[Hans Blom, 950921]
(Rick Marken (950920.1030))
I finally figured out why Hans' model based controller works.
Congratulations. Do you like it?
It works because it is essentially the same as the PCT model that
Bill Powers posted.
That is how we usually understand things: by comparing them to some-
thing that we already know, i.e. by linking them to and subsequently
extending or refining our "internal model". Fine.
The only difference is that Hans' model adds a "noise" term to the
error signal; this noise term improves control (relative to the
basic control model) if ...
I wouldn't call something that systematically improves things
"noise", not even "intelligent noise".
It is "noise" in the sense that it is an independent addition to the
error signal (u-x) that drives the integrated output (u).
Independent? No! Extra. Your equation shows that it is not indepen-
dent. If it were, it would not be able to improve things and hence be
"noise". It isn't that.
If the actual disturbance is smooth over time, this noise term
improves control by adding what usually turns out to be an
appropriate amount to the output integral; if the disturbance is not
smooth (if, for example, it is a square wave), this noise term
degrades control (relative to that produced by the basic PCT model).
Have you verified this last assertion? It is incorrect, except under
very exceptional conditions (the discovery of which I posed as a
problem to you :-). Have you found those yet? What kinds of square
wave did you test with? How often do you estimate that the conditions
that make the basic PCT model better exist in practice?
So Hans' model is fundamentally the same as the PCT model; it
controls a perceptual variable, x, keeping it close to the reference
signal value despite disturbances.
If that makes it "fundamentally the same" to you, fine.
Although Hans' model based addition to the PCT model can improve
control under certain circumstances, there is no evidence that this
addition is needed to explain anything about the behavior of living
"Certain circumstances" only? Not generally? There IS no evidence? Or
do YOU have no evidence? If there is no evidence, let's try to obtain
some. They must be there, in my opinion, which I base on my under-
standing of the evolutionary process: if something that gains a lot
in terms of better control is easy to achieve by a small increment in
structural complexity, it will probably have been discovered by
... Hans model can be used to illustrate the basic point of PCT,
viz. when a system (living or artifactual) controls, what it
controls is a perceptual representation of a variable or variables
in its environment.
I would formulate this differently. What a controller produces as an
output/action will produce an effect/perception SOMEWHEN IN THE
FUTURE, if only fractions of a second away. Knowing -- having an
estimate of -- what this FUTURE effect/perception will be, will in
most cases improve control. It is this control improving prediction
that I have shown a simple mechanism for.
And remember that the example that I used in my "challenge control-
ler" was the bare minimum that I could think of to demonstrate both
mechanism and effect.