[Martin Taylor 940809 17:00]
Bill Powers (940808.1845 MDT)
Aren't you
reinventing the wheel a bit? I pointed this out, gently, in the exchange
you quote, but apparently you didn't get it.
If you had intended criticism of my posting in the earlier exchange, I
certainly didn't get it. Apparently you did, but covered in words of
approbation, including mentioning that you had a demonstration of the
basic (pun intended) concept in your Byte article.
To reinvent something is to invent it as if it had not been invented before.
I hoped that I had been careful enough everywhere to credit you. Sorry if
not, and you felt that I was trying to steal some of your thunder. You had
asked for the math to be posted, and I felt it much easier and better to
do so from the earlier version than to waste time reconstructing it. And
to make matters clear to Bill Leach and others, I included what I had thought
to be your approving comments, to show that we were at least in agreement
on something. Apparently not, at least not any more. I don't know why, and
it disturbs me a little (in both the colloquial and the PCT sense).
What I thought you had been approving was the extension to N dimensions,
and the demonstration that the effective virtual control system's control
law was related to the derivative of the control law of the contributing
one-way systems (the difference between the derivatives, in the case of an
opposed colinear pair). If I remember, I had asked you whether that relation
had been demonstrated. You said that it was true, but did not provide the
proof. That was one thing I provided, and what I thought you were asking for
a couple of days ago.
···
==================
Here is a Simcon 4.5 simulation of two opposed systems.
I can't run Simcon, and I don't find it easy to decode by eye so that I
can build it into a Control Builder simulation (I thought Allan had made
the CB so that it imported Simcon files, but my copy crashed when I tried).
(I just checked the source code, and there is a primitive Simcon import
module, but it seems not to understand comments or "group" or, most
importantly, "limit," so it wouldn't have been much use even if it hadn't
crashed :-()
Maybe it is there, but I don't understand it--is the output in each side
related to the square of the error, or just the linear error? In the Byte
article, so far as I can see, it is the linear error, and when you oppose
two linear control systems, nothing happens to the CEV. Something seems
to be happening different from the setup we discussed in December. Is
it the result of the cross-connection of the error signals? Is that what
you mean by:
If it's any comfort, when I first set up the simulation I forgot the
cross-connections between the halves of the system, and got just a plain
old conflict.
One would get that, and no control, with linear opposed systems. With
square-law control, one would get conflict, too--that's what "tone" is,
isn't it? If the output integrator had a reasonably short time-constant,
it seems to me (without simulating it) that the outputs should stabilize
at a fixed level in maintaining their individual errors at the right
magnitude to bring the perception to the reference level that is the
average of the two individual reference levels.
In commenting on your Simcon illustration, you say:
Note that the
outputs take over just when they are needed, and turn off when not
needed.
Since I can't run the Simcon program, maybe you could suggest when one
of the opposed outputs might not be "needed." Surely the point of opposed
square-law systems is that they are both needed all the time? Do the feedback
paths using cross-over error connections lead to a situation in which only
one of the outputs is active at any one moment?
======================
... I forgot the cross-connections between the halves of the system, ...
This is a very interesting comment in its own right. Hitherto, as far as I
can remember, the error signal in an ECU has been said to be available ONLY
to its own output function. Error signals normally cannot affect any
other ECU. But here you specify a direct connection of error(1) to output(2)
and vice-versa. In the system you were contemplating when you said
[Bill Powers (931220.1120)]:
One can almost
visualize all the thousands of individual spinal control loops as
being usable to create fine subdivisions of effort vectors, with
no clearly preferred axes (except what the joints impose).
would you expect all of the thousands of individual error signals to be
cross-connected to all of the other outputs? This seems an awfully complicated
structure, but maybe it is so.
This is the actual
arrangement in the spinal cord. The same arrangement will work at any
level.
I'm not a physiologist, and can't comment; it would be helpful if some
of our physiological readers could shed light on whether these millions
of cross connections among the individual spinal control loops exist, and
how the positive and negative signs relate (are they ALL inhibitory, or
are the connections among control systems whose ouputs pull in much the
same direction additive?). But as far as I can see, at least in the
diagrams for the Byte article you didn't include any cross-connections
of the error signals.
Anyway, much food for thought, and I retract my comment about the
excitatory reference system being uninteresting. (I said "inhibitory"
in some kind of Freudian slip in my earlier response to Tom.)
Martin