[From Bill Powers (940808.1845 MDT)]
Martin Taylor (940808.1200 MDT) --
RE: one-way control
If the reference signal is excitatory and the perceptual signal
inhibitory, you can't get that function. In that arrangement, the
error signal is limited to a maximum value of R.
Right. Glad I wasn't totally confused. Better you than me.
Then of course if R=0, there will never be any error. A most
uninteresting and unuseful control system. ... There might be reasons
for such systems in nature, but I can't think of one.
Well, I think that the spinal reflexes (which are organized that way,
although not entirely obviously) are both interesting and useful. In the
third installment of my Byte articles, I used that kind of system to
show how three non-collinear muscles could create independent force
control in x and y, provided there was a non-zero tone control system
that controlled the sum of the effects of muscle tension. 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.
Here is a Simcon 4.5 simulation of two opposed systems. Note that the
outputs take over just when they are needed, and turn off when not
needed. No special arrangements required; it just falls out of the
design. The cv is initialized to -10 to avoid a large starting transient
that shrinks the scale.
Note that BOTH halves of the control system use excitatory reference
signals and inhibitory perceptual signals. Setting both reference inputs
to zero turns this system completely off. All modeled neural signals are
one-way. A disturbance occurs in the middle of the run.
The BYTE article extends this principle to three non-opposing outputs
used by three control systems.
···
=======================================================================
title TWO OPPOSED ONE-WAY CONTROL SYSTEMS as one control system
time 10.0 0.005
#control systems
#right side
e1a comparator r1 p1 # e1a = r1 - p1
e1 limit e1a 0.0 10000 # positive error signals only
o1a summator e1 40.0 e2 -40.0 # effects of both errors, with gain
o1 limit o1a 0.0 10000 # output signal one-way, too
p1 limit cv 0.0 10000 # perceptual signal is one-way
#left side
e2a comparator r2 p2 # e2a = r2 - p2
e2 limit e2a 0.0 10000 # positive error signals only
o2a summator e2 40.0 e1 -40.0 # effects of both errors, with gain
o2 limit o2a 0.0 10000 # output signal one-way, too
p2i summator cv -1.0 # invert perception on left side
p2 limit p2i 0.0 10000 # perceptual signal is one-way
# environment
cva summator o1 1.0 o2 -1.0 d 1.0 # o1 acts to right, o2 to left
cv amplifier cva -10.0 1.0 1.0 # time constant for stability
d generator puls 3.0 6.0 10.0 # pulse disturbance applied to cv
# source of reference signals
r1 generator ramp 0.0 10.0 10.0 #
r2 summator r1 -1.0 tone 1.0 # balanced output to r2
tone const 10.0
# directives
group cv e1a e1 o1a o1 p1
group cv e2a e2 o2a o2 p2 p2i
group cva cv
print o1 o2 cv e1a e2a d
plot
An interesting quotation, picked up from Howard Margolis (1993),
_Paradigms and Barriers_, Chicago: U of Chicago Press. p. 201:
[Bohr] never trusted a purely formal or mathematical argument. "No,
no" he would say, "You are not thinking, you are just being logical."
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. In the design that works, each error signal affects itself
through all available feedback paths, as in the BYTE article. So the
left and right output variables are each affected by both error signals
with opposite signs to preserve negative feedback. This is the actual
arrangement in the spinal cord. The same arrangement will work at any
level.
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Best,
Bill P.