[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.