VS: Behavioural Illusion (was Re: What is revolutionary about PCT?)

[EetuP]

[Eetu Pikkarainen 2017-10-12]

Yes Fred, I agree. We have here both direct (immediate) and indirect (mediated) cause-effect relationships or causations. Also we have linear and circular causations. And in addition
we still have combined effects (and multiple consequences) or branching mediated causal chains.

One immediate causation could be thought to take no time. But in causal chain these causations happen one after another. So the lengthier the chain, the more time it takes.

That’s why the equations in
[From Rick Marken (2017.10.11.1640)] seems to depict a strange or specific kind of a situation where both reference and disturbance are stable. Then the error must be zero. It seems a happy situation for the controller, but not very
realistic. If the disturbance is changing like in life it often seems to be then if at the moment t0 the disturbance changes X units then some moments later - after the causal chain has taken place - the output can change approximately -x units, but at that
time the disturbance has already changed x + y units from the original value. So in changes control is in principal always late because causal chains take time - even if they were circular.

Probably I have understood something wrong?

···

Eetu

–

Please, regard all my statements as questions,

no matter how they are formulated.

Lähettäjä: Fred Nickols [mailto:fred@nickols.us]
Lähetetty: 12. lokakuutata 2017 15:20
Vastaanottaja: csgnet@lists.illinois.edu
Aihe: RE: Behavioural Illusion (was Re: What is revolutionary about PCT?)

[From Fred Nickols (2017.10.12.0815)]

I don’t agree with Rick when he says there is no causal path from disturbance to output.

Consider a car in a crosswind. The crosswind is a disturbance to the position of the car. The driver compensates for that; in other words, he corrects.

Now, are output and disturbance directly connected? No. The path from disturbance to output is via the driver’s perceptions, reference, comparison of the two and any resultant error.

Perhaps thinking in terms of direct cause-effect relationships and indirect cause-effect relationships might help.

Fred Nickols

From: Bruce Abbott [mailto:bbabbott@frontier.com]
Sent: Thursday, October 12, 2017 7:40 AM
To: csgnet@lists.illinois.edu
Subject: RE: Behavioural Illusion (was Re: What is revolutionary about PCT?)

[From Bruce Abbott (2017.10.12.0740 EDT)]

Rick Marken (2017.10.11.1608) –

Bruce Abbott (2017.10.09.2240 EDT)

Rick Marken (2017.10.09.1030) –

RM: The relationship between disturbance and output is not causal. The causal link from disturbance to output is “erased” by the simultaneous effect of the output on the controlled variable. The actual cause of the output in a closed loop
is the controlled variable itself. But this causal connection is difficult to see – especially when control is good --because the effect of the CV on output is quickly reduced by the output itself.

BA: Let’s trace the events once around the loop. (I assume a constant reference value.) The disturbance causes the controlled variable (CV) to change, which causes
the sensed input to change, which causes the perceptual signal to change, which causes the error signal to change, which causes the output to change which causes the feedback output to change in a direction opposite to that of the disturbance. All this takes
place in the time it takes these causes to propagate around the loop. At no point is the series of causal links between disturbance and output broken.

RM: The problem is in the step where the disturbance causes the CV to change. It’s actually the simultaneous effect of the disturbance and output that causes the CV to change That makes all the difference. And it’s why
you will not find a causal path through the organism from disturbance to output.

Best

Rick

BA: Perhaps I was not clear. My paragraph above (“Let’s trace . . .) begins with the following initial condition: perception = reference. Therefore the initial error is zero and the output is zero. So the “problem�
you describe does not exist on this first sequence of cause and effect around the loop, because there is not yet any effect of the feedback on the CV.

BA: I dealt with what happens on subsequent trips around the loop in the subsequent paragraphs (reproduced below). By responding only to the first paragraph, you left the misleading impression that I had not done so
and that this omission was a fatal flaw in my reasoning.

BA: The feedback from previous circuits around the loop does not erase the effect of the disturbance, even if on this particular trip around the loop the feedback
happens to equal the effect of the disturbance on the CV. To see that this is so, I present the simple case in which the error and output are currently zero and a disturbance is suddenly applied to the CV and held constant. This disturbance causes the input
to change, which causes the perceptual signal to change, which causes the error signal to change to some nonzero value. This error is multiplied by the output gain. In our digital simulations, if the resulting high output were to be applied full force to
the feedback function, the huge level of feedback would drive the system into destructive oscillation. This is because time is being left out of the calculations, as if the output could be applied instantaneously at full force. But real systems change over
some finite period of time. To bring time into the computations, we impose a “leaky bucket� integration to the output, which causes the output to rise as a negative exponential function over iterations. Only a small portion of the total change in output
that would otherwise be produced by the error signal is allowed to appear, and this then determines the level of feedback that is applied to the CV on this cycle around the loop.

