operation of each subsystem is modeled as an event graph representing a single resource activity cycle. The extended Petri net system model is synthesized from these component nets using certain synthesis rules. A software package has been developed to simulate the execution of the model obtained. >

In previous papers we investigated the problem of deriving an optimal control law for continuous Petri nets under infinite server semantics. In particular, the problem was studied through Model Predictive Control (MPC), an advanced control method, extensively used in industrial applications. In this work we discuss some properties of the resulting closed-loop system, such as feasibility and asymptotic stability. We prove that for continuous Petri nets feasibility is always guaranteed, while asymptotic stability is not ensured. Finally, we demonstrate that the introduction of an appropriate terminal constraint may guarantee asymptotic stability provided that certain assumptions on the initial state and the moving horizon are satisfied.

The traffic flow theory is concerned with finding a relation among the variables of traffic flow. We propose a new approach which consists of representing these variables by those of continuous Petri nets with variable speed (VCPN). A model of VCPN is suggested for the analysis and control design in urban and interurban networks. The proposed model provides representation for both motorway corridors and complex road junctions.

Controllability is a property related to the capability of driving a system to any desirable (steady) state or state trajectory. As in discrete nets, continuous nets can be controlled by means of control actions applied on the transitions. For the sake of generality, the set of transitions is partitioned into controllable and uncontrollable; control actions can be applied only on controllable transitions. These actions may only reduce the flow of the uncontrolled model, because transitions (machines for example) cannot work faster than their nominal speed. Under this framework, the chapter overviews conditions for controllability, different control approaches for systems working under infinite server semantics and introduces a basic control method based on consensus for distributed systems.