[From Rick Marken (970302.1700 PST)]
Bruce Abbott (970302.1515 EST)--
I am _not_ asserting that _any_ observable _behavior_ occurs
open-loop, but only that certain components of the system
either are themselves open-loop systems, or can be modeled as
such for certain analytic purposes.
The problem is that you can't determine the open-loop characteristics of
these "open-loop" systems while they are part of a closed loop.
When we write the system equations that define a control system we write
separate "open loop" equations for the functional relationships in the
loop. For example, one functional relationship in the loop is
p = f(q.i); perception is a function of sensory input, q.i. This
equation looks like an "open-loop" relationship between sensory input
and perception -- the very relationship studied by psychophysicists--
but it is part of a closed loop.
The relationship p = f(q.i), for example, exists in a closed loop system
where it is _simultaneously_ true that p = f(q.i) and
q.i = g(r-p)+d. In this situation it is impossible to _manipulate_
q.i as an _independent variable_ in order to determine the nature
of the relationship, f(), between q.i and p. This is because q.i
is also a dependent variable -- indeed, it is ultimately dependent
on itself via the closed loop. If the feedback in the closed loop is
negative then q.i is a _controlled variable_ making it mathematically
and _physically_ impossible to treat q.i as an indenpedent variable.
The only way to determine the open-loop charateristics of functional
relationships that are part of a closed loop system is by _modeling_ the
system and seeing how well the behavior of model (based on guesses
about the open-loop characteritics of the functional relationships in
the loop) matches observed behavior. Of cousre,
it is necessary to know what variable the system is controlling
(that is, it is necessary to know what aspect of the environment
corresponds to q.i) before one can start modeling the open loop
characteristics of the functional relationships in the control loop.
An this is the step that is almost always skipped in conventional
approaches to determining "open loop" system characteristics.
Well, the first organisms evolved out of the muck...A few
million years later some of these evolved into behaviorists,
and now a few of them are beginning to take those first steps
toward evolving into control theorists. Evolution takes a long
time -- one has to be patient!
Maybe evolution is heating up again;-)
Here's a quick progress report on my comparision of MCT and PCT
using proportional and integral control. I ran into problems because I
had to do my taxes (well, at least I started them) and I can't seem to
turn off the "arrow cursor" that shows up in the Java display. This
means that when the cursor disappears the arrow cursor is still visible.
I couldn't find any method that turns off the arrow cursor; I'll check
with some experts at work tommorrow. But I did do the experiment anyway,
using an envelope taped to the screen to hide the arrow cursor. The
result was just what we expected. When the cursor becomes invisible in
the proportional control case, I can still keep the RMS error reasonably
low (only about 3 or 4 times what it is in the "closed loop" case)
probably because I can match my perception of mouse (hand) movements to
my perception of target movements. However, when the cursor becomes
invisible in the integral control case things quickly go to hell (to wax
technical); RMS error quickly becomes 50
to 100 times larger than what it is in the closed loop case.
The results of this little experiment lead me to believe that any
observed ability to control open-loop is probably an artifact; a
side effect of a person's ability to control another perception
(like the perception of the relationnship between hand and target
movement) that is highly correlated with the perception that is
supposedly being controlled "open loop".