Petri net control of a kanban loop

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)

2000

We recently introduced a new stochastic Petri net model called "batch deterministic and stochastic Petri nets" (BDSPNs) capable of describing the synchronization of discrete and batch token flows in discrete batch processes. It is a powerful formal model for the study of inventory systems and supply chains where materials are processed or ordered in finite discrete quantities (batches) and many

2003

The paper presents an analysis of continuous Petri nets using linear algebra of matrices. It provides a link between the classical results of linear systems and Petri nets via the continuous model. A class of variable speed continuous Petri nets (VCPNs), namely Extended State Machines VCPNs (ESMVCPNs) is studied. A state-variable representation and its associated matrix algebra are used to describe systems modeled by ESMVCPNs. The state variable formulation introduced here is that of a linear continuous time-invariant system with nonnegative state (marking) and control vector. The stability and asymptotic stability concepts of linear dynamic systems are applied to continuous Petri nets. A necessary and sufficient condition of conservativeness of ESMVCPNs, based on eigenvalues, is proved. These results are used for the control of a production system.

2009

Abstract A supply chain (SC) is a network of independent manufacturing and logistics companies that perform the critical functions in the order fulfillment process. This paper proposes an effective and modular model to describe material, financial and information flow of SCs at the operational level based on first-order hybrid Petri nets (PNs), ie, PNs that make use of first-order fluid approximation.

2004 IEEE International Conference on Systems, Man and Cybernetics (IEEE Cat. No.04CH37583), 2004

Rairo-operations Research, 1995

Revue française d'automatique, d'informatique et de recherche opérationnelle. Recherche opérationnelle, tome 29, n o 3 (1995), p. 321-352. <http://www.numdam.org/item?id=RO_1995__29_3_321_0> © AFCET, 1995, tous droits réservés. L'accès aux archives de la revue « Revue française d'automatique, d'informatique et de recherche opérationnelle. Recherche opérationnelle » implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/ legal.php). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Recherche opérationnelle/Opérations Research (vol. 29, n° 3, 1995, p. 321 à 352) PRODUCTION MANAGEMENT IN A PETRI NET ENVIRONMENT (*) by Jean-Marie PROTH (*" 2) and Ioannis MINIS (2) Abstract.-The objective of this paper is to show that Pétri nets facilitate a comprehensive approach to production management and allows us to reduce the complexity of the problems involved at the expense of some constraints imposed on the décision making System. The first part of the paper focuses on cyclic manufacturing Systems. For this type of Systems, iî is always possible to propose an event graph model which represents both the physical and the décision making Systems. We use such a model to propose a near-optimal scheduling algorithm that maximizes productivity while minimizing the work-in-process (WIP) in the deterministic case. The approach usedfor non-cyclic manufacturing Systems is different in the sensé that only the manufacturing processes fi.e. the physical part of the System) and the related constraints are modelled using Pétri nets. We use such a Pétri net model to propose a short-term planning process which results in a trade-off between the computation burden and the level of resource utilization. The short-term planning model is then enhanced to obtain the scheduling model. The latter is used to develop an efficient scheduling algorithm that is able to satisfy the requirements imposed by short-term planning.

IFAC Proceedings Volumes, 2001

Methods of dioid algebras have been succesfully applied to the modelling, analysis and control of timed Petri nets. Continuous and hybrid Petri nets are usually described using systems of nonlinear differential equations. It is shown that deterministic continuous Petri nets can be represented by systems of functional equations of the fixed-point type, which can be viewed as linear integral equations in the sense of idem potent integration. The class of hybrid Petri nets (HPN) allowing a linear representation in the idempotent semiring of functions ranging in the (min, +) semi ring is identified. This representation is applied to the optimal control. Moreover, these concepts are generalized to the case of variable maximal firing speeds of continuous transitions.

Nonlinear Analysis: Hybrid Systems, 2014

This paper is dedicated to an extended class of hybrid Petri nets called controlled Generalized Batches Petri Nets. The novel feature of these nets is that the firing flow of continuous and batch transitions and the transfer speed of batch places are control variables. First we propose a linear programming problem to compute the instantaneous firing flow vector and the instantaneous transfer speed vector solving an optimization problem, where the objective function depends on the control goal. Second we analyze and characterize the steady state of this model solving a programming problem that takes into account the net structure and the initial marking. This problem is linear if the transfer speeds are preassigned while it is nonlinear if the transfer speeds are control variables. In such a last case, a viable technique to compute a family of solutions by linear relaxation of the non linear problem is presented. The optimality of steady states for given linear objective functions is also addressed.

Mathematical and Computer Modelling of Dynamical Systems, 1999

A Petri-net based approach for the modeling of batch plants as well as products is presented. The different units of a plant are modeled as bounded Petri nets and products are represented by way of their recipes. With the focus on synchronization and booking issues arising when merging and splitting material flows, we propose general Petri net building-blocks for the construction of these recipes. Both resource and recipe models support formal supervisor synthesis for dynamic resource allocation according to the Ramadge-Wonham framework.

2002

Petri nets are widely used as an underlying framework for formalizing UML-based system models. Based on their precise semantics and easy-to-understand graphical representation, they are appropriate to model production systems together with their quantitative properties. The production of desired materials can be modeled as a reachability problem of its Petri net model, which can be analyzed by linear algebraic techniques (solving linear inequality systems) providing a qualitative solution structure. However, traditional reachability analysis techniques can result in a state space explosion, while numerical methods for invariant computations give either sufficient or necessary conditions. The main advantage of Petri nets is the ability to describe complex and even adaptive control structures. Another mathematical paradigm, Process Network Synthesis (PNS) algorithms are widely used in chemical engineering to estimate optimal resource allocation and scheduling in order to produce desired products from given raw materials. In the current paper it will be shown that PNS algorithms that exploit the specific combinatorial features of PNS problems, can be applied to Petri nets in order to give more efficient mathematical methods for their analysis. This combination of Petri nets and PNS algorithms can unify the efficiency of the optimization algorithms in the PNS fields with the power of Petri nets in modeling complex processes. The current paper presents efficient semi-decision and optimization methods for the reachability problem based on PNS algorithms: Solution Structure Generation (SSG) and Accelerated Branch and Bound (ABB) algorithms. We show that the ABB algorithm can be used to solve scheduling problems efficiently and can be extended for other Petri net analysis. Obviously, the combined methodology can be used for a variety of application fields like IT systems, workflow optimization, etc., including production processes as a special case.