Simcon simulation of Martin's setup

[From Bill Powers (930331.1430 MST)]

Martin Taylor (930331) --

Rick is right. Simulate your proposed setup with Simcon and see
what happens. It is not what you say happens. The signal X does
not reproduce the waveform of the disturbance. However, the
variable q = p - o does reproduce it.

Here is a Simcon program to try:

title reconstructing disturbance from perceptual signal

···

#
time 10.0 0.05
t generator puls 2.0 6.0 10.0
y generator puls 4.0 8.0 -5.0
d summator t 1.0 y 1.0 # composite disturbance waveform
p summator o 1.0 d 1.0 # p = o + d
r const 5.0 # ref signal constant at 5.0
e summator r 1.0 p -1.0 # error signal
o integrator 0.0 e 1.0 # output signal
v summator r 1.0 p -1.0 # Mystery function
x integrator 0.0 v 1.0 # Mystery function, X
q summator p 1.0 o -1.0
group p e o
print d o x q # show disturbance, output, X, q
plot

I leave it as an exercise for the student to explain why p - o is
not the same as O(r - p). Hint: feedback has something to do with
it.
--------------------------------------------------------------
Best,

Bill P.

[Martin Taylor 930401 12:00]
(Bill Powers 930331.1430)

I leave it as an exercise for the student to explain why p - o is
not the same as O(r - p). Hint: feedback has something to do with
it.

It would be kind of extraordinary, a real coincidence in the literal
sense, if p-o turned out to have much relation with O(r-p). In fact,
I think it could only happen (intuition mode here) with output gain = 1
and zero time lag, unless the disturbance waveform were carefully crafted.

But this has no relation to the proposed experiment that we will indeed
simulate. Why do you mention it?

Martin