[Martin Taylor 920721 18:30]
(Rick Marken 920720.1130)
Actually, what I found in the simulation is that two control systems,
one with the wrong connection to one envrionmental variable, DO blow
up. I took this to mean that there was no way to "hide" a "positive
feedback system" in the hierarchy, as Martin suggested.
Actually, I think they needn't blow up. I don't know whether my message in
response to your simulation result ever got distributed, but your result is
"intuitively" correct. If Z is the ECS with the bad connection, and Y affects
some variable alse affected by Z, then the fact of Y controlling will tend
to stabilize or "stiffen" that variable. Z will be acting more through any
overlapping variables, increasing the cotnribution by the one with the
positive feedback, and reducing Z's effective negative gain. If Y stiffens
enough the overlapping variables, then Z will go into positive feedback.
Whether this happens depends both on the gain of Y and the degree of overlap
between Y and Z. Of course, if Y overlaps on the variable with the positive
feedback, it will help Z to stabilize.
I think that there are parts of this situation that require a dynamic analysis
rather than the DC analysis Bill produced. And yes, Bill, the expressions
get horrendous. After getting Rick's result, I went through the algenbra
to get the result discussed above.
Martin