Hello, all --
My model of the compensatory tracking experiment has an error in it that
invalidates the Bode plots it presents for compensatory tracking (pursuit
tracking is OK). The force disturbance was erroneously added into the
statement that defines the force ouput (the variable C in Flach's figures).
It should have been put where it is in the procedure below, in the
computation of acceleration (1st line of code). The corrected procedure is
appended. The behavior of the model isn't affected, but the variables used
to obtain the Bode plot are incorrect.
The result is that when the error is fixed, the same Bode plot is seen for
all three compensatory-tracking conditions: proportional, integral, and
double integral. A .jpg screen snapshot is appended.
So what conclusions can we draw? There are choices.
(a) The mistake in the analytical solution may not have been a mistake,
(b) The final analytical solution, if carried out as I suggested, would
show that the response is independent of the plant characteristics when k1
and k2 are large.
(c) Even if (b) is true, the experimental situation used by McReuer may not
have been the same as assumed here (force-independent disturbance of load).
(d) We have to try a positional disturbance that is inserted after the
plant. I'll get onto that.
Pursuant to (d), we need an exact description of the McRuer and Jex
experiment cited in Jagacinski and Flach, "Control theory for humans". The
manner of applying a disturbance is evidently critical.
Best,
Bill P.
(Attachment hierar5.jpg is missing)