[From Bill Powers (931111.0830 MST)]
Hans Blom (931111) --
Your description of the tracking experiment is a little
confusing. Are you visualizing a target that moves horizontally
while it traces out a sine or triangle wave vertically? That
would imply a two-dimensional control task, and would be
difficult to implement on a computer screen because the screen is
only 25 cm wide.
Although we normally present our tracking results as a time plot
of amplitude or error, the display on the screen does not look
like such a plot. What the participant sees is a short target
line that is moving normal to its length, either vertically or
horizontally. If the target line is oriented vertically, it would
move right and left in a smooth but irregular (or in the case you
suggest, regular) pattern, slowing, speeding up, reversing, and
so forth, but always remaining on the same horizontal path and
staying on the screen. The cursor is another such short line,
moved by the control handle in a similar path parallel to the
target path. For the horizontal movement case, we see
target
\
> <--- Target motion --->
> < --- cursor motion --->
These movements do not leave any traces on the screen, nor can
the future positions of the target be seen. From your description
The subject will see something like a dotted line at first.
... I infer that you are visualizing a path shown on the screen,
first as a continuous curve and then in the form of shorter and
shorter segments of the curve spaced farther and farther apart.
This, in effect, shows the subject the future states of the
target, allowing high-order systems to adjust the curvature of
cursor-handle movement to pass through future points. While this
is an interesting mode of control (path control), it introduces
complexities that I don't know how to model yet.
To modify our current experiments along the lines you suggest, we
would simply blank out the target line and show it periodically.
Toward the end of the sequence you suggest, the participant would
see the target blink at one position, then a while later in a
different position, and so on. I would predict a deterioration in
control as soon as the samples were spaced farther apart in time
than a few tenths of a cycle, and that by the time the samples
were several cycles apart control would be very poor and even
nonexistent.
I will be happy to program the experiment you describe as soon as
a current project reaches a stage where I can leave it for a
while. I would need a clearer picture of the experimental
display, however -- what you visualize taking place on the
screen.
Even better, of course, would be for you to design and run the
experiment yourself. I hope you realize that if you haven't
actually done experiments like these with human subjects, your
statements about how people would behave under various
circumstances would be considerably weakened. They would be
reduced from observations to predictions from a theory that has
not yet been supported by experiment.
You say
Design a controller (feedback, feed- forward or combination of
both), CSG-style or not, that performs equally well when whole
periods or more of the signal are missing. And not only equally
well on ONE sine wave signal with a fixed period and a fixed a
mplitude, but on ANY periodic signal that a human subject can
easily handle after his one minute's training
You assume here that there ARE periodic signals that a human
being could "easily handle after one minute's training." This
implies that you have already done this experiment. If you have,
why not just report the results?
I suspect, if you'll forgive my skepticism, that any
"experiments" that have been done have been mathematical, not
using real human subjects. In a mathematical treatment it's easy
to make the simulated control system produce a regular waveform
that is predictable thousands of cycles into the future, and that
can be made to follow another waveform that is equally precise
and predictable. When you use 80-bit floating point calculations,
the simulated universe is ideally regular.
But in the real experiment, whether you intend it or not,
disturbances will be present, if only those arising from noise in
the neural control system. The subject will not be able to
maintain an accurate sine or triangle wave from cycle to cycle
when the target is invisible. The phase and frequency of the
open-loop waveforms as well as the amplitudes will vary
unintendedly. The phase errors will be cumulative all during the
time that the target cannot be seen. Frequency errors will appear
as cumulative phase errors, too. The zero-point of the handle
movements will drift.
You note these defects, but seem to dismiss them. In fact, you
suggest cheating a little:
Amplitude noise is, I think, evaluated fairly by a correlation
function, phase noise is not. By some "time warping" of the
time scale a much better fit is possible.
