[Martin Taylor 940807 12:30]
Bill Leach 940807.01:50 EST
Without pulling your message out of archive...
Please do.
Martin, there HAS to be a reference value for each of the control loops
that results in NO control action.
Not if the PIFs don't saturate, which has been implicit in everything so far.
For each of the loops, if P>R (assuming error = P-R) or if P<R (assuming
error = R-P) there will be output. There is no possible setting of R in a
non-saturating system for which P<R (respectively P>R) for all values of P.
The control system cannot dictate to the environment what will disturb
the CEV and by how much. As we all know well, the control system cannot
even DETECT the disturbance, let alone limit it. (Just to stop Rick from
going to sleep, this is quite independent of saying that the control system
is informationally isolated from the disturbance).
Bottom line. For ANY non-saturating control system, one-way or two-way, it
is impossible to set a reference level such that there is no output for
all values of P.
If Ra and Rb are at maximum then no control action will occur (for your
example as I remember it). I admit that this assume that P is not able
to vary beyond the maximum values for the reference but I don't think
that such an assumption is taking too much leave.
The concept of "maximum" is unlikely to be the same as the concept of "zero,"
whether the system saturates or not.
"Maximum" is a applicable to a saturating system, and in that case, you
are quite right. But the discussion to date has considered only linear
and square-law outputs, with linear relationship between the CEV and P
(in other words a linear PIF). Furthermore, the original argument was that
if you set both reference signals to zero in an opposed one-way pair,
neither member of the pair would provide output for any P. Nothing was
said about differentially setting the two references to opposed maximum
values.
Pa and Pb CAN be the same signal IF and ONLY IF, the comparitor operation
for loop A and loop B are reversed.
Exactly as specified in my message that you don't want to reread.
The fact that the references can be set so that both loops are generating
output has nothing to do with the idea that those same references have to
have a setting that results in no output regardless of perception.
This statement is correct as it stands, since you say "the idea that." But
it is irrelevant, since there is no such setting for the references unless
the PIF saturates at some level between zero and the maximum setting for
the reference signal.
In any event, the control systems that I am
familiar with that do have a "don't care" mode achieve that mode by
reduction of loop gain to zero (that is the error signal is allowed to
become quite large - in fact maximum - with no control output generated).I gather that there is no evidence that biological systems have this
behaviour - that of setting gain to zero.
Why do you gather this? On what evidence? I would think it almost
inevitable that they do, if only because it is one way of avoiding
permanent conflict. To put it on a personal subjective level, have you
never adjusted something to(ward) a reference and left it, saying to
yourself "That's good enough"? That behaviour is what is meant by
setting gain to zero, and by a dead zone or "don't care" mode. Perceptual
values outside the dead zone still lead to output, though. I assume you
are not talking about simply switching the power off to the control system.
ยทยทยท
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Further in respect of:
Pa and Pb CAN be the same signal IF and ONLY IF, the comparitor operation
for loop A and loop B are reversed.
This point is correct, but it implies some special relationship between the
two pull-only loops of an opposed pair. I used it because it greatly
simplifies the discussion. In any practical case, PIFa and PIFb are
developed independently, and Pa is most unlikely to equal Pb. In fact,
Pa and Pb are unlikely to be colinear (by that, I mean that if they are
based on the same two sensory inputs x and y, then if Pa= ax + by and
Pb = cx+dy, it is unlikely that a/b = c/d). And it is even unlikely
that the two PIFs have exactly the same set of sensory inputs.
The normal situation is that there are lots of pull-only control systems
with PIFs based on sensory data from the "real" world. If there are several
that are affected by the position of an object C, the outputs of some may
increase in value when the object moves north, some when it moves southwest,
some when it moves NNE (or rather, when the projection of the object's
position on those directions increases). The opposition occurs between
a set of one-way ECUs whose PIFs project positively on the direction the
object moved and another set whose PIFs project positively on the opposite
direction. Imagine the rubber-band demo with three bands connected at the
knot:
A
>
>
/ \
/ \
B C
When a disturbance tries to move the knot eastward, A does nothing, B pulls
harder, and C pulls less strongly. When a disturbance pulls the knot
northward, A relaxes, and B and C pull harder. You can extend this to
a system of any number of bands connected at the knot, with the people
holding the other ends pulling in all sorts of directions.
The only link among the various ECUs is in the environment. In analyzing
this system, there is no need to consider reversing the sense of the
comparator when one is looking from the point of view of any individual
ECU. In the world, the pulls are opposed. In the ECU, all that happens
is that perceptions differ from references and output is generated.
Only an outside observer, applying "The Test" sees that the group controls
as if there were a linear control system acting in EVERY direction the knot
is disturbed. The linear control system doesn't exist in this setup. It
is an illusion. The FACT of linear control, though, is no illusion--only
the existence of the linear control system as an implementation of control.
The actual implementation is a whole bunch of square-law one-way control
systems.
I'm not sure when we went through all the algebra of this; perhaps a year
or 18 months ago. There's lots more, including some very interesting
effects when you have saturating one-way systems that are nearly colinear,
in arrays of same-directional ECUs arranged so that the zero point of one
PIF is near the saturation value of its neighbour.
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We haven't really explored such systems, at least not on CSG-L in the
time I've been on it (and so far as I remember not in Bill P's published
writings either). One thing they can do is to map intensity into place
representation and vice-versa, which might be a useful capability in
some control situations. There was a short discussion on the matter many
months ago, but the issue got dropped before being thoroughly studied.
And such arrays have not, so far as I know, been considered in conjunction
with the opposed pull-only systems that initiated this thread.
Martin