[From Rick Marken (930831.0830)]
Michael Fehling (930830 12:42 PM PDT) --
So, please provide me with the most precise description you
can of (a) what will count as a controlled variable in theoretical terms, (b)
the corresponding operational test for such, and (c) any other factors that
Ah. I see you're calling and raising?
This is actually a VERY GOOD question. As an answer I will copy the steps
of "The Test" as they were described in the final (4th) article in Powers'
Byte series entitled "The Nature of Robots" (Byte, June-Sept, 1979):
" 1. Define a variable.
2. Apply various amounts and directions of disturbances directly to the
3. Predict the expected effects of the disturbances, assuming no control
system is acting.
4. Measure the actual effect of the disturbances.
5. If the actual effect is essentially the same as the predicted effect,stop.
No control system is found.
6. If the actual effect is markedly smaller than the predicted effect, look
the cause of the opposition to the disturbance and determine that it results
from systematic variations in some other variable. If such a cause is found,
may be associated with the output of a control system.
7. Look for a means of _sensing_ the controlled variable. If none is found,
stop: no control system is proven to exist.
8. If a means of sensing is found, block it, so the variable cannot be sensed.
If control is _not_ lost, the sensor is not the right one. If no such sensor
found, stop: no control system is proven to exist.
9. If all steps of the test are passed, the variable is a controlled variable,
state is its reference level and the control system has been identified."
Now some commentary by me:
Step 1 says "come up with a hypothesis about what variable is controlled".
This hypothesis is just a guess based on obvervation. Step 1 will almost
certainly be carried out iteratively since one's first guess about what is
controlled is likely to be wrong (or, at least, tangentially related to the
variable; for example, my first guess about Beaver's would have been
that they are controlling the rate of flow of the river; they are actually
controlling the SOUND of the flow of the water). It is also important
to remember that the hypothesized controlled variable must be a VARIABLE.
So it makes no sense to guess that a driver is controlling the "car". The
word "car" refers to the a collection of variables -- shapes, sounds,
engine types, etc. The driver might be controlling the shape of the front
bumber, the sound of the engine, the position of the car on the road, the
number of cylinders, etc. All these are potential controlled variables
they are VARIABLES. Controlled variables need not be continuous, however.
Logical variables, for example, have only two legitimate values but they can
be controlled (kept at one or the other of those values). For example, it is
possible to control the truth value of the variable "there is a Porshe in my
driveway"; the variable is true if there is a Porshe in my driveway and false
if there is not.
Step two just means "do things that should influence the state of the hypo-
thetical controlled variable". If you guess that the Beaver is controlling
rate of flow of the river than do things to change the rate of flow. If you
guess that I am controlling for having "Porshe in my driveway = true" then
add or subtract a Porshe from my driveway. Things that would influence
the state of hypothetical controlled variables are called disturbances.
Opening a sluce gate to increase the rate of river flow is a disturbance;
putting a Porshe in my driveway is a disturbance.
The "application of disturbance" step is the "business end" of The Test.
Caveats of good experimental procedure apply. For example, disturbances
should (if possible) be applied ONLY to the hypothetical controlled variable;
one should avoid "confounding" the effect of the disturbance on other
variables. "Confounding", as its name implies, can confuse the results of
The Test. For example, opening the sluce to increase water flow also
the SOUND of the water flow. Beavers will compensate for this disturbance --
by building a dam -- but NOT (it turns out) because they are controlling water
flow but because they are controlling SOUND.
Another important consideration in the "application of disturbance" is TIME
SCALE. Disturbances should not be applied (and removed) faster than the
time scale on which they can be delt with by the control system. This
time scale problem has created enormous confusion in the motor control
literature where the return of a variable to a steady state after an impulse
disturbance is counted as an example of control. This has led to the
of "point attractors" with reference states for controlled variables. The
simplest example of this is a mass-spring system. When a mass on a spring
is pulled down and then released the mass returns (after some oscillation) to
it's original position. This looks like disturbance resistance -- the
of the mass seems to be a controlled variable. Some researchers have
(seriously) compared the equilibrating behavior of the mass on a spring to
the behavior of a control system. The problem here is _time scale_ -- the
disturbance was applied and removed too quickly. If the disturbance were
continuous the researchers would see that there is no control at all; a
continuous downward pull on the mass changes its position in exactly the
way predicted by Newton's laws (see Step 3). A good rule of thumb for
applying disturbances is to apply them relatively gradually and keep them
in effect for some time while monitoring the hypothetical controlled variable.
There are other ways to perform the test that are not included in the
steps described above. These involve comparison of the behavior of
a control model to that of an actual control system. An example of the
use of modelling to do The Test is described in a paper that starts on
p. 47 of Powers "Living Control Systems". This version of The Test
reveals the (perhaps not terribly exciting) fact that rats in a "shock
avoidance" experiment are controlling the _probability_ of getting a
shock rather than the _rate_ at which they are shocked. I also describe a
version of The Test based on modelling on pp. 200 - 202 of "Mind
Readings". I found (by accident) that people are controlling a Cartesian
rather than a polar representation of the two dimensional position of
the cursor in a tracking task.
The Test is the basic methodology for the study of living control
systems. There's a lot to it (for example, I haven't delt with problems
that arise from the fact that reference levels for controlled variables
can CHANGE continuously). The Test is not as mechanical and easy to apply
as Bill's step by step description in the Byte article might suggest; these
steps are an idealization. The toughest part of The Test (for me) is Step 1 --
coming up with hypotheses about what variable(s) MIGHT be under control.
This is the step that takes creativity, imagination and just plain smarts --
ie. it's the part that involves science at its best.