[Hans Blom, 950920]
(Rick Marken (950919.1330))
On a control system needing to "know" what it "does"
Please read your own (or Bill's code) of the "classical"
PCT-controller with its "leaky integrator". In all of these
controllers I find a statement that starts with u := u + ...
This means that the controller, in computing its new u, uses
(and therefore must know!) its previous u.
The PCT model doesn't need a precise measure of its own output and
neither does your model. This can be seen by adding a random noise
term to the outputs of both models.
That does not contradict what I said. The "knowledge" of a control
system of its previous actions need not be precise. In that you are
correct. Control systems are remarkably robust against disturbances
of their perceptions. I consider its knowledge of its previous action
as a kind of "internal" perception, coming from some sort of memory.
Memory contents can degrade, just like an integrator can leak. And a
controller needs to be able to cope with that.
It can, as you have observed. If an action isn't quite adequate, you
can correct things again almost immediately, even with another action
that also isn't quite adequate. It is the continuing correction pro-
cess that gets things done, not its precision.
The fact that your model works without a precise measure of output
leads me to suspect (along with Bill Powers (950919.0530 MDT)) that
your method is simply a limiting case of a general control method.
Model-based control IS a general control method, with a huge body of
literature supporting it. It is an approach, however, that neither
Bill nor you seem to be familiar with. But it's a worthwhile one, I
think, because it can "explain" psychological issues like anticipat-
ion and expectation.
In other words, itUs a control of perception model; itUs just not
clear yet how it relates to the PCT algorithm.
It is NOT a "control of perception" model. It is a "processing of
perception" or "knowledge extraction" model, where the results of the
processing represent what the control system "knows" about the world,
and where that knowledge is subsequently used for control. This is an
intermediate step that is lacking in the PCT model. Or rather is not
explicit in the PCT model, where a designer is needed to "tune" the
"perceptual input functions". It models LEARNING rather than control;
that such a system can control is almost incidental on its having
learned.
Although your model is a control model, it doesn't seem to control
(in simple situations) like a person does. That is, it doesnUt deal
with square wave disturbances the way a human controller (and the
PCT model) does.
It does very well on square wave disturbances, except on the moments
where the steps occur. That is because this simple model isn't
complex enough to be able to predict when those moments will occur.
But do also compare the performance on square wave REFERENCE LEVEL
changes and see how "zero" response delays come about in the model-
based controller, but not in the PCT controller.
Greetings,
Hans