0
Research Papers

Determination of Essential Orders From a Bond Graph Model

[+] Author and Article Information
Mariem El Feki, Audrey Jardin, Laurent Krähenbühl, Eric Bideaux, Daniel Thomasset

Ampère Laboratory,  University of Lyon, INSA-Lyon, Villeurbanne 69621, France

Wilfrid Marquis-Favre1

Ampère Laboratory,  University of Lyon, INSA-Lyon, Villeurbanne 69621, Francewilfrid.marquis-favre@insa-lyon.fr

The integers ni are assumed to be decreasingly ordered.

Attention has to be paid to the fact that an exception to this definition may happen. As highlighted in Ref. [16], if there are two paths involving the same input, having the same minimal order ωimin and such that the sum of their gains is equal to zero, then the relative degree of the output in question can be greater than ωimin. In fact only niωimin is true in the general case.

This proposition was enunciated in Ref. [2] for right-invertible systems.

1

Corresponding author.

J. Dyn. Sys., Meas., Control 134(6), 061006 (Sep 13, 2012) (9 pages) doi:10.1115/1.4004772 History: Received September 19, 2010; Accepted June 03, 2011; Published September 13, 2012; Online September 13, 2012

The notion of essential orders was first introduced for the handling of decoupling problems. This paper focuses more on their interpretation, namely on the fact that each essential order corresponds to the highest time-differentiation order of a specific output appearing in the inverse model. During inverse modeling, this can in particular be useful for checking whether the specifications are appropriate to the structure of the given model. The aim of this paper is to define two procedures to graphically determine the essential orders directly from a bond graph (BG) model of a linear time-invariant system. Their usefulness is then justified in the context of a bond-graph based methodology for design problem analysis.

FIGURES IN THIS ARTICLE
<>
Copyright © 2012 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Technological diagram of example 1: three masses in series

Grahic Jump Location
Figure 2

Causal BG model of example 1

Grahic Jump Location
Figure 3

Causal bond graph model of example 1: I/O causal paths analysis

Grahic Jump Location
Figure 4

Causal analysis of example 1: determination of the infinite zero orders n¯ij

Grahic Jump Location
Figure 5

Technological diagram of example 2: four masses in series

Grahic Jump Location
Figure 6

Causal BG model of example 2

Grahic Jump Location
Figure 7

Causal analysis of example 2: set of different I/O causal paths

Grahic Jump Location
Figure 8

Causal analysis of example 2: determination of the infinite zero orders n¯ij

Grahic Jump Location
Figure 9

Determination of the relative degrees of example 2

Grahic Jump Location
Figure 10

Inverse BG model of example 1

Grahic Jump Location
Figure 11

Inverse bond graph model of example 1: I/O causal paths analysis

Grahic Jump Location
Figure 12

Inverse BG model of example 2

Grahic Jump Location
Figure 13

Inverse bond graph model of example 2: I/O causal paths analysis

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In