Hi, Martin --
With reservations, I can see how you get range/resolution for the
perceptual signal. You could estimate resolution from the
mismatch between the smooth model's controlled quantity and the
real person's. But how do you get it for the disturbing variable?
In the experiments, we could say that the disturbance resolution
is 1 pixel, because that's the minimum amount the target can move
on the screen. Is that r for the disturbance, with the range
being the actual peak-to-peak value? But what about the case of a
person controlling a physical variable like the position of a car
in its lane? The disturbances include things like wind velocity,
which would not seem to have any minimum r. Disturbing variables
are defined in the physical model of the environment, and as far
as I can see nearly all macroscopic disturbances have an r that
might as well be zero.
In your discussion of maximum effective gain, you introduce the
noise component in the perceptual signal. I agree, that is what
limits the gain for the control system, if there are no other
noise sources prior to or in the comparator. But why should that
gain depend on the presence of a disturbing variable, or on the
frequency distribution of the disturbing variable? What matters
is the noise generated in the loop, not what is generated outside
the loop. Even setting the disturbance to zero, you still have
the noise in the loop to contend with, and the maximum gain is
set by that noise (dynamical considerations aside). If you crank
the gain up too high, the system will start producing a large
noisy output. Adding a disturbance won't change that, will it?.
Best,
Bill