BA: On the next cycle around the loop, the effect of the disturbance on the CV is now being opposed by a only small fraction of what the feedback would otherwise
have been. The same level of disturbance is present, but its effect on the CV is now being partly compensated for by the feedback. The smaller net effect on the CV causes a smaller change in input value from its initial value, which causes a smaller change
in perceptual signal, which causes a smaller error signal. Due to the leaky integrator nature of the output function, the output rises by a small portion of the difference between its present and final levels until feedback and disturbance effects on the
CV are equal and opposite. It takes a few trips around the loop for the full effect of the disturbance on the feedback level to appear, nevertheless, it is the disturbance that is the ultimate cause of the change in feedback.

BA: Only a portion of the change in output that would be necessary to fully compensate for the disturbance can occur on each iteration, but this merely spreads
the cause-effect chain across several iterations of the loop. It in no way “erases� that effect. The effect of the disturbance is taken apart, transmitted in small packets across several iterations, where their effects are in effect reassembled by the output
function to produce the full level of compensatory feedback.

BA: By the way, analog systems do not normally require a leaky integrator as changes in physical variables naturally require time to complete.

Bruce

[EetuP]

[Eetu Pikkarainen 2017-10-13]

[From Bruce Abbott (2017.10.12.1100 EDT)]

(…)

BA: Eetu, it would be helpful if you would copy the line indicating the post to which you are responding, as I have done above.

EP: Sorry, it was [From Fred Nickols (2017.10.12.0815)]. I thought it was self-evident because the original message was after my text, but now I saw that the two minus characters in my signature
did cut the end away in your reply. I removed those characters now.

BA: You must distinguish equations that describe the steady state from those that characterize the system’s dynamics. If I impose a constant disturbance, the variables around the loop will
change, eventually reaching steady-state values and remaining there so long as nothing further changes. Steady-state equations tell you what those ending values will be. Dynamic equations indicate how the variables will change over the course of time during
the transition.

EP: OK, Now I understand this. Those steady-state equations alone can then tell nothing about causality.

BA: By the way, when both the reference and disturbance are stable and the disturbance is not zero, then the proportional control systems we normally assume when discussing control systems
will not have a zero error . In the steady state, the feedback to the controlled variable must be approximately equal and opposite to the effect of the disturbance on the CV. If the error were zero, the system would produce zero output. What actually
happens is that the system stabilizes at an error level that produces just enough output to nearly (but not quite) cancel the effect of the disturbance. How much error will be required in order to produce this level of output depends on the loop gain – the
higher thee loop gain, the smaller the residual error will be. Proportional controllers are called such because their output is proportional to the level of error.

BA: Integral controllers, in contrast, produce output that is proportional to the
sum of the error across iterations of the loop. The error will grow so long as the effect of the disturbance on the CV has not been completely offset by the feedback, and thus so will the output and the level of feedback. But as the error summates,
the output (and thus the feedback) increases until the effects of disturbance and feedback are equal and opposite. At that point the error will be zero but in the case of a non-zero disturbance, the output will be non-zero.

EP: That is interesting. Can you give some examples of proportional controllers? Seemingly I can at the moment think only about integral controllers where remaining error causes the strengthening of the output. If I want
to move an object to a place x and it will not go there I will push more and more until it is there (in the tolerance zone) and the error is zero or then I change my reference and also then the error will be zero. If I want to lift an object (say with my hand)
to a certain height (say to the level of my eyes) and there is a disturbance (weight of the object or some invisible cord or spring connected between it and the floor) which stops the rising in the half way. That would produce a steady state but only after
the strength of my output had risen to the maximum I can produce. And then I would probably give in and change my reference. But if I have enough power to reach my goal, then when the object is in a level of my eyes there will be a steady state where the output
and disturbance are in the balance and the error is zero. Here the zero error does not stop the output – that would lead immeddiately to falling of the object and rising of the error again. Only the increasing of the output will be stopped.

Eetu

Please, regard all my statements as questions,

no matter how they are formulated.

[MartinT]

[Eetu
Pikkarainen 2017-10-13]

        [From Bruce Abbott

(2017.10.12.1100 EDT)]

(…)

[EP]

···

Seemingly I can at the moment think
only about integral controllers where remaining error causes
the strengthening of the output. If I want to move an object
to a place x and it will not go there I will push more and
more until it is there (in the tolerance zone) and the error
is zero