A Question about Control

[From Fred Nickols (2006.11.08.0942 EST)] --

I've got a question about control. First a lead-in:

If output (i.e., behavior) occurs only in the presence of error - a
discrepancy between perceptual input and reference condition - it would seem
to me that error controls (or at least occasions) output.

If error is determined by comparing reference condition with perceptual
input, it would seem to me that this comparison of reference condition and
perceptual input controls error.

If perceptual input is an analogue of the controlled condition, then any
changes in the controlled condition result in changes in perceptual input.
In other words, the controlled condition determines or controls perceptual
input.

The controlled condition reflects the integral of the effects of output and
disturbances. Thus, this integral determines or controls the controlled
condition.

What controls the reference condition? In the hierarchical arrangement, my
understanding is that higher-levels supply reference signals to lower-levels
and that, at the highest level, reference signals are intrinsic. In that
scheme, everything is more or less built-in. But I can set goals, can't I?
Aren't those reference signals? Or, are my goals simply articulations of
lower-level reference signals that owe to some kind of discrepancy in some
intrinsic reference signal? For example, did my goal of becoming a
consultant reflect some built-in desire/goal/want/need/reference condition
and if so, what might it have been?

Regards,

Fred Nickols
www.nickols.us
nickols@att.net

Regards,

Fred Nickols
"Assistance at a Distance"
nickols@att.net
www.nickols.us

[From Bill Powers (2006.11.08.0905 MST)]

Fred Nickols (2006.11.08.0942 EST) –

I’ve got a question about
control. First a lead-in:

If output (i.e., behavior) occurs only in the presence of error - a

discrepancy between perceptual input and reference condition - it would
seem

to me that error controls (or at least occasions)
output.

Controlling something and causing or affecting it are two different
things. I have said that A controls B if, for every disturbance tending
to alter B, A changes its effect on B so as to counteract the
disturbance. I now see that that’s not correct, because the error signal
could be said to control the output of the system under that definition.
Any disturbance tending to change the output quantity would in fact
result in a change in the error signal, the change that counteracts the
disturbance.
While I still like the original definition, something has to be done to
distinguish “control” from “cause” or
“influence.” The error signal has a direct effect on the output
quantity via the output function. That is a simple open-loop effect: a
change in the error signal causes a change in the output quantity under
normal conditions (the output function doesn’t change). That means
that if there is a change in the error signal, the output quantity will
change in a predetermined way. That remains true whether the rest of the
loop is there or not.
Control always depends on the existence of an entire negative feedback
loop. It also necessarily implies that disturbances applied anywhere in
the loop are resisted by the part of the loop just prior to the part that
is disturbed. For example, the immediate effect of a sudden change in the
perceptual signal is a sudden change in the error signal, because e = r -
p. However, because of the negative feedback that is present, this will
be followed by a change in the input quantity, and therefore a change in
the perceptual signal back toward its undisturbed value. So we can say
that the perceptual signal is controlled by the whole negative feedback
loop. This will be true of all the variables in the loop: the perceptual
signal, error signal, output quantity, and input quantity. If any one of
those variables is directly disturbed, feedback effects will result in a
change of the just-prior variable in the loop that tends strongly to
cancel the effect of the disturbance. Just to make this clearer, if
something changes the gain of the output function and thus disturbs the
value of the output quantity, the just-prior variable, the error signal,
will change so as to counteract this effect on the output
quantity.
We have to distinguish three terms: CONTROL, DETERMINE, and INFLUENCE.
“Control” is defined in terms of resistance to disturbances
(anywhere in the loop) due to feedback effects.
“Determine” means that one variable has an exclusive effect on
another variable: that is, the state of one variable guarantees that
another variable will be in some corresponding state.
“Influence” (or “affect”) means that one variable has
non-exclusive effects on another variable. In other words, the affected
variable is influenced by two or more variables, so one of the
influencing variables cannot determine the state of the affected
variable. To predict the state of the affected variable, one must know
the values of all the variables that influence it.
In a control system with any loop gain greater than zero, we can say that
the reference signal and the disturbing variable influence the states of
all the variables in the loop. We have to say “influence”
rather than “determine” because with small loop gains, both the
reference signal and the disturbing variable contribute significantly to
changes in each of the loop variables. Knowing the value of only the
reference signal or only the disturbing variable is not sufficient to
allow calculating the state of any loop variable (p, e, qo, or
qi).
As the loop gain becomes larger so control gets better and better, we
approach the case in which the reference signal determines the
state of the input quantity and the perceptual signal, while the
disturbing variable merely influences the output quantity while
losing most of its influence on the input quantity and perceptual
signal.
So rather than saying that the reference signal entering a good control
system controls the input quantity, we should say that it
determines the input quantity. Because both the reference signal
and the disturbing variable affect the output quantity, we should say
only that they both influence or affect or contribute
to
the output quantity. The control system as a whole controls all
the variables in the loop in the sense that a disturbance of any of them
by variables outside the loop will result in an action that opposes the
effect of the disturbing variable.

