Language and semantics of expressions for Grafcet model synthesis in a MDE environment

The GRAphe Fonctionnel de Commande Étapes Transitions (GRAFCET) is a powerful graphical modeling language for the pecification of controllers in discrete event systems.It uses expressions to express the conditions of transitions and conditional actions as well as the logical and arithmetic expressions assigned to stored actions. However, several research works has focused on the transformation of Grafcet specifications (including expressions) into control code for embedded systems. To make it easier to edit valid Grafcet models and generate code, it is necessary to propose a formalization of the Grafcet expression language permitting to validate its constructs and provide an appropriate semantics. For this, we propose a context-free grammar that generates the whole set of Grafcet expressions, by extending the usual grammars of logical and arithmetic expressions. We also propose a metamodel and an associated semantics of Grafcet expressions to facilitate the implementation of the Grafcet language. A parser of the expressions Grafcet emph G7Expr is then obtained thanks to the generator of parsers ANTLR, while the metamodel is implemented in the Eclipse EMF Model Driven Engineering (MDE) environment. The combination of the two tools makes it possible to analyze and automatically build Grafcet expressions when editing and synthesizing Grafcet models. Le GRAphe Fonctionnel de Commande Étapes Transitions (GRAFCET) est un puissant lan-gage de modélisation graphique pour la spécification de contrôleurs dans des systèmes à événe-ments discrets. Il fait usage des expressions pour exprimer les conditions de franchissement des transitions et des actions conditionnelles ainsi que les expressions logiques et arithmétiques assi-gnées aux actions stockées. Cependant, de nombreux travaux se sont penchés sur la transformation de spécifications Grafcet (y compris les expressions) en code de contrôle pour systèmes embar-qués. Pour faciliter l'édition de modèles Grafcet valides et la génération du code de contrôle, il est judicieux de proposer une formalisation du langage des expressions Grafcet, permettant de valider ses constructions et d'en pourvoir une sémantique appropriée. Pour cela, nous proposons une gram-maire hors-contexte qui génère tout l'ensemble des expressions Grafcet, en étendant les grammaires usuelles des expressions arithmétiques et logiques. Nous proposons également un métamodèle et une sémantique associée des expressions Grafcet pour faciliter la mise en oeuvre du langage Grafcet sous la forme d'un parseur des expressions Grafcet G7Expr obtenu grce au générateur d'analyseurs syntaxiques ANTLR, alors que le métamodèle est mis en oeuvre dans l'environnement d'Ingénie-rie Dirigée par les Modèles (IDM) Eclipse EMF. L'association des deux outils permet d'analyser et de construire automatiquement les expressions Grafcet lors de l'édition et la synthèse des modèles Grafcet.

An Accurate Linearization of Electromagnetic Force of Heteropolar Magnetic Bearings With Redundant Structures

Fault tolerance is one of the practical and effective approaches to improve the reliability of magnetic bearings. The linearization of the electromagnetic force (EMF) from the redundant structures is the crucial basis of the design of a fault-tolerant controller. In this paper, we propose an accurate linearization approach for the heteropolar magnetic bearings with redundant structures by solving the Taylor series expansion equation of the current distribution matrix (W) in the nonequilibrium position and introducing a set of displacement compensation matrices to establish a unified accurate EMF model including the controlled current and rotor position. The proposed approach can effectively decrease the EMF error between the actual physical model and the linearized model compared with the existing methods for the consideration of the rotor position. Moreover, the solutions of the current distribution matrix and the relevant optimization approach have been presented on the basis of the proposed approach to help to design a high-performance fault-tolerant controller in the entire rotor displacement range. The numerical results demonstrated the noticeable accuracy advantages of the proposed EMF model.

Time-Stepping FEM-Based Multi-Level Coupling of Magnetic Field–Electric Circuit and Mechanical Structural Deformation Models Dedicated to the Analysis of Electromagnetic Actuators

The present paper introduced a framework for multi-level coupling transient electromagnetic fields (EMF) and mechanical structural dynamics based on the finite element method (FEM). This framework was dedicated to predicting, with better accuracy, the wave magnetic force density for obtaining the mechanical deformation occurring in electromagnetic actuators (EMAs). The first-level EMF transient model coupling is related to the magnetic field equations that are strongly coupled with the electric circuit input voltage equations. This is done by considering the magnetic saturation through the Newton–Raphson (N–R) method. The time-stepping solution of the EMF model resulted in the magnetic force densities being computed from the Lorentz force (LZ) expressions, based on the space–time variation of the induced eddy current. For the second coupling level, the EMF model was sequentially coupled with the mechanical structural deformation equations (MDef) through the local magnetic force density to achieve minimal material dynamic displacement and deformation. The developed multi-physics EMF–MDef time-stepping (FEM) model tools were implemented using the Matlab software.

U.S. CARBON TAX SCENARIOS AND BIOENERGY

This paper documents application of the Future Agricultural Resources Model (FARM) to stylized carbon tax scenarios specified by the Stanford Energy Modeling Forum (EMF). Model results show that the method of tax revenue recycling makes a difference. Either labor-tax, or capital-tax, recycling can reduce the welfare cost of a carbon tax policy relative to lump sum recycling. Of the two tax recycling options, reducing capital taxes provides the greater reduction in welfare costs. However, carbon tax revenues decline with stringent carbon dioxide (CO2) emission targets and the availability of a negative-emissions technology such as bio-electricity with CO2 capture and storage (BECCS). As BECCS expands, net carbon tax revenues peak and decline due to an offsetting subsidy for carbon sequestration, limiting the potential for labor- or capital-tax recycling to reduce welfare costs of a climate policy.