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EMR bases

Interaction principle

The system can be decomposed inti subsystems in interactions using 4 basic EMR elements (Table 1) :
- energy sources (green ovals, terminals of the systems),
- accumulation elements (orange rectangles with diagonal line, en,ergy storage),
- conversion element without energy accumulation (various orange pictograms, energy conversion),
- coupling elements for energy distribution (orange overlapped pictograms, energy distribution).

Other elements have been added for specific use. All the elements are interconnected according to the action and reaction principle using exchange variable (arrows). The product of action and reaction variables between two elements leads to the instantaneous power exchanged.

Table 1. EMR pictograms.


Causality principle

As in Causal Ordering Graph [Hautier 96], [Hautier 04], only the integral causality is considered in EMR. This property leads to define accumulation element by a time-dependant relationship between its variables, in which its output is an integral function of its inputs. Other elements are described using relationships without time dependence. In order to respect the integral causality specific association rules are defined, but there are taught only in the expert level unit.


Inversion principle

The inversion based control theory has been initiated by Causal Ordering Graph [Hautier 1996]. The control structure of a system is considered as an inversion model of the system because the control has to define the appropriated inputs to apply to the system from the desired output (Fig. 1).
In this method, relationships without time-dependence are directly inverted (with neither control nor measurement).

Because the derivative causality is forbidden, a direct inversion of time-dependence relationships is not possible. An indirect inversion is thus made using a controller and measurements. These inversion rules have been extended to EMR (blue pictograms, see Table 1):
- conversion elements are directly inverted,
- accumulation elements are inverted using a close-loop control,
- moreover inversions of coupling element require a criteria inputs, which lead an organization of the energy distribution.
This inversion methodology is another way to locate controllers and measurements or estimations.

inversion principle
Fig.1. Inversion-based control.

[Hautier 96] J. P. Hautier, J. Faucher, "Le Graphe Informationel Causal", Bulletin de l'Union des Physiciens, (text in French), vol. 90, juin 1996, pp. 167-189.

[Hautier 04] J. P. Hautier, P. J. Barre, "The causal ordering graph - A tool for modelling and control law synthesis", Studies in Informatics and Control Journal, vol. 13, no. 4, December 2004, pp. 265-283.

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