# Semantic Conventions in Bond Graphs

This letter is a reprint of a letter that was sent by F.E.Cellier to one of his students. It might be of general interest.

Dear Antonio:

Your question brings up an interesting point about BGs, an issue that was discussed quite a bit in the recent ICBGM'97 conference: BGs are inherently ambiguous, unless accompanied by a number of conventions.

The problem has to do with the following property of BGs:

The EQUATIONS governing a system described by BGs are associated with the objects (R,C,I,SE,SF,TF,GY,0,1), whereas the VARIABLES used in these equations are associated with the bonds, i.e., the connectors between the objects.

This awkward dichotomy makes the BGs inherently ambiguous, and makes it necessary to accompany the BG syntax with a number of semantic conventions.

You wrote:

``` > I'm in the stage of generating equations for the bond graph and came across
> with the following question:
>
> Lets say we have a TF as follows:
>
>      e1        e2
>    |----\ TF |----\
>      f1   m    f2
>
> then according to the constitutive relations, we have:
>
>      e1 = m*e2
>      f2 = m*f1
```

This is correct, or at least, it is in accordance with my red book. Unfortunately, not all BGers use the same convention, thus, BGs drawn by different people may not necessarily be consistent. Some people may claim the "correct" equations to be:

```        e1 = (1/m)*e2
f2 = (1/m)*f1
```

i.e., they declare (implicitly) that the m-factor that is shown on the BG is the effort gain from the primary to the secondary side, whereas my definition declares the m-factor to be the flow gain from the primary to the secondary side.

1st Convention: The gain factor written below the TF element is the flow gain from the primary to the secondary side of the transformer.

Of course, we need a similar convention relating to GY elements:

2nd Convention: The gain factor written below the GY element is the gain from the primary flow to the secondary effort.

Moreover, I always draw the effort variable at the side of the harpoon, whereas some other BGers (such as Jean Thoma) draw the flow variable always at the side of the harpoon. Yet others are not systematic at all, and do it either way more or less arbitrarily. As long as the variables are mnemonically called "e" and "f," it doesn't really matter either way, but if they are called something else, let's say "u" and "i," then how do you know which one is the effort and which the flow, unless you use some sort of strict convention?

3rd Convention: The variable written on the side of the harpoon is the effort variable, whereas the variable written on the other side is the flow variable.

You wrote further:

``` > That's ok but what if we had:
>
>       e1        e2
>    |\---- TF |\----
>       f1  m     f2
>
> then the equations become:
>
>      -e1 = -m*e2
>      -f2 = -m*f1
>
> because of the reversal of the power flow??
```

This question is another outflow of the aforementioned dichotomy. You assume that a transformer comes with readable labels that tell the user which is the primary side, and which the secondary side. In BGs, this is not the case. "e1" and "f1" are simply names, the "1" cannot be construed to mean that this is where the primary side is. However, this gives rise for the need to yet another convention:

4th Convention: The two bonds attached to a two-port TF or GY element have opposite positive power directions, i.e., one of the harpoons points at the object, whereas the other harpoon points away from the object. The harpoon pointing at the object denotes the primary side of the TF or GY element.

Using this convention, the constitutive equations with their correct causality assignment for the above bond graph become:

```         e1 = e2/m
f2 = f1/m
```

If you really mean to connect the TF element "the other way around" into the BG, you need to replace "m" by "1/m."

In accordance with the 4th convention, the following BG is incorrect:

```        e1         e2
|----\ TF |\----
f1   m     f2
```

because we have no way of knowing any more, which side of the TF is the primary side, and which is the secondary side.

The problem becomes worse when we start using hierarchical bond graph objects (i.e., new objects that have one or several power connectors). For example:

```                |
|
/
----\ BJT
|
|
/
```

How are you supposed to know, which is the base, which the collector, and which the emitter? How do you know whether this is an NPN or a PNP transistor? How do you know whether it is horizontally or vertically diffused? Clearly, unless we add more syntactic elements to the BG drawing, e.g. by naming the three ports as "b," "c," and "e," respectively, we need to add yet more semantic conventions to the use of these hierarchical elements to make them unambiguous.

It might be useful to create a systematic list of all implicit semantic conventions associated with the standard BG elements. To my knowledge, such a list has never been composed and published.

It makes sense to request that R, C, and I elements have there associated bonds always with their harpoons pointing at the element. There is no good reason to allow reversed power conventions.

5th Convention: All harpoons of bonds attached to R, C, I, RF, and CF elements point at the objects, never away from the objects. RS elements (and RFS fields) have only their thermal harpoon pointing away from the object.

A small problem may occur with source elements. The usual convention is:

6th convention: The harpoons of bonds attached to one-port SE and SF elements always point away from the object.

BGers are sometimes inclined to denote a power drain (e.g. the gravitational force acting on a mechanical body) by a source element with reverse power convention, i.e.:

```              mg
|----\ SE: mg
v
```

However, this becomes ambiguous, as soon as we allow two-port source elements, i.e., as soon as we wish to model the "other side of the wall," i.e., the side where the power comes from or goes to. In this case, we use a convention similar to that relating to TF and GY elements:

7th Convention: The two bonds attached to a two-port SE or SF element have opposite positive power directions, i.e., one of the harpoons points at the object, whereas the other harpoon points away from the object. The harpoon pointing away from the object denotes the secondary side of the SE or SF element, i.e., the side where the source law is computed. The primary side simply denotes the power continuity, and can have both causalities.

In order to be consistent with the 7th convention, power drains should be depicted as follows:

```              -mg
|\---- SE: -mg
v
```
I hope this helps! Maybe, you could create in your dissertation a complete list of semantic conventions associated with BGs ?

Best regards