[From Bill Powers (930902.0630 MDT)]
Hans Blom (930902), Rick Marken (930901) --
I saw this one coming. The adaptive control discussion is running
aground on words. Hans is using "input" and "output" differently
from the way Rick is. In Hans' discussion, the "output" of the
"controlled system" (and the model) is what we call the
perceptual signal, represented by p (and pm), and the input to
the model is what we call the output quantity, "u" in Hans'
diagram or "qo" in ours. In the PCT model, the objective is to
make the signal p correspond to r. In the diagram Hans drew, the
objective is only to make something inside the controlled system
come to a state corresponding to r, and it is the designing
engineer's objective, not that of the system itself.
There are two stages in Hans' diagram. One is the stage of
adjusting the model so that its output pm behaves like the output
p of the controlled system, given any arbitrary input u common to
both. The other is adjusting the parameters of the control system
(arrow labelled "adjust") on the basis of the model's behavior,
or perhaps on the basis of the amount of correction of the
model's behavior required to make p correlate highly with pm.
In terms of the PCT model, the adaptive control model is
confusing, because it does NOT assume, as we PCTers always
assume, that the variable to be controlled is exactly the
variable represented by the feedback signal p. If p is an exact
proportional representation of the controlled variable, then
matching the model to the controlled system simply produces
another copy of p: pm = p at all times. This alone does not
provide any information about how the control system, on the left
(basic controller) should have its parameters adjusted: we are no
better off than we would be given only p.
This makes no sense from the standpoint of PCT, where we assume
that the behaving system (the "basic controller") has to
accomplish all adjustments by itself, and where we assume that
the objective is to make p follow r as exactly as possible. In
PCT, the "controlled system" is what we call the environmental
feedback function, the link from the output quantity ("u") to the
input quantity (not shown, hidden inside the "controlled system"
box somewhere). We assume that the perceptual signal p is
generated by an input function in the controllING system that
receives information about the controlled quantity and creates
the perceptual signal as some function of the variables
constituting that information. In Hans' diagram, there is no
input function -- it, too, is hidden inside the "controlled
system." Also, it exists partly in the engineer who designed this
system.
A PCTer might well wonder how an organism made of systems like
this could possibly know what it is controlling. The answer is
that that question is irrelevant to the engineer who uses Hans'
diagram, for the ENGINEER knows what is to be controlled inside
the controlled-system box. The perceptual signal p, to the
engineer, is just a feedback signal. It doesn't have to indicate
the state of the controlled variable; in fact its behavior can be
completely different from the behavior of the variable inside the
controlled system that the engineer is interested in controlling.
The "basic controller" is simply adjusted so that the difference
between the signal r and the signal p, which can be substantial,
produces an output u such that the variable of interest inside
the controlled system comes to the state that the engineer wants.
In several designs I have seen, a function is inserted between
the signal r and the basic controller, so that the effective
reference signal is different from the one that the user
manipulates, the difference being whatever is required,
statically or dynamically, to make the controlled variable,
buried inside the controlled system box, come to the desired
state in the desired way. To the engineer, the whole problem is
simply to make some variable inside the controlled system
correspond as closely as possible to the reference signal
manipulated by the user. Whatever is inside the "basic
controller" box does not have to contain any indication that this
desired condition has been reached. The engineer and the user
know that it has been reached.
I am not saying that a system designed as in Hans' diagram would
not work. It undoubtedly would, provided that certain kinds of
disturbances do not enter in the wrong places. But it would work
because there is an engineer present, who can select the kinds of
adjustments that are designed into the system, and alter them
until the desired result, adaptive control of a variable inside
the controlled system, is achieved. If the adjustments initially
designed into the system are the wrong ones, the system itself
can't do anything about them; it's the engineer who has to change
the design until the adaptive adjustments are the right ones.
This result can be achieved. But it can be achieved only because
the engineer is a control system and knows what result is to be
achieved and what to do when it isn't.
To translate this diagram into a PCT model, the first thing we
would have to do would be to make the controlled variable
explicit and pull out of the "controlled system" box the function
that generates the perceptual signal p. That function would
become part of the basic controller. That function would receive
information about the state of the controlled system and create a
signal exactly representing the controlled variable. From the
standpoint of the controlling system, of course, the input
function DEFINES the controlled variable. The state of the
controlled variable is EXACTLY the inverse input function of the
state of the perceptual signal. The controlling system controls
whatever aspect of the controlled system is represented by the
perceptual signal.
Notice what this input function does. It provides to the control
system the same information that the engineer must be using in
judging the state of the controlled variable.
Now, when the perceptual signal is compared with the reference
input, there is an indication inside the controlling system of
the discrepancy between the actual and desired states of the
controlled variable. There is no requirement for an external
observer who knows what either the actual or the desired state
is. Perfect control is now indicated by an error signal that is
always zero. The error signal itself, inside the controlling
system and not in its environment, now becomes the criterion that
could be used to drive adaptive changes that improve control.
Because the criterion is located inside the controlling system,
it is no longer necessary to have some external engineer present
with his or her own idea about what constitutes perfect control.
We have shown that a system which senses the time rate of change
of the square of the error signal, and adjusts the integration
factor of an integral control system randomly but at intervals
that decrease when the rate of change of squared error is
positive, will quite rapidly approach and maintain the state of
mimimum possible error signal. This requires an auxiliary system,
of course, but it is inside the controlling organism, not in its
environment, and it uses only information available to the
control system. This same principle should be able to achieve
optimal PID control as well, although we haven't demonstrated
that.
I think that Hans' diagram illustrates very clearly the
difference between the PCT approach and that of standard control
engineering. To the control engineer, the difference between
organism and environment is irrelevant; it's all one system, and
the engineer can change any part of it as necessary to achieve
the desired end result, a controlled variable in a desired state.
Organisms, of course, have no helpful engineers standing by to
adjust their manner of adaptation. All that organisms can know
about environments has to be carried in their perceptual signals;
there's no other route by which the states of external variables
or properties of external systems can be known. All that
organisms can know about the success of their control efforts is
contained in signals inside the organism, in particular error
signals. If models are involved, they must be constructed on the
basis of how signals act, not how the environment acts.
I think that control engineering could benefit from understanding
how organisms accomplish control. When you think of the problem
as it must appear to an organism, you see it differently, and
perhaps in a more direct and simple way. Engineers really have
TOO MUCH freedom in their design of control systems; they don't
have to distinguish between what they know and what the control
system knows. I suspect that being subject to the discipline of
working strictly from the standpoint of the controlling system
would lead to more organized designs -- it might even lead to
formal organizational design principles, which are remarkably
lacking in all the textbooks I've ever seen.
···
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Best,
Bill P.