Modeling of Water Treatment Plant using Hybrid Petri Nets

Hybrid Petri nets are modeling framework for a system that contains discrete and continuous states. In this paper, we construct a model of water treatment plant using Hybrid Petri nets. We choose hybrid petri nets because the water treatment plant contains discrete and continuous parts. The discrete part consists of the state of pumps and the continuous part consists of water volume in each processing unit. The Petri Nets obtained were further simplified to facilitate simulation. Through simulation we can determine the amount of water production with certain specifications

Modelling and controlling traffic behaviour with continuous Petri nets

Traffic systems are discrete systems that can be heavily populated. One way of overcoming the state explosion problem inherent to heavily populated discrete systems is to relax the discrete model. Continuous Petri nets (PN) represent a relaxation of the original discrete Petri nets that leads to a compositional formalism to model traffic behaviour. This paper introduces some new features of continuous Petri nets that are useful to obtain realistic but compact models for traffic systems. Combining these continuous PN models with discrete PN models of traffic lights leads to a hybrid Petri net model that is appropriate for predicting traffic behaviour, and for designing trac light controllers that minimize the total delay of the vehicles in the system

Petri net models of microgrids with distributed generators

This thesis introduces some basic concepts and control methods about a microgrid. Then, two hot issues are investigated. One is how to control multiple distributed generators; and another is how to model both discrete event and continuous behaviors of a microgrid. To address these two issues, this thesis work applies Petri nets to both modeling and control of a microgrid. Ordinary Petri nets, hybrid Petri nets, and finite capacity Petri nets, are introduced with their examples targeted at modeling the behavior of a microgrid. Coordination control of multiple distributed generators based on a Petri net model is proposed. Compared with multi-V/f control, the Petri net based control enables the system to operate with a longer stable time interval. Finally, a hybrid Petri net model is constructed to model both discrete event and continuous behaviors of an on-load tap changing transformer system. Compared with an algebraic method, the hybrid Petri net offers a clear and easy-to-understand method to describe such a system

Modeling and analysis using hybrid Petri nets

This paper is devoted to the use of hybrid Petri nets (PNs) for modeling and control of hybrid dynamic systems (HDS). Modeling, analysis and control of HDS attract ever more of researchers' attention and several works have been devoted to these topics. We consider in this paper the extensions of the PN formalism (initially conceived for modeling and analysis of discrete event systems) in the direction of hybrid modeling. We present, first, the continuous PN models. These models are obtained from discrete PNs by the fluidification of the markings. They constitute the first steps in the extension of PNs toward hybrid modeling. Then, we present two hybrid PN models, which differ in the class of HDS they can deal with. The first one is used for deterministic HDS modeling, whereas the second one can deal with HDS with nondeterministic behavior. Keywords: Hybrid dynamic systems; D-elementary hybrid Petri nets; Hybrid automata; Controller synthesi

On reachability and deadlock-freeness of Hybrid Adaptive Petri nets ⋆

Abstract: Petri nets (PN) represent a well known family of formalisms for the modeling and analysis of Discrete Event Systems (DES). As most formalisms for DES, PNs suffer from the state explosion problem. A way to overcome this difficulty is to relax the original discrete model and deal with a fully or partially continuous model. In contrast to continuous Petri nets that consider a full continuous firing of transitions, what can lead to the loss some properties of the original discrete model, this paper deals with Hybrid Adaptive Petri nets (HAPNs), that consider partially continuous firings. In an HAPN, a threshold is associated with each transition: if the load of the transition is higher than its threshold, it behaves as continuous; if it is lower, it behaves as discrete. This way, transitions adapt dynamically to their load. The reachability space and the deadlock-freeness property of HAPNs are studied and compared to those of discrete and continuous Petri nets

Computation of the Reachability Graph of untimed Hybrid Petri nets

Untimed hybrid Petri nets are a formalism for the analysis of dynamical systems, which combines discrete and continuous behaviour. The study of its reachability is interesting for analysis purposes, such as the study of behavioural properties. A method to compute its reachability graph and reachability space is proposed here

Simulation of a low voltage customer microgrid using petri nets

With renewable energy coming to the forefront of how power is generated and delivered to the modern consumer, Microgrids are emerging as an optimal and efficient method for implementing renewables and changing the infrastructure of the dated transmission and distribution grid. This thesis work presents mathematical models of Petri Nets for the simulation of a low voltage customer Microgrid. Using previous work created in this specific field, a Hybrid Petri Net is modified such that it consists of multiple distributed generators, storage, and the utility which is referred to as the main distribution grid in this thesis. A Discrete Petri Net is developed for load shedding which is critical for simulation purposes. Two types of Scheduling are developed, heuristic and reliability ones for the Microgrid to operate. Equations for firing rates are obtained for continuous transitions. Input weather data is obtained from outside sources and modified for the simulation. Computer programs are created for the microgrid simulation and the creation and presentation of the reachability graphs. A total of twelve simulations are run with the data analyzed and reachability graphs for the hybrid and discrete load shedding Petri nets developed for two simulations

Continuous flow Systems and Control Methodology Using Hybrid Petri nets

International audienceIn this paper, we consider the controller synthesis for continuous flow systems. These lasts are a sub-class of hybrid dynamic systems. Their main characteristics are positiveness and linearity. Transport, manufacturing, communication and biological systems are examples of continuous flow systems. Numerous tools and techniques exist in the literature for modelling and analyzing such systems. As positiveness is a hard constraint, an appropriate tool integrating naturally this constraint is strongly needed. Hybrid Petri Nets are an elegant modeling tool of positive systems, while Hybrid Automata are a powerful tool giving formally the reachable dynamic space. Combining these two tools aim to a sound approach for control synthesis of continuous flow systems. We start by considering the process to control and compute its reachable state space using specialized software like PHAVer. Algebraic inequalities define this reachable state space. The constrained behaviour is obtained by restricting this state space into a smaller desired space. This reduction is expressed in term of linear constraints only over the continuous variables; while the control is given by the discrete transitions (occurrence dates of controllable events). The controller synthesis methodology is based on the control of a hybrid system modelled by a D-elementary hybrid Petri Net. The control consists in modifying the guard of the controllable transitions so as the reachable controlled state space is maximally permissive

Vérification efficace de systèmes à compteurs à l'aide de relaxations

Abstract : Counter systems are popular models used to reason about systems in various fields such as the analysis of concurrent or distributed programs and the discovery and verification of business processes. We study well-established problems on various classes of counter systems. This thesis focusses on three particular systems, namely Petri nets, which are a type of model for discrete systems with concurrent and sequential events, workflow nets, which form a subclass of Petri nets that is suited for modelling and reasoning about business processes, and continuous one-counter automata, a novel model that combines continuous semantics with one-counter automata. For Petri nets, we focus on reachability and coverability properties. We utilize directed search algorithms, using relaxations of Petri nets as heuristics, to obtain novel semi-decision algorithms for reachability and coverability, and positively evaluate a prototype implementation. For workflow nets, we focus on the problem of soundness, a well-established correctness notion for such nets. We precisely characterize the previously widely-open complexity of three variants of soundness. Based on our insights, we develop techniques to verify soundness in practice, based on reachability relaxation of Petri nets. Lastly, we introduce the novel model of continuous one-counter automata. This model is a natural variant of one-counter automata, which allows reasoning in a hybrid manner combining continuous and discrete elements. We characterize the exact complexity of the reachability problem in several variants of the model.Les systèmes à compteurs sont des modèles utilisés afin de raisonner sur les systèmes de divers domaines tels l’analyse de programmes concurrents ou distribués, et la découverte et la vérification de systèmes d’affaires. Nous étudions des problèmes bien établis de différentes classes de systèmes à compteurs. Cette thèse se penche sur trois systèmes particuliers : les réseaux de Petri, qui sont un type de modèle pour les systèmes discrets à événements concurrents et séquentiels ; les « réseaux de processus », qui forment une sous-classe des réseaux de Petri adaptée à la modélisation et au raisonnement des processus d’affaires ; les automates continus à un compteur, un nouveau modèle qui combine une sémantique continue à celles des automates à un compteur. Pour les réseaux de Petri, nous nous concentrons sur les propriétés d’accessibilité et de couverture. Nous utilisons des algorithmes de parcours de graphes, avec des relaxations de réseaux de Petri comme heuristiques, afin d’obtenir de nouveaux algorithmes de semi-décision pour l’accessibilité et la couverture, et nous évaluons positivement un prototype. Pour les «réseaux de processus», nous nous concentrons sur le problème de validité, une notion de correction bien établie pour ces réseaux. Nous caractérisions précisément la complexité calculatoire jusqu’ici largement ouverte de trois variantes du problème de validité. En nous basant sur nos résultats, nous développons des techniques pour vérifier la validité en pratique, à l’aide de relaxations d’accessibilité dans les réseaux de Petri. Enfin, nous introduisons le nouveau modèle d’automates continus à un compteur. Ce modèle est une variante naturelle des automates à un compteur, qui permet de raisonner de manière hybride en combinant des éléments continus et discrets. Nous caractérisons la complexité exacte du problème d’accessibilité dans plusieurs variantes du modèle

Modeling and Analysis of Hybrid Dynamic Systems Using Hybrid Petri Nets

International audienceWe consider in this paper the extensions of the PN formalism in the direction of hybrid modeling. We briefly presents hybrid dynamic systems. Then the hybrid automata model. Is introduced and we discuss continuous Petri nets. These models are obtained from discrete PNs by the fluidification of the markings. They constitute the first steps in the extension of PNs toward hybrid modeling. Two hybrid PN models, which differ in the class of HDS they can deal with, are studied. The first one is used for deterministic HDS modeling, whereas the second one can deal with HDS with nondeterministic behavior. The general control structure based on hybrid PNs is briefly described