Therefore the following two of your conclusions, while true under my
initial definition of control, no longer hold given the elaborations
above:

If error is determined by
comparing reference condition with perceptual

input, it would seem to me that this comparison of reference condition
and

perceptual input controls error.

If perceptual input is an analogue of the controlled condition, then
any

changes in the controlled condition result in changes in perceptual
input.

In other words, the controlled condition determines or controls
perceptual

input.

We have now made a distinction between control and
determine.

There’s a terminology misunderstanding in the following:

The controlled condition
reflects the integral of the effects of output and

disturbances. Thus, this integral determines or controls the
controlled

condition.

As used in PCT, the term “integral” means “time
integral”, the cumulative sum of a variable over time. You are using
the term in the sense of a sum of simultaneously-existing variables, as
in A = B + C, or in your case qi = qo + d. If you simply substitute sum
for integral you will be understood correctly.

In a good control system, qo + d is close to zero, so neither the output
quantity nor the disturbance has any significant influence on the input
quantity or the perception. The disturbing variable, being outside the
loop, does not control anything. Neither qo nor d controls or determines
the controlled condition; at best, they influence it. Because they
influence it oppositely and almost equally, the amount of influence is
far less than it would be if the negative feedback didn’t exist.

What controls the reference
condition? In the hierarchical arrangement, my

understanding is that higher-levels supply reference signals to
lower-levels

and that, at the highest level, reference signals are intrinsic. In
that

scheme, everything is more or less built-in. But I can set goals,
can’t I?

Yes, and in that case the “I” refers to a higher system than
the one for which a goal is being set. A fixed goal at a high level does
not mean static behavior at lower levels (as Bandura seems to think).
Suppose I have the fixed goal of improving my education. To be achieving
this goal perfectly, I must be acting continuously, musn’t I?
You may be asking about setting arbitrary goals, independently of
what any higher-order existing systems are doing. That is probably
possible, but it involves the concepts of awareness and volition, as well
as reorganization. If you change a goal arbitrarily, without regard to
the higher-order reasons for its current setting, you are very likely to
arouse opposition from those higher systems. For example, if your
higher-order goal is to drive from home to a movie theater, one effect of
this control process will be to vary the reference-angle for the system
using the steering wheel as you navigate toward the theater. There is
nothing to prevent you from voluntarily and arbitrarily altering the
reference-angle for the steering wheel, but if you do that you will
create a considerable error in the going-to-the-theater control system,
not to mention the intermediate systems concerned with avoiding
collisions and staying on the road. Your voluntary change will probably
be immediately overridden by the existing higher-order control
systems.

This is another example of why the Method of Levels came into being. You
can make arbitrary changes in reference signals – reorganize the output
functions creating them – at the level where a problem exists, but if
you do, they are likely to be canceled or circumvented by the
higher-order systems that set those reference signals in the first place.
Somehow you have to change the locus of reorganization to the systems at
higher levels that set those reference signals. Reorganizing at the
higher levels will not arouse the same kind of opposition to the
changes.

