[From Bill Powers (930407.1130)]
I promise to quit after this one.
Here is the middle segment of an elaboration on the previous demo
of "information in the output."
time sum d qo sp sr
(all zero for 1st 3 sec)
3.000000 0.000000 0.000000 0.000000 0.000000
3.100000 0.666667 -82.069655 0.568273 0.000000
3.200000 1.500000 -141.249488 0.900032 0.000000
3.300000 2.333333 -150.591656 0.936003 0.000000
3.400000 3.166667 -134.448692 0.826247 0.000000
3.500000 4.000000 -110.705833 0.677098 0.000000
3.600000 4.833333 -88.620706 0.541584 0.000000
3.700000 5.666667 -71.150209 0.435400 0.000000
3.800000 6.500000 -58.141844 0.356538 0.000000
3.900000 7.333333 -48.519096 0.298132 0.000000
4.000000 8.166667 -41.256064 0.253930 0.000000
4.100000 9.000000 -35.619415 0.219532 0.000000
4.200000 9.833333 -31.130971 0.192077 0.000000
4.300000 10.666667 -27.481077 0.169710 0.000000
4.400000 11.500000 -24.462910 0.151187 0.000000
4.500000 12.333333 -21.932774 0.135640 0.000000
4.600000 13.166667 771.646168 16.566640 20.000000
4.700000 14.000000 -51.838003 20.388107 20.000000
4.800000 14.833333 -82.662249 20.514545 20.000000
4.900000 15.666667 -76.941349 20.476839 20.000000
5.000000 16.500000 -70.759663 20.438630 20.000000
5.100000 17.333333 -65.280101 20.404800 20.000000
5.200000 18.166667 -60.422758 20.374797 20.000000
5.300000 19.000000 -56.095886 20.348058 20.000000
5.400000 19.833333 -52.223891 20.324120 20.000000
5.500000 20.666667 -48.744358 20.302599 20.000000
5.600000 21.500000 -45.605351 20.283178 20.000000
5.700000 22.333333 -42.763350 20.265588 20.000000
5.800000 23.166667 -40.181643 20.249603 20.000000
5.900000 24.000000 -37.829081 20.235034 20.000000
6.000000 24.833333 -35.679079 20.221714 20.000000
6.100000 24.333333 36.391219 19.776806 20.000000
6.200000 23.500000 36.885087 19.768154 20.000000
6.300000 22.666667 39.064616 19.754417 20.000000
6.400000 21.833333 41.442973 19.739421 20.000000
6.500000 21.000000 44.042926 19.723024 20.000000
6.600000 20.166667 46.892587 19.705047 20.000000
6.700000 19.333333 50.024597 19.685283 20.000000
6.800000 18.500000 53.477046 19.663490 20.000000
6.900000 17.666667 57.294582 19.639385 20.000000
7.000000 16.833333 61.529798 19.612634 20.000000
7.100000 16.000000 66.244965 19.582840 20.000000
7.200000 15.166667 71.514216 19.549532 20.000000
7.300000 14.333333 77.426318 19.512145 20.000000
7.400000 13.500000 84.088220 19.469997 20.000000
7.500000 12.666667 91.629618 19.422263 20.000000
7.600000 11.833333 -789.176254 3.665245 0.000000
7.700000 11.000000 -27.711923 0.098478 0.000000
7.800000 10.166667 21.029568 -0.138267 0.000000
7.900000 9.333333 27.222049 -0.172418 0.000000
8.000000 8.500000 30.669891 -0.193863 0.000000
8.100000 7.666667 34.373408 -0.217348 0.000000
8.200000 6.833333 38.717600 -0.244967 0.000000
8.300000 6.000000 43.897116 -0.277932 0.000000
8.400000 5.166667 50.136426 -0.317683 0.000000
8.500000 4.333333 57.731556 -0.366125 0.000000
8.600000 3.500000 67.083289 -0.425842 0.000000
8.700000 2.666667 78.743374 -0.500398 0.000000
8.800000 1.833333 93.484300 -0.594791 0.000000
8.900000 1.000000 112.407386 -0.716161 0.000000
9.000000 0.166667 137.113832 -0.874908 0.000000
9.100000 0.000000 93.459806 -0.550665 0.000000
9.200000 0.000000 51.813973 -0.305288 0.000000
9.300000 0.000000 28.725586 -0.169251 0.000000
9.400000 0.000000 15.925421 -0.093832 0.000000
9.500000 0.000000 8.829029 -0.052021 0.000000
9.600000 0.000000 4.894800 -0.028840 0.000000
9.700000 0.000000 2.713670 -0.015989 0.000000
9.800000 0.000000 1.504454 -0.008864 0.000000
9.900000 0.000000 0.834067 -0.004914 0.000000
(etc to all zeros again)
Here is the simcon program:
title ECS with disturbance affecting feedback function
time 12.0 0.01 # duration 12 sec; dt 0.1 sec
qd1 generator ramp 3.0 6.0 25.0 # disturbance is a ramp
qd2 generator ramp 6.0 9.0 -25.0 # disturbance is a ramp
qd3 generator puls 6.0 9.0 25.0 # disturbance is a pulse
qsum summator qd1 1.0 qd2 1.0 qd3 1.0 # sum of disturbances
sr generator puls 4.5 7.5 20.0 # ref signal is pulse
qf1 integrator 0.0 qo 4.5 # qf1 = integral(output)
c1 const 5.0
c2 summator c1 1.0 qsum 1.0 # c1 = 5 + sum disturbances
qf2 mult c2 qf1 # qf2 = output*c1
qf summator qf2 0.0015 # qf = 0.0015*qf2
sp summator qd1 1.0 qd2 1.0 qd3 1.0 qf 1.0 # percept signal
se comparator sr sp # comparator
qo amplifier se 0.0 160.0 0.01 # output
group qo qf sp se c2 qf1 qf2
print qsum qo sp sr
plot 1.0 0.02 1.0 1.0 #plot to see what happens
I wrote a quickie program to copy every tenth data output line.
The actual time increment is 0.01 sec.
This is like the previous one, except that the sum of the
disturbances, a triangular wave, plus 5, multiplies the effect
that the output quantity has on the perception. The feedback
function thus includes an integrator as before, but now also
includes a multiplier so that the feedback effect varies from 5
to 30 and back down to 5 during the run. This is in addition to
having the three disturbances act directly on the input of the
control system.
Also, in the middle the reference signal sr jumps to 20 for a
while, then back down to 0.
In the numbers, you can see that the perceptual signal tracks the
changes in reference signal within a few percent of the reference
signal's maximum amplitude. But the behavior of the system's
output quantity has nothing to do with either the perceptual
signal or the disturbance. Note that the output is rising while
the total disturbance is rising, and also while the total
disturbance is falling. Note also that the output stays in about
the same range whether the reference signal and disturbance are
near zero or near 20.0.
Rick has been quite right all along -- or at least his argument
has been quite right (whether _Rick_ is right is a matter to vote
on in closed session).
Note that there is no CEV per se. The three disturbances plus the
effect of the output through the variable environmental feedback
function simply add together to produce the perceptual signal.
Yet this control system faithfully keeps its perceptual signal
matching the reference signal just as a good control system
should do.
This control system lives in an environment that not only
directly disturbs its perceptual signal in three independent
ways, but also rapidly changes the connection between its output
and the perceptual signal all during the run. Nevertheless ...
Best,
Bill P.