Warping of the time scale can, of course, remove phase errors
very nicely, if you don't want to admit that phase errors
occurred. Tom Bourbon has data to show that open-loop phase
errors do not average to zero. You would just have to keep
warping and warping without limit to make the data fit the
theory.
As to visual evaluation, my crition is simple: the experimental
points should stay close to the theoretical points over
experiments of any length.
As I say, I will program and run these experiments if you will
give me exact specifications (assuming I can meet them). I'll
send you the program so you can run it, too.
···
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Martin Taylor (931110.1800) --
One point we should be very clear on: the fact that open-loop
control might suffice in a given circumstance does NOT indicate
that the behaving system is operating open-loop. The open-loop
design is a solution looking for a problem. Even the Lang-Ham
design is a hypothetical one which may not be needed at all.
Before we spend a lot of time trying to devise practical open-
loop models, or closed-loop models with feedforward, we should do
the required experiments and see if there is anything left for
them to explain. We can set up a situation that looks as though
it HAS to be open-loop, but if the critical variable proves
resistant to disturbance, we have misconceived what is going on.
FIRST we must show that the outcome can be disturbed without
producing an opposing change in the action of the system. Only
then can we be sure that we're dealing with an open-loop
phenomenon, and only then does it make sense to try to devise a
suitable open-loop model.
------------------------
As a personal anecdote, one of my last actions before going to
bed each night is to put the cats into the kitchen and turn off
the light. I then walk three or four paces and put my hand on
the door handle, usually with no apparent error or hesitation.
I do not have any apparent sensory cues to the location of the
handle relative to my hand between the time I turn off the
light and the time my hand closes on it.
How do you know you walk "three or four" "paces?" Is that not
sensory information about your position? I suggest that you also
have sensory information about your direction of walking and
about the position of your reaching hand. It's just not visual
information.
I also remind you of the elapsed time involved here. It can't be
more than 2 or 3 seconds. If you stop and count to 20 after
turning the light off, I'll bet you make more errors. And if you
rotate your body through 360 degrees in the dark before taking
those two or three strides, I'll bet you miss by even more. These
"mental models" we speak of might be nothing more than an
integrator with a long -- but not very long -- time constant.
----------------------------
Walking in a blacked-out room requires imagining one's
position in the room, on the basis of a model. The inputs to
this model are now totally kinesthetic.
And do not, so far as I can see, provide by themselves adequate
input to the relation perception that is being brought near its
reference.
Right. The fact is that the models are inadequate for good
control over any prolonged time. If you do some real experiments
with your ability to get around in the dark, I think you will
find the precision to be a lot less than you tend to remember. I,
too, can walk through a darkened bedroom and find the switch to
turn on the bedside lamp. But there is a pronounced statistical
spread amounting to six inches or a foot and sometimes three
feet, even though I am walking only about 12 feet around the foot
of the bed. I remember best the instances where my hand feels the
switch on the first try. But the other instances are just as
real, if not as memorable. And I make a lot of use of tactile
sensations and sound to update the model; all it takes is a touch
of my knee against the bed to correct the modeled position by a
foot or so. I aim for tactile landmarks before I try to put my
hand on the switch. The model of where I am is not just a visual
model. And it needs to be updated frequently to maintain any kind
of accuracy.
-----------------------------
I could find nothing in Bill's posting with which to disagree
(though I might, if pushed, I suppose-- thinking of the phrase
"Hans Blom to the contrary" in context of how I read Hans).
Thanks for the main clause. As to the parenthesized one, my full
statement was
It makes no difference whether the person is "paying
attention" to the feedback signals that are still operating
(Hans Blom to the contrary).
Hans had said
(Hans Blom, 931103)
Sometimes there is no feedback signal, either because it just
isn't there, or because you do not pay attention to it.
Perhaps I am misreading this sentence, but to me this implies
that attention is required to make a feedback signal operative in
a control system, and I disagree with that.
---------------------------------------------------------------
Best,
Bill P.