Aren’t those reference signals?
Or, are my goals simply articulations of

lower-level reference signals that owe to some kind of discrepancy in
some

intrinsic reference signal? For example, did my goal of becoming
a

consultant reflect some built-in desire/goal/want/need/reference
condition

and if so, what might it have been?

I have no idea, but if you’ll stretch out on this couch and start looking
at your background thoughts, I’ll be happy to explore the subject with
you.

Best,

Bill P.

[Martin Taylor 2006.11.08.23.17]

[From Fred Nickols (2006.11.08.0942 EST)] --

I've got a question about control. First a lead-in:

If output (i.e., behavior) occurs only in the presence of error - a
discrepancy between perceptual input and reference condition -

Bill P. has made a long response to this post, but I think he didn't make the point that this assertion is fundamentally wrong.

In an effective control system, output counters disturbance so as to maintain error near zero. If we were to believe you assertion that output is zero when error is zero, how would it then be countering an ongoing disturbance?

The correct statement is that if the error is zero, behaviour will not change. That includes behaviour such as always buying the paper on your way to work (if that keeps the error of some control system near zero). If you didn't go buy the paper, your error in that control system would probably be high.

Not behaving is no way to maintain zero error.

Martin

[From Fred Nickols (2006.11.09.0520 EST)] --

[Martin Taylor 2006.11.08.23.17]

>[From Fred Nickols (2006.11.08.0942 EST)] --
>
>I've got a question about control. First a lead-in:
>
>If output (i.e., behavior) occurs only in the presence of error - a
>discrepancy between perceptual input and reference condition -

Bill P. has made a long response to this post, but I think he didn't
make the point that this assertion is fundamentally wrong.

In an effective control system, output counters disturbance so as to
maintain error near zero. If we were to believe you assertion that
output is zero when error is zero, how would it then be countering an
ongoing disturbance?

What if the "disturbance" is discrete instead of continuous or ongoing?

I thought zero error was a null position, one where no action is required.
I can see how an ongoing disturbance would require ongoing action and I
would say I was hunting or hovering about the point of correspondence
(between reference condition and perceptual signal) but that seems to me to
be a situation in which the error signal itself is fluctuating as a result
of an ongoing disturbance. I could be "tracking" that error quite closely
so that any error stays minimal but if the disturbance ceases, is there any
need for action?

Let's say I walk over to a chair and sit down. Presumably, I had a goal
state or reference condition of being seated (for whatever reason). In any
event, I seat myself. No further "seating" behavior is required. Any
"I-am-not-seated" error signal was reduced as a result of sitting down and
is now zero (or close to it).

The correct statement is that if the error is zero, behaviour will
not change. That includes behaviour such as always buying the paper
on your way to work (if that keeps the error of some control system
near zero). If you didn't go buy the paper, your error in that
control system would probably be high.

Not behaving is no way to maintain zero error.

Is that true if there is no disturbance?

Regards,

Fred Nickols
nickols@att.net

[Martin Taylor 2006.11.09.10.27]

[From Fred Nickols (2006.11.09.0520 EST)] --

[Martin Taylor 2006.11.08.23.17]

>[From Fred Nickols (2006.11.08.0942 EST)] --

> >
> >If output (i.e., behavior) occurs only in the presence of error - a
> >discrepancy between perceptual input and reference condition -
>

In an effective control system, output counters disturbance so as to
maintain error near zero. If we were to believe you assertion that
output is zero when error is zero, how would it then be countering an
ongoing disturbance?

What if the "disturbance" is discrete instead of continuous or ongoing?

Do you mean an impulse, such as being hit by a falling rock? No behaviour can do much to counter an impulse disturbance. It's not really worth considering impulse disturbances as such.

However, the conditions that lead to the impulse may themselves constitute ongoing disturbances. To continue the example, one probably does not have a reference for seeing a rock falling towards one, and may well act to bring about a perception that the rock is falling elsewhere (the action being to jump out of the way). But the sight of the falling rock is an ongoing disturbance, isn't it?

Likewise, after being knocked down by the rock, one is lying on the ground, whereas the reference is to be standing upright. Again, the disturbance effect is ongoing. We can only control against disturbance effects that last long enough to allow our action processes to have their effect. That could be less than a second for fast motor actions, or years for political disturbances.

I thought zero error was a null position, one where no action is required.

Change that to "no change of action" and you have it.

I can see how an ongoing disturbance would require ongoing action and I
would say I was hunting or hovering about the point of correspondence
(between reference condition and perceptual signal) but that seems to me to
be a situation in which the error signal itself is fluctuating as a result
of an ongoing disturbance.

You seem to be making the presupposition that the disturbance is fluctuating, and that the disturbance's fluctuation is the only reason for action. That is an unwarranted assertion.

Let's take a very simple situation, the rubber band demo. The knot is lying on the target on the table, both experimenter and subject having their fingers in the loop but letting their ends lie slack. In respect of the rubber band, the subject is not acting.

Now the experimenter starts a steady pull, with a prescribed force of say 4 ounces. The subject gets the knot back on the target (comes to zero error) by pulling with 4 ounces in the opposite direction. He acts to do so.

The experimenter keeps up the 4 ounce pull, very steadily and with no fluctuation. The subject keeps the knot on target (maintains zero error). Is the subject now acting, or has she stopped acting because the error is zero and stays zero?

Let's say I walk over to a chair and sit down. Presumably, I had a goal
state or reference condition of being seated (for whatever reason). In any
event, I seat myself. No further "seating" behavior is required. Any
"I-am-not-seated" error signal was reduced as a result of sitting down and
is now zero (or close to it).

You don't mention the disturbance that caused you not to be seated in the first place. Is that disturbance still present? If so, what is keeping you seated?

> Not behaving is no way to maintain zero error.

Is that true if there is no disturbance?

If, in any of the multitude of control loops in a person, there is a moment of zero disturbance and at the same time the error is zero, then the output will also be zero. If you call a moment of zero output "not behaving", that's fine.

However, in PCT discussions, a distinction is usually made between producing an output to oppose disturbances, that output being zero for the monent (behaving), and producing zero output because disturbances are not being opposed (not behaving). Inasmuch as an external observer can't see the error value, it's hard to tell the difference from outside without applying "The Test" -- introducing a deliberate disturbance to the variable whose perception might or might not be being controlled.

So, my preference would be to say that someone is behaving while remaining still if there is reason to believe that a push would be resisted, but not behaving if there is reason to believe a push would make them fall over and not get up again.

Martin

[From Bill Powers (2006.11.09.0835 MST)]

Fred Nickols (2006.11.09.0520 EST) --

I thought zero error was a null position, one where no action is required.
I can see how an ongoing disturbance would require ongoing action and I
would say I was hunting or hovering about the point of correspondence
(between reference condition and perceptual signal) but that seems to me to
be a situation in which the error signal itself is fluctuating as a result
of an ongoing disturbance.

"Hunting" and "hovering" are misconceptions of how a control system works -- only borderline-unstable control systems (or control systems containing significant internal noise generators) behave that way.

Hardly any control systems maintain a state of exactly zero error. Since the only thing that can produce output from a control system is the error signal, there must be some error if there is to be any output. As you intuit, disturbances produce error and thus output; the main question is "How much error is required to generate enough output to keep the error from getting any larger?" That usually depends on the gain in the output function since the other gains in the loop are usually much smaller. If the output function is very sensitive to error signals, then only a small error is enough to produce maxiumum ouput, and when smaller outputs suffice, the errors are even smaller. But they are never zero.

External disturbances are not the only things that produce error, however. If you raise the reference signal to some positive amount, there must be output to bring the controlled variable to the required magnitude. That means there must be some error to produce that output, even when there are no independent external disturbances acting. In some cases, such as moving a mass to a new reference position, output is required only during the transition to a new state. But if there is any energy cost in maintaining that new state, then the output cannot be zero, and therefore the error cannot be zero.

