d, r. and q0

[From Bill Powers (2002.09.26.0425 MDT)]

Rick Marken (2002.09.25) --

I don't have your last post in front of me, since I'm on a different
computer right now. But you asked if I was comfortable with saying that the
steering wheel "caused" the car's path to deviate left and right. Now that
you ask, I have to say no. Causation is just the wrong language -- it
forces us into an either-or mode when we should be talking about how
variables depend on other variables. The steering wheel does not determine
deviations of the path of the car because there are other variables acting
at the same time which also affect the car's path: crosswinds, tilts of
roadbed, I don't have to go through the list again. You can't predict where
the car will end up just by measuring the steering wheel angle.

So while turning the steering wheel may have modestly reliable effects on
the car, our predictions of where the car will go will be increasingly
uncertain as disturbances become larger. And by the same token (this is
what it has taken me some time to put into words), disturbances may have
pretty reliable effects in producing the actions that oppose them (given a
control system), but these effects become increasingly uncertain as
variations in the reference signal become larger. In our analyses, we
typically assume the reference signal to be constant in order to show how
changes in disturbances relate to changes in actions. But in most real
cases, we have to allow for changes in the reference signal to be occurring
at the same time that the disturbance is varying. All we observe is the
composite effect of these two sources of variation; without knowing how
_both_ d and r are varying, we can account for only part of the variance of qo.

But the real answer to our problem is simpler than that. Consider
controlling the speed of a car. The action variable, qo, we could say is
the force with which the foot presses down on the accelerator. To bring the
car to a reference speed like 60 mph, we find we must press with some
amount of force which is determined by the feedback function that converts
a pressure on the pedal into a speed of the car. The reference speed we
have chosen determines the final speed, and that in turn determines the
required pressure according to the inverse of the feedback function. Of
course we don't need to calculate that inverse; we just keep increasing or
decreasing the foot pressure according to the difference between the
observed speed and the desired speed, and this results in bringing the
speed to the reference level. When that has been achieved, the foot
pressure, obviously, has become what is necessary to maintain that speed.
That pressure happens to correspond to the inverse feedback function of the
reference signal, but it isn't achieved by calculating that inverse.

Now let the car come to a slope and start going upward or downward. The
slope produces a force equal to the weight of the car times the sine of the
angle of ascent or descent, and the car starts to speed up or slow down.
The control system experiences an error between desired and indicated
speed, and adjusts the foot pressure until the error is gone. Now the
_change_ in foot pressure corresponds to the disturbing force that exists,
so the "behavioral illusion" is demonstrated for this relationship between
changes.

However, we must not forget that by far the largest part of the foot
pressure being applied is due to the reference signal, not the disturbance,
unless the slope is extreme. "The behavior" does not consist solely of the
small changes in foot pressure due to changes in slope of the road, or
headwinds, or soft tires. We must also account for the amount of foot
pressure that is applied when the speed is constant, road is level, and the
air is still, and that is ultimately traceