Storage Device Sizing for a Hybrid Railway Traction System by Means of Bicausal Bond Graphs

In this paper, the application of bicausal bond graphs for system design in electrical engineering is emphasized. In particular, it is shown how this approach is very useful for model inversion and parameter dimensioning. To illustrate these issues, a hybrid railway traction device is considered as a case study. The synthesis of a storage device (a supercapacitor) included in this system is then discussed

Model inversion of electrical engineering systems from bicausal bond graphs

In this paper, the application of bicausal bond graphs for model inversion of typical electrical engineering systems is emphasised. Inverse models are particularly useful for the synthesis step of the system design process. To illustrate these issues, a typical railway traction device and an Aeronautic Electro Hydrostatic Actuator are considered as case studies. From the requirements applied to the system outputs, we show how the synthesis of electrical constraints can be carried out from the inverse bicausal Bond Graph

A bond graph representation of an optimal control problem: the example of the DC motor

International audienceOptimization has become of great importance in present day Systems Engineering. Also, bond graph language proves to be a very efficient tool for modelling, analysing and designing mechatronic systems from an energy and dynamic point of view. The idea presented in this paper is to combine an optimization formulation in the optimal control context with bond graph language. The objective is to transpose the optimization problem into bond graph formalism so that its exploitation will solve this optimization problem. This paper, being a primary investigation, restricts itself to an optimal control problem formulation applied to the example of the classical DC motor. Developments are based on the use of Pontryagin's classical Maximum Principle where the cost function is expressed as the integral of a quadratic form of the state space vector and the control input to be determined. This type of expression may correspond to a certain energy loss-minimization. It is shown that the formulation of this optimal control problem in bond graph makes logical use of the adjoint system concept. Later variable mapping enables an augmented bond graph representation of the whole problem to be set up. Finally the bicausality assignment to this augmented bond graph representation furnishes the solution to the optimal control problem under consideration

Bicausality-based Procedures for Transfer and Transmission Matrix Determination of Single Source Single Load Linear Systems

International audienceIn linear SISO systems the energy flows from the source to the load through each actuating power line. Bond graph representation is well suited for studying the energy transfer in these systems because, in most of the systems, we can consider that energy flows through a power line embedded in two-port subsystems. Moreover, with bond graph language, we benefit from the ease of analytical exploitation introduced by the calculus causality and bicausality concepts.In the bond graph representation of a system the power in some port is associated to a power bond to which two power variables are attached. The determination of the transmission matrix linking two power variables is an efficient tool for studying the energy transfer. Furthermore it is often useful to study the bi-directional energy transfer i.e. from the source to the load and vice versa. The latter case (namely from the load to the source) is quite useful for the energy sizing of asystem from its dynamic specifications on an output variable.This paper proposes different procedures for determining direct and inverse transmission matrices and the transfer matrix between an internal bond and an environmental one for Single Source Single Load Linear systems represented by bond graphs. The procedures are based on the bicausality concept and the loop rule

Sizing of an Electric Power Steering system on dynamic and energetic criteria

International audienceThis paper presents the methodology to size a mechatronic system on dynamic and energetic criteria. The methodology is based on the establishment of the inverse model from the bond graph representation of the system by using the bicausality concept. By means of an automotive example, we illustrate the methodology and we present a solution to extend it to more complex problem

Structural analysis by bond graph approach: Duality between causal and bicausal procedure

Postprint version.International audienceThe infinite structure of linear time-invariant systems has been principally used to solve control problems. Nevertheless, this system characterization appears interesting in the design and sizing of mechatronic systems as well. Indeed, based on the bond graph language and inverse modelling, a methodology has already been developed for sizing mechatronic systems according to energy and dynamic criteria. One of the novelties of this methodology is its structural analysis step. This step enables structural properties to be deduced and helps in the formulation of the specifications. The aim of this paper is to add new graphical procedures to the structural analysis step to determine some structural properties (infinite pole orders and relative orders) from the inverse model (bicausal bond graph model). The structural analysis of the inverse model remains interesting since the essential orders are immediately obtained on the bicausal model. A discussion is carried out regarding the duality between the causal and bicausal procedures

Aspects of bond graph modelling in control

Abstract available: p. i

Méthodologie de conception systémique en génie électrique à l'aide de l'outil bond graph : application à une chaine de traction ferroviaire

L'hétérogénéité et le caractère souvent multidomaines des systèmes au sein desquels le Génie Electrique intervient complexifient leur analyse globale. Pourtant, l'approche système est essentielle car elle met en exergue les couplages entre éléments situés dans différentes disciplines. pour faciliter cette démarche, le formalisme de modélisation unifiant "Bond Graph" est utilisé pour visualiser les transferts énergétiques. Par ailleurs, cette méthodologie offre des perspectives intéressantes en terme d'analyse systémique, objet de ce mémoire. Deux méthodes de simplification de modèle ont été étudiées et comparées. Il s'agit de la Méthodes des Perturbations Singulières, basée sur la séparation de dynamique des éléments, et de la méthode MORA (Model Order Reduction Algorithm), basée sur l'activité énergétique. Ces méthodes peuvent nous conduire à la simplification du modèle Bond Graph en fonction de la gamme de fréquence des signaux d'entrées/sorties. Pour analyser la stabilité, la méthode du lieu des pôles et la deuxième méthode de Lyapunov ont été étudiées et appliquées à l'aide du formalisme Bond Graph. Ces différentes techniques d'analyse sont appliquées à l'aide du formalisme Bond Graph. Ces différentes techniques d'analyse sont appliquées au cas d'étude d'une chaîne de traction ferroviaire industrielle. ABSTRACT : In Electrical Engineering, the global analysis of systems is difficult because of their heterogeneity and their multidomain nature. Nevertheless, this system approach is essential because it underlines couplings between elements of different physical fields. To facilitate this analysis, the unified formalism Bond Graph is used. This modeling method illustrates the energetic transfers in the system. Moreover, this methodology offers interesting solutions in terms of system analysis. Two simplification methods have been investigated and compared, i.e. the Singular Perturbations Method (SPM), based on the dynamic analysis of elements, and the Model Order Reduction Algorithm (MORA), based on the energetic activity. By these methods, a simplified bond graph model can be obtained for a given frequency range. The stability analysis by the root locus method and the Lyapunov’s second method have been examined and applied with the Bond Graph formalism support. An industrial railway traction system is considered as the case study in the application of these different analysis techniques