If the reference signal and all disturbances are exactly zero, then the output of the control system can be zero and the error signal will be zero. That happens so seldom that we are safe in ignoring that case. Mathematically speaking, the probability of all signals and outputs being zero is -- zero.

The "integrating" type of control system (where the term refers to time integration, not just addition) is said to be able to produce nonzero values of output when the error signal is zero. This is almost, but not quite, true, because there are no perfect integrators (especially not in a nervous system or muscle). A perfect integrator would produce a continuously increasing output as long as any amount of error was present. The output would stop increasing only when the error was exactly zero. But real integrators are not perfect; if the error is zero, the output will begin slowly declining. In order to maintain the output exactly cancelling the disturbance, in equilibrium with it, some amount of error must exist to compensate for the "leakage" in the integrator. An integrating output function should be thought of as a high-gain amplifier with a slowing factor that prevents rapid changes in output, but which allows changes to go on until equilibrium is reached.

Let's say I walk over to a chair and sit down. Presumably, I had a goal
state or reference condition of being seated (for whatever reason). In any
event, I seat myself. No further "seating" behavior is required. Any
"I-am-not-seated" error signal was reduced as a result of sitting down and
is now zero (or close to it).

This is a good example of an integrating control system.The goal state is to be "seated in the chair." The error is that your current position is far from the chair. The error signal produces not just a steady output position proportional to the error, but a continuing change in position; this change continues as long as there is error, and slows down as zero error approaches. It will come exactly to zero only when the error is exactly zero. Strictly speaking, we know that the error is not quite zero, but it is close enough to bring the output(s) into equilibrium with whatever disturbances are still acting, so no further change occurs.

A lot of the difficulties that arise in talking about control systems come from the common tendency to speak qualitatively when quantitative matters are discussed. Speaking qualitatively, we can say that control systems maintain a state of zero error. That may be close enough for government work, but it's not close enough for correct understanding. In fact, you can tell by looking at the diagram of a control system that if the error were really zero, there would be nothing to produce output, or maintain the output that already exists. If you realize that maintaining any amount of output requires at least a little error, then the paradoxes disappear. Only in a few very rare cases can we say that an output can continue literally without any error to produce it. While there is little difference in a qualitative discussion between saying there is zero error and saying there is a tiny amount of error, there is a huge difference in understanding.

Best,

Bill P.

[From Fred Nickols (2006.11.09.1207 EST)] --

[Martin Taylor 2006.11.09.10.27]

Thanks for taking the time to respond, Martin. The cut and paste and insert
comments is getting tedious and confusing so let's start with a fresh
example.

Maybe I've got the wrong picture of "disturbance." Let's use a driving the
car example. A gust of wind would to me be a temporary, discrete
disturbance of finite duration. I would counter it and continue on my way.
However, owing to "looseness" in the connections between the steering wheel
and the wheel (not to mention my "pumping" the gas pedal which drives my
wife nuts), the actions of other drivers, gravity's effects on the car as I
go around curves, etc, etc, I perceive the car as "drifting" from my
reference condition for it; namely, squarely in the center of the lane and
so I make minor corrections. As you said earlier, if my control of the
car's position is good, the error signal "approaches" zero (and as I would
have said years ago, the position of my car "hunts" around the point of
correspondence, which is between the lane lines - visible or imagined).

So, in that "dynamic" case of driving the car, I can see how error signal
approaches but might never or only momentarily actually reach zero and how
behavior is continuing also.

But, what if I'm doing something less "dynamic" or at least of much shorter
duration. Suppose I'm emptying the dishwasher. I have reference conditions
for where those clean dishes should go and, usually, I'm pretty good at
getting them where they're supposed to be. The placement of a single plate
or glass is of much shorter duration than the larger task of emptying the
dishwasher but, in both cases, once done I'm done. There is no more
"emptying the dishwasher" behavior. This is true even if our two little
dogs are underfoot and posing a "disturbance" to my dishwasher emptying.

Is there some kind of start and stop or beginning and end aspect that is
absent from my thinking or do I simply have it all gummed up?

Regards,

Fred Nickols
nickols@att.net

[From Bill Powers (2006.11.09. 1030 MST)]

Bruce Nevin (2006.11.08.21:19 EST) --

You know that we do not perceive our reference signals as such. So what
are these things that we verbalize as our goals?

One source of confusion at the levels at which you are talking about
"goals" is that what we say our goals are is always subject to post-hoc
rationalization. Another is that words make tidy patterns of their own
and sometimes we think the map is the territory.

While I agree with a lot of what you're saying, I think you're overly pessimistic about our ability to identify reference signals. Remember that imagination, according to PCT, is the perception of reference signals instead of the perceptual signals that would normally result. While we may not say to ourselves,"That is a reference signal," this doesn't prevents us from knowing that we would like to experience in reality what we are at the moment only imagining.

If we are acquainted with PCT, we can also identify reference signals, indirectly, in terms of what feels wrong and right. There are some perceptions that lead to feeling afraid, or angry, or discouraged, and while we may not have access to the reference signal via imagination, we can still recognize that these feeling signify the presence of error, and that error signifies a reference condition different from what we are experiencing. Such ideas can steer us to the regions where the reference condition might be identified.

I do agree that verbalizations about reference signals tend to be as much theoretical as factual. We like to make up stories that give the appearance of understanding, but plausibility is only a distant cousin of truth.

In the Method of Levels, identification of reference conditions often occurs, and is verbalized, but the verbalizations are descriptive rather than explanatory. In fact, if the "explorer" says "I guess I must be angry about that," you know that the client is not reporting on what has just been observed, but is theorizing instead of observing. When the client says "I really feel like throttling that son of a bitch," you can be more sure that the words are descriptive and closely related to some reference signal(s). When that happens I think there are good chances for identifying reference conditions that actually exist in present time.

Best,

Bill P.

[From Bill Powers (2006.11.09.1058 MST)]

Fred Nickols (2006.11.09.1207 EST) –

So, in that “dynamic”
case of driving the car, I can see how error signal

approaches but might never or only momentarily actually reach zero and
how

behavior is continuing also.

Martin Taylor tells you that if you think of error as changing the
behavior, you will have it. He is talking about (perfect) integral
control. Some behavior works that way, some doesn’t. Some individuals
will use integral control where others will use proportional control and
other will use rate-of-change control. There is no “average”
way of doing these things; you have to look at each individual.
Note, too, that some environments provide integral control while the
controller can remain proportional. Controlling the position of a
free-floating mass (like an astronaut moving a piece of equipment around
on the space station) involves double integral control: a force
that is integrated to produce velocity, and a velocity that is integrated
to produce position. The velocity and position controllers can both use
proportional output functions, because the environment is doing the
integrations.

Just remember that most of the qualitative things we say about control
and control systems are approximations; whenever there’s confusion, is
has to be resolved by looking at the situation quantitatively.

Best,

Bill P.

[Martin Taylor 2006.11.09.14.00]

[From Bill Powers (2006.11.09.1058 MST)]

Fred Nickols (2006.11.09.1207 EST) --

So, in that "dynamic" case of driving the car, I can see how error signal
approaches but might never or only momentarily actually reach zero and how
behavior is continuing also.

Martin Taylor tells you that if you think of error as _changing_ the behavior, you will have it. He is talking about (perfect) integral control.

Actually, I'm not talking about any particular kind of control. I'm just pointing out to Fred that if the disturbance persists at a constant level, then so must the output, if error is to stay near zero. The process for getting from error value to output value is irrelevant.

Martin

[From Bill Powers (2006.11.09.1445 MST)]

Martin Taylor 2006.11.09.14.00 --

Actually, I'm not talking about any particular kind of control. I'm just pointing out to Fred that if the disturbance persists at a constant level, then so must the output, if error is to stay near zero. The process for getting from error value to output value is irrelevant.

Right. But it makes a considerable difference whether you say the error is "near zero" or just plain "zero." I've seen many people flounder while trying to explain how there can be any output if the error is zero, or how (the next time around) the error could be zero if there's no output because the error is zero.

Best,

Bill P.