Book Review

CSGnet Archive CSG2000
21

[From Rick Marken (2002.12.04.1120)]

Bill Powers (2002.12.03.1048 MST)–
For those who have not seen some of the correspondence, the subject
of Bode plots comes up in Chapter 14 of the book, purporting to show that
subjects actually change their internal organization when the nature of
the external part of the loop (that we call the environmental feedback
function) is changed. The Bode plot shows the frequency response of a control
system given sine-wave variations in its reference signal, or else sine-wave
disturbances. In the simplest application, the frequency of the sine wave
is gradually raised, while a record is kept of the amplitude and the phase
of the output (as Flach defines the controlled variable) relative to the
input (the reference signal, as Flach defines input). For human beings
the data have to be obtained indirectly using randomized inputs, but the
results should be the same.

The connection between the control handle and the cursor is selected
from three choices: a direct, proportional connection, a single integration,
and a double integration. The experimental results for these conditions
are shown in Chapter 14, Figs. 14-3, 14-4, and 14-5, The conclusion is
that the human being changes internally so as to make the overall system
function look like a first-order lag in all three cases, or as we call
it in PCT, a leaky integrator. The data certainly show that this effect
occurs, no doubt about that.

I have been able to come up with a two-level model that reproduces these
effects without any changes in model parameters, a fact that calls
into doubt all conclusions about “adaptation” drawn from these experimental
findings. It is possible to set up a two-level control system controlling
velocity at the lower level and position at the higher level, which shows
the same effects as in Ch. 14 when the external part of the loop is changed
from a proportional to an integral to a double integral response. Bode
plots show the same phase behavior and the same 20-db per decade frequency
rolloffs. While this does not prove that no adaptation at all takes place,
it does show that the major part of the data can be accounted for without
assuming any adaptation (that is, any changes in the model’s parameter
values from one case to another).

I think it’s worth pointing out that what you have produced (I think) is
basically a frequency domain analog of the “behavioral illusion”.
In the behavioral illusion, a change in the feedback function connecting
system output to controlled variable is seen as a change in the time domain
functional relationship between disturbance and output. The “illusion”
is taking the change in the functional relationship between disturbance
and output as a reflection of a change in the characteristics of the organism
– when , in fact, it is actually a reflection of the change in the
environmental connection between organism and controlled variable.
The Bode plots are simply a frequency domain representation of the functional
relationship between disturbance and output. When the feedback function
(the connection between control handle and cursor) changes from proportional
to single integration to double integration, there are changes in disturbance-output
function in the frequency domain. Your model shows that, if a control system
can maintain control of the cursor in all feedback function conditions
(which is what your two level system can do), one will see frequency
domain changes in the disturbance-output function when there are changes
in the feedback function with no adaptive changes in the organization of
the control systems themselves (as in the case of the behavioral illusion).
I believe J&F miss this possibility (that what they are seeing as
adaptation may be a behavioral illusion) because of their failure to clearly
identify a controlled variable. Although they are clearly talking about
“controlled variables” when they talk about “output”, failure to distinguish
“actions” (PCT outputs) from results (PCT controlled variables) made it
impossible for them to see how the functional relationship between output
(PCT actions) and disturbances depends on the nature of the functional
relationship between outputs (PCT actions) and controlled variables (PCT
results, J&F outputs). In other words, I think it all comes down
(once again) to a failure to properly map control system variables to actual
behavioral variables and the resulting failure to identify the unique
and important status of the variable that behavioral scientists always
fail to identify: the controlled variable.

Best regards

Rick

···

–

Richard S. Marken, Ph.D.

The RAND Corporation

PO Box 2138

1700 Main Street

Santa Monica, CA 90407-2138

Tel: 310-393-0411 x7971

Fax: 310-451-7018

E-mail: rmarken@rand.org

22

[From Bill Williams UMKC 4 December 2002 3:00 PM CST]

Bill Powers [ 3 December 1048 MST] wrote:

"... a stall condition is defined as the velocity ..." and "THe angle of
attack... depends on airspeed [ and etc....] "

In level, unaccelerated flight, given all the etc, there is a dependable
relation between airspeed and the occurance of a stall. But, this doesn't
mean that a stall can't occur at a much higher airspeed, or that a stall
must occur at a slower airspeed when maneuvering. The only dependable
relationship which generates a stall is the angle of attack.

This relationship can be exploited to generate exotic maneuvers. Start with
a climbing vertical roll. As the airspeed falls off gradually convert the
roll into an inverted spiral. If you time it correctly a very gentle spin
can be generated at an extremely low airspeed with the aircraft inverted
but the direction of the spin initially being upward. The spin selected can
be either in the conventional orrientation by pulling back and down or
inverted by pushing forward and up and pressing full rudder. It makes for
an interesting exercise because the inertial forces are for short period
larger than the airodynamic forces and the aircraft tumbles in random
directions.

from a control theory perspective, what's wrong with defining aircraft
operations in terms of airspeed is that the airspeed is in many
circumstances an intergral over time of terms like the aircrafts attitude
and its angle of attack. So, its easy to get into oscilations by attempting
to control airspeed-- its like inserting a delay line or another integrator
into a control loop. Better control is possible by paying attention first
to power settings, attitude and the angle of attack. If I had control of
the situation, I'd do initial flight instruction with an airspeed
indicator. THen their wouldn't be any, or at least much less of an occasion
for the confusion generated by the term "stall speed."

best

Bill Williams