scholarly journals Behaviour equivalent max-plus automata for timed petri nets under open-loop race-policy semantics

2021 ◽  
Author(s):  
Lukas Triska ◽  
Thomas Moor
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Discrete Event Systems ◽  
Discrete Event ◽  
Open Loop ◽  
Single Server ◽  
Loop Model ◽  
Timed Petri Nets ◽  
Reachability Graph ◽  
Supervisor Control

AbstractTimed Petri nets and max-plus automata are well known modelling frameworks for timed discrete-event systems. In this paper we present an iterative procedure that constructs a max-plus automaton from a timed Petri net while retaining the timed behaviour. Regarding the Petri net, we essentially impose three assumptions: (a) the Petri net must be bounded, i.e, the reachability graph must be finite; (b) we interpret the Petri net with single server semantics; and (c) the Petri net operates according to the race policy, i.e., the earliest possible transition will fire and thereby possibly consume tokens required by other competing transitions. Under these assumptions we show that the proposed procedure terminates with a finite deterministic max-plus automaton that realises the same timed behaviour as the Petri net. As a variation of the plain race policy, we also consider that a subsequently designed supervisor may temporarily disable distinguished transitions. Again, we present a terminating procedure that constructs a behaviour equivalent deterministic max-plus automaton. We demonstrate by example how the latter automaton can be utilised as an open-loop model in the context of supervisor control.

scholarly journals Petri nets properties related to the unboundness and analyzed using coverability multigraph

2014 ◽  
Vol 10 (2) ◽  
pp. 51-67 ◽  
Author(s):  
Branislav Hrúz ◽  
Iveta Dirgová Ľuptáková ◽  
Miroslav Beňo
Keyword(s):  
Petri Nets ◽  
State Space ◽  
Petri Net ◽  
Discrete Event Systems ◽  
Discrete Event ◽  
System Model ◽  
Reachability Graph ◽  
Reachability Set ◽  
Event Systems ◽  
System States

Abstract Petri nets represent a powerful tool for modeling the discrete event systems. The Petri net markings correspond to the system states. The infinity of the marking set means that the Petri net is unbounded and this may be the sign of an incorrect system model. In that case instead of the reachability set and the reachability graph the coverability set and the coverability multigraph can be used to represent the Petri net state space. A systematic way of building the notion of the coverability set and coverability multigraph based on the notion of the ω -marking is given in the paper. Algorithm for its construction is introduced. Then the use of the coverability multigraph for the analysis of several properties of the unbounded Petri nets is described.

Fault Detection, Isolation and Characterisation for Discrete Event Systems Based on Petri Nets Models

2010 ◽  
pp. 387-416
Author(s):  
Dimitri Lefebvre ◽  
Edouard Leclercq ◽  
Souleiman Ould El Mehdi
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Discrete Event Systems ◽  
Discrete Event ◽  
Practical Interest ◽  
Transportation Systems ◽  
Intermittent Faults ◽  
Event Systems ◽  
Stochastic Time

Petri net models are used to detect and isolate faults in case of discrete event systems as manufacturing, robotic, communication and transportation systems. This chapter addresses two problems. The first one is the structure designs and parameters identification of the Petri net models according to the observation and analysis of the sequences of events that are collected. Deterministic and stochastic time Petri nets are concerned. The proposed method is based on a statistical analysis of data and has a practical interest as long as sequences of events are already saved by supervision systems. The second problem concerns the use of the resulting Petri net models to detect, isolate and characterize faults in discrete event systems. This contribution includes the characterization of intermittent faults. This issue is important because faults are often progressive from intermittent to definitive and early faults detection and isolation improve productivity and save money and resources.

scholarly journals Equivalent and Efficient Optimization Models for an Industrial Discrete Event System with Alternative Structural Configurations

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Juan-Ignacio Latorre-Biel ◽  
Emilio Jiménez-Macías ◽  
Mercedes Pérez de la Parte
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Discrete Event Systems ◽  
Discrete Event ◽  
Discrete Event System ◽  
Optimization Techniques ◽  
Event System ◽  
Event Systems ◽  
Structural Configurations ◽  
Computational Resources

Discrete event systems in applications, such as industry and supply chain, may show a very complex behavior. For this reason, their design and operation may be carried out by the application of optimization techniques for decision making in order to obtain their highest performance. In a general approach, it is possible to implement these optimization techniques by means of the simulation of a Petri net model, which may require an intensive use of computational resources. One key factor in the computational cost of simulation-based optimization is the size of the model of the system; hence, it may be useful to apply techniques to reduce it. This paper analyzes the relationship between two Petri net formalisms, currently used in the design of discrete event systems, where it is usual to count on a set of alternative structural configurations. These formalisms are a particular type of parametric Petri nets, called compound Petri nets, and a set of alternative Petri nets. The development of equivalent models under these formalisms and the formal proof of this equivalence are the main topics of the paper. The basis for this formal approach is the graph of reachable markings, a powerful tool able to represent the behavior of a discrete event system and, hence, to show the equivalence between two different Petri net models. One immediate application of this equivalence is the substitution of a large model of a system by a more compact one, whose simulation may be less demanding in the use of computational resources.

scholarly journals A New Modular Petri Net for Modeling Large Discrete-Event Systems: A Proposal Based on the Literature Study

Computers ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 83 ◽  
Author(s):  
Reggie Davidrajuh
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Discrete Event Systems ◽  
Discrete Event ◽  
Real Life ◽  
World Systems ◽  
Literature Study ◽  
State Spaces ◽  
Event Systems ◽  
And Performance

Petri net is a highly useful tool for modeling of discrete-event systems. However, Petri net models of real-life systems are enormous, and their state-spaces are usually of infinite size. Thus, performing analysis on the model becomes difficult. Hence, slicing of Petri Net is suggested to reduce the size of the Petri nets. However, the existing slicing algorithms are ineffective for real-world systems. Therefore, there is a need for alternative methodologies for slicing that are effective for Petri net models of large real-life systems. This paper proposes a new Modular Petri Net as a solution. In modular Petri net, large Petri net models are decomposed into modules. These modules are compact, and the state spaces of these modules are also compact enough to be exhaustively analyzed. The research contributions of this paper are the following: Firstly, an exhaustive literature study is done on Modular Petri Nets. Secondly, from the conclusions drawn from the literature study, a new Petri net is proposed that supports module composition with clearly defined syntax. Thirdly, the new Petri net is implemented in the software GPenSIM, which is crucial so that real-life discrete-event systems could be modeled, analyzed, and performance-optimized with GPenSIM.

scholarly journals On–The–Fly Diagnosability Analysis of Bounded and Unbounded Labeled Petri Nets Using Verifier Nets

2018 ◽  
Vol 28 (2) ◽  
pp. 269-281 ◽  
Author(s):  
Ben Li ◽  
Manel Khlif-Bouassida ◽  
Armand Toguyéni
Keyword(s):  
Complex Systems ◽  
Petri Nets ◽  
Discrete Event Systems ◽  
Discrete Event ◽  
Reachability Graph ◽  
Combinatorial Explosion ◽  
Engineering Approach ◽  
Event Systems

Abstract This paper considers the problem of diagnosability analysis of discrete event systems modeled by labeled Petri nets (LPNs). We assume that the LPN can be bounded or unbounded with no deadlock after firing any fault transition. Our approach is novel and presents the on-the-fly diagnosability analysis using verifier nets. For a given LPN model, the verifier net and its reachability graph (for a bounded LPN) or coverability graph (for an unbounded LPN) are built on-the-fly and in parallel for diagnosability analysis. As soon as a diagnosability decision is established, the construction is stopped. This approach achieves a compromise between computation limitations due to efficiency and combinatorial explosion and it is useful to implement an engineering approach to the diagnosability analysis of complex systems.

Hybrid adaptive Petri nets: a conceptual framework for partial fluidization of Petri nets

1970 ◽  
pp. 50
Author(s):  
E. Fraca ◽  
J. Júlvez ◽  
M. Silva
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Dynamic Systems ◽  
Discrete Event Systems ◽  
Discrete Event ◽  
Modeling And Analysis ◽  
Analysis Techniques ◽  
High Transition ◽  
Large Systems ◽  
Event Dynamic

Petri nets (PNs) constitute a well known family of formalisms for the modeling and analysis ofDiscrete Event Dynamic Systems (DEDS). As most formalisms for discrete event systems, PNssuffer from the state explosion problem, which renders enumerative analysis techniquesunfeasible for large systems. A technique to overcome the problem is to relax integralitycontraints of the discrete PN model, leading to continuous PN. This relaxation highly reducesthe complexity of analysis techniques but may not preserve important properties of theoriginal PN system such as deadlock‐freeness, liveness, reversibility, etc. This work focuses onHybrid Adaptive Petri nets (HAPNs), a Petri net based formalism in which the firing oftransitions is partially relaxed. The transitions of a HAPN can behave in two different modes:continuous mode for high transition workload, and discrete in other case. This way, a HAPN isable to adapt its behaviour to the net workload, it offers the possibility to represent morefaithfully the discrete model and use efficient analysis techniques by behaving as continuouswhen the load is high. Reachability space and the deadlock‐freeness property of hybridadaptive nets is studied in this work.

Conversion methodologies from Signal Interpreted Petri Nets to Ladder Diagram and C language in Arduino

2018 ◽  
Vol 46 (4) ◽  
pp. 302-314 ◽  
Author(s):  
Matheus Ungaretti Borges ◽  
Eduardo José Lima
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Discrete Event Systems ◽  
Discrete Event ◽  
Ladder Diagram ◽  
Programmable Logic ◽  
Electronic Components ◽  
C Language ◽  
Arduino Microcontroller ◽  
And Robotics

With the advent of electronics in the last decades, automation is becoming a wide and strong area to be studied. Its applications go from industrial machinery and robotics processes to home illumination and security system processes. Electronic components are becoming more efficient, more productive, safer and cheaper, which justifies its growing usage. Inside automation’s area is an area called discrete event systems, which presents an organized and graphical way to represent these events through a tool called Signal Interpreted Petri Nets. The purpose of this paper is to formally define Signal Interpreted Petri Net and to develop two didactic methodologies to be used in laboratory classes: to convert Signal Interpreted Petri Net into Ladder Diagram for Programmable Logic Controller and to convert Signal Interpreted Petri Net into C language for Arduino microcontroller. These methodologies will be illustrated by applying the formal Signal Interpreted Petri Net’s definition on an example.

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