Modelling by Petri nets of the hybrid systems in electrical engineering BELKACEM SAIT, HASSANE ALLA Department of Electrical Engineering University of Ferhat ABBES Sétif, ALGERIA [email protected], http://www.univ-setif [email protected], http://www.lag.ensieg.inpg Abstract: - Petri nets enable a discrete event system of any kind whatsoever to be modeled. They present two interesting characteristics. Firstly they make it possible to model and visualize behaviors comprising concurrency, synchronization and resource sharing. Secondly the theoretical results concerning them are plentiful. The aim of this paper is to present a new approach of modelling of the Hybrid Dynamic Systems HDS in the field of the electrical engineering systems. The modelling tool is the Hybrid Petri net HPN, an extension of the Petri nets PN. The HPN unify within the same formalism the modelling of the continuous and discontinuous phenomena basically non dissociable in an electrical engineering unit. It integrates two types of PN: The continuous Petri net CPN models the part continues HDS; traditional PN models the discrete part of the SDH. We represent in this article in the first time the tool of modelling the hybrid Petri net. Then the methodology of representation by HPN of the static inverters, these constituting of the real examples of the hybrid dynamic systems the discrete aspects of these systems are due to operations and the order of the semiconductors (on/off) and the aspects continuous are due to the electrical and mechanical variables of system. The designed model can be uses at the same time for simulation, the control and the monitoring of the system. Key-Words: - Hybrid dynamic systems, hybrid Petri nets, converter, modelling, simulation, monitoring 1 Introduction The Dynamic Continuous Systems DCS have variables which have a continuous behavior in time (voltage, current, speed, torque). They are often model by differential or difference equations or transfer functions. The systems based on the principles of physics are continuous dynamic systems. For the Dynamics Discrete systems DDS, the space of the variables of the exits is a discrete whole of value (states opening/closing of a switch, numbers simultaneous switches input/output in a static inverter, pulse repetition frequency for the order of the interrupters). The traditional models used for DDS are: Petri nets, automats, Grafcet. The systems including the two characteristics continuous and discrete are called the hybrid dynamic systems. If the techniques of modeling of the continuous and discrete systems are known, for the hybrid dynamic systems a unified tool of modeling is necessary: - To understand and ensure the consistency of the interaction of the two parts, continuous and discrete of the hybrid system; - To contribute with the design, the supervision and the development of the order; - To simplify simulation and to carry out more precise formal analyses. The modern electrical engineering sets constitute a class of fast processes who’s at the same time structural and functional complexity all is growing These sets generally incorporate electromechanical parts, static inverters concern the power electronics and the element of control often treated on a hierarchical basis providing the functions of brought closer order, control, management of and the reliability operating modes [1] and [2] The Petri nets PN can thus be made profitable for the study of the converters [3] in particular hybrid Petri net HPN which associated within the same formalism of the discrete representation and continuous. In this article we are interested in modeling of the hybrid dynamic systems in electrical engineering; it is composed of 3 parts. After the introduction, the second left described the tool hybrid PN modeling, in third parts applications of HPN to the modeling of the static inverters. 2 Discrete, continuous and hybrid Petri net We will represent in this section the discrete, continuous and hybrid Petri net 2.1 Timed discrete Petri net In timed discrete PN, the temporizations can be constant or variable, they are associated are in the Proceedings of the 6th WSEAS Int. Conf. on Systems Theory & Scientific Computation, Elounda, Greece, August 21-23, 2006 (pp151-156)
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Modelling by Petri nets of the hybrid systems in electrical engineering