Towards Integrating Hybrid DAEs with a High-Index DAE Solver
نویسندگان
چکیده
J.D. Pryce and N.S. Nedialkov have developed a Taylor series method and a C++ package, Daets, for solving numerically an initial-value problem differential-algebraic equation (DAE) that can be of high index, high order, nonlinear, and fully implicit. Numerical results have shown this method to be efficient and very accurate, and particularly suitable for problems that are of too high an index for present DAE solvers. However, Daets cannot be applied to systems of DAEs that change at points it time, also called hybrid or multi-mode DAEs. This paper presents methods for extending Daets with the capability to integrate hybrid DAEs. Methods for event location and consistent initializations are given. Daets is applied to simulate a model of a parallel robot: a hybrid system of index-3 DAEs with closed-loop control. Key-words: high-index differential-algebraic equations, hybrid systems, structural analysis, consistent initialization This work was supported in part by the Natural Sciences and Engineering Research Council of Canada and INRIA France ∗ Department of Computing Software, McMaster University, Hamilton, Ontario, Canada, L8S 4K1, [email protected] † INRIA Sophia Antipolis – Méditerranée, COPRIN project, [email protected] in ria -0 03 60 99 9, v er si on 1 13 F eb 2 00 9 Vers l’intégration numérique d’équations algébro-différentielles hybrides avec un solver de DAE à grande valeur d’indice Résumé : J.D. Pryce et N.S. Nedialkov ont développé une méthode basée sur le dévelopement en série de Taylor et un package C++, Daets, pour résoudre numériquement le problème de la valeur initiale pour des systèmes algébrodifférentiels (DAE) de grand ordre, non linéaires, totalement implicites et dont la valeur d’indice peut être grande. Les résultats numériques ont montré que cette méthode est efficace, très précise, et particulièrement adaptée aux problèmes dont la valeur d’indice est trop grande pour être résolus par les solveurs actuels. Cependant, Daets ne peut pas être utilisé avec des systèmes de DAE qui changent à des instants donnés, ou plus généralement des DAEs hybrides ou multi-modes. Ce rapport de recherche présente des méthodes pour rendre Daets capable d’intégrer numériquement les DAEs hybrides. Des méthodes pour la détection d’événements et la recherche des nouvelles conditions initiales sont aussi introduites. Daets est utilisé pour simuler le modèle d’un robot parallèle fonctionnant en boucle fermée, écrit sous la forme d’un système DAE hybride de valeur d’indice 3. Mots-clés : équations algébro-différentielles à grande valeur d’indice, systèmes hybrides, analyse structurelle, initialisation in ria -0 03 60 99 9, v er si on 1 13 F eb 2 00 9 Integrating Hybrid DAEs 3
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