Timed Petri Net Models of Cluster Tools

Hierarchical analysis of manufacturing systems is performed in a top-down manner in which a general, approximate model is used to capture the main effects of component interconnections, while more detailed models of components provide the detailed information needed for the derivation of performance characteristics of the entire system. For Petri net models, this approach corresponds to stepwise refinements of models. Structural analysis, based on place invariants combined with simple net transformations, is used to obtain performance characteristics of the modeled systems

Petri Nets and Timed Petri Nets in Modeling and Analysis of Concurrent Systems – An Overview

Petri nets are formal models of systems which exhibit concurrent activities. Communication networks, multiprocessor systems, manufacturing systems and dis- tributed databases are simple examples of such systems. As formal models, Petri nets are bipartite directed graphs, in which the two types of vertices represent, in a very gen- eral sense, conditions and events. An event can occur only when all conditions associated with it (represented by arcs directed to the event) are satisfied. An occurrence of an event usually satisfies some other conditions, indicated by arcs directed from the event. So, an occurrence of one event causes some other event to occur, and so on. In order to study performance aspects of systems modeled by Petri nets, the durations of modeled activities must also be taken into account. This can be done in different ways, resulting in different types of temporal nets. In timed Petri nets, occurrence times are associated with events, and the events occur in real–time (as opposed to instantaneous oc- currences in other models). For timed nets with constant or exponentially distributed occurrence times, the state graph of a net is a Markov chain, in which the stationary prob- abilities of states can be determined by standard methods. These stationary probabilities are used for the derivation of many performance characteristics of the model. Analysis of net models based on exhaustive generation of all possible states is called reachability analysis; it provides detailed characterization of model’s behavior, but often re- quires generation and analysis of huge state spaces (in some models the number of states increases exponentially with some model parameters, which is known as “state explo- sion”). Structural analysis determines the properties of net models on the basis of connections among model elements; structural analysis is usually much simpler than reachability analysis, but can be applied only to models satisfying certain properties. If neither reachability nor structural analysis is feasible, discrete–event simulation of timed nets can be used to study the properties of net models. This paper overviews basic concepts of Petri nets, intro- duces timed Petri nets, and provides brief summaries of sev- eral case studies of performance analysis which are discussed in greater detail in other publications of the author

Étude des comportements chaotiques dans les convertisseurs statiques

This thesis deals with the analysis of chaotic behaviors in serial multicellularconverters. These switching systems can have a variety of complex phenomenaassociated with bifurcations and chaos. Knowing that a power converter that has a purely dissipative load cannot generate chaotic behavior, we've in the first part of this thesis, we connected a two-cell chopper to a nonlinear load not strictly dissipative and we've analyzed its behaviors by using some basic dynamic properties and thus presented the routes to chaos. The end of this part was devoted to the study of the 5-cell chopper which is a generalization of the two-cell chopper. In order to eliminate the chaotic behavior, the second part was devoted to the synthesis of a controlled law based on hybrid modeling of Petri nets for the regulation of capacitor voltages and current load.Les travaux de cette thèse portent sur l'analyse des comportements chaotiques dans les convertisseurs multicellulaires séries. Ces systèmes à commutationpeuvent présenter une variété de phénomènes complexes liés à des bifurcationset au chaos. Sachant qu'un convertisseur de puissance qui a une charge purementdissipative, ne peut générer un comportement chaotique, nous avons dans la première partie de cette thèse, connecté un hacheur à deux cellules à une charge non linéaire non strictement dissipative et nous avons analysé ses comportements à l'aide des propriétés dynamiques de base et présenté les routes vers le chaos. La fin de cette partie a été consacrée à l'étude du hacheur à cinq cellules qui est une généralisation du hacheur à deux cellules. Afin de supprimer le comportement chaotique, la deuxième partie du travail a été consacrée à la synthèse d'une loi de commande hybride basé sur la modélisation par réseaux de Petri pour la régulation des tensions des condensateurs flottants et du courant de charge