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1

Modelling and control of flexible manufacturing systems by means of interpreted Petri nets

Čapkovič František

Journal of Automation Mobile Robotics and Intelligent Systems

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2018

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Vol. 12, No. 4

3--10

EN

Because flexible manufacturing systems (FMS) are discrete event systems (DES), their modelling and control by means of Petri nets (PN) is widely used. While PN transitions are observable and controllable and PN places are measurable, place/transition PN (P/T PN) are suffcient for this aim. However, when some PN transitions are unobservable and/or uncontrollable and some places are non-measurable/unobservable, P/T PN are insufficient for modelling and especially for control. In such a case interpreted Petri nets (IPN) seem to be an appropriate replacement for P/T PN. In this paper a possibility of usage of IPN for FMS modelling and control is pointed out. Illustrative examples as well as the case study on a robotized assembly cell are introduced. By means of using timed PN (TPN) also the performance evaluation of the IPN model of controlled plant is accomplished whereby the simulation in Matlab.

2

A timed Petri net framework to find optimal IRIS schedules

Werner M.

Control and Cybernetics

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2006

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Vol. 35, no 3

703-719

EN

IRIS (increasing reward with increasing service) realtime scheduling appears frequently in real-time control applications such as heuristic control. IRIS requires not only meeting deadlines, but also finding the schedule with the best result (highest reward). In this paper, a framework is presented that uses Timed Petri nets (TPN) to transform an IRIS problem into a dynamic programming (DP) problem, allowing the application of known TPN and DP techniques. In the presented approach, an IRIS problem with tasks having discrete-time optimal parts is transformed into a (possibly unbounded) TPN. Then, the critical path problem of the TPN state graph can be tackled with DP. This approach allows for the IRIS problem multiple constraints and negative rewards.

3

Minimization Algorithms for Time Petri Nets

Półrola A., Penczek W.

Fundamenta Informaticae

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2004

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Vol. 60, nr 1-4

307--331

EN

The paper presents three methods for applying partitioning algorithms, used for generating abstract models for timed automata, to the case of time Petri nets. Each of these methods is based on a different approach to the concrete semantics of a net, and can potentially be more efficient than the others in a particular case. Besides the theoretical description, we provide some preliminary experimental results, obtained from the implementation integrated with the model checking tool VeriCS.

4

Timed Petri-Net Based Formulation and an Algorithm for the Optimal Scheduling of Batch Plants

Gu T., Bahri P. A., Cai G.

International Journal of Applied Mathematics and Computer Science

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2003

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Vol. 13, no 4

527-536

EN

The effective scheduling of operations in batch plants has a great potential for high economic returns, in which the formulation and an optimal solution algorithm are the main issues of study. Petri nets have proven to be a promising technique for solving many difficult problems associated with the modelling, formal analysis, design and coordination control of discrete-event systems. One of the major advantages of using a Petri-net model is that the same model can be used for the analysis of behavioural properties and performance evaluation, as well as for the systematic construction of discrete-event simulators and controllers. This paper aims at presenting a Petri-net based approach to the scheduling of operations in batch plants. Firstly, the short term of the `scheduling of batch plants' is formulated by means of a timed Petri net which can accommodate various intermediate storage policies, such as unlimited intermediate storage (UIS), no intermediate storage (NIS), finite intermediate storage (FIS), and mixed intermediate storage (MIS). Secondly, a heuristic search algorithm for the optimal scheduling of batch plants is given, which is based on generating and checking the markings in the reachability tree of the Petri-net model. Finally, the novel formulation and algorithm are tested with several simulation case studies.

5

Using State Equation to Prove Non-Reachability in Timed Petrinets

Popova-Zeugmann L., Werner M., Richling J.

Fundamenta Informaticae

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2003

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Vol. 55, nr 2

187-202

EN

Non-reachability proofs in Timed Petrinets were usually done by proving the non-reachability within the underlying timeless net. However, in many cases this approach fails. In this paper, we present an approach to prove non-reachability within the actual Timed Petrinet. For this purpose, we introduce a state equation for Timed Petrinets in analogy to timeless nets. Using this state equation, we can express reachability as a system of equations and inequations, which is solvable in polynomial time.

6

Analysis of Performance Bottlenecks in Multithreaded Multiprocessor Systems

Zuberek W.M.

Fundamenta Informaticae

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2002

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Vol. 50, nr 2

223-241

EN

The performance of modern multiprocessor systems is often limited by the delays of interconnections or long latencies of memory subsystems. Instruction-level multithreading is a technique to tolerate such long latencies by switching from one instruction thread to another and continuing instruction execution concurrently with the long-latency operations. Using timed Petri net models, the paper analyzes performance limitations introduced by different components of distributed-memory multithreaded multiprocessor systems. Simulation results are used to compare performance improvements obtained by replicating critical components of the system to those obtained using components with better performance characteristics.

7

Time extensions of Petri nets for modelling and verification of hard real-time systems

Samolej S., Szmuc T.

Computer Science

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2002

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Vol. 4

55-76

EN

The main aim of the paper is a presentation of time extensions of Petri nets appropriate for modelling and analysis of hard real-time systems. It is assumed, that the extensions must provide a model of time flow, an ability to force a transition to fire within a stated timing constraint (the so-called the strong firing rule), and timing constraints represented by intervaIs. The presented survey includes extensions of classical Place/Transition Petri nets, as welI as the ones applied to high-level Petri nets. An expressiveness of each time extension is illustrated using simple hard real-time system. The paper includes also a brief description of analysis and verification methods related to the extensions, and a survey of software tooIs supporting modelling and analysis of the considered Petri nets.

PL

Głównym celem pracy jest prezentacja rozszerzeń czasowych sieci Petriego pod kątem przydatności do modelowania i analizy systemów czasu rzeczywistego o twardych wymaganiach losowych. Zakłada się, że rozważane rozszerzenia winny spełniać następujące warunki: modelowania upływu czasu, forsowania odpalenia przejścia w określonych warunkach czasowych (tzw. silna reguła odpalania), przedziałowej reprezentacji ograniczeń czasowych. Przegląd dotyczy zarówno klasycznych sieci miejsc i przejść, jak również sieci Petriego wyższego poziomu. Siła ekspresji poszczególnych rozszerzeń jest ilustrowana na wspólnym przykładzie systemu o twardych wymaganiach czasowych. Artykuł zawiera również krótki opis metod analizy i weryfikacji ograniczeń czasowych oraz przegląd systemów wspomagających modelowanie i analizę rozważanych sieci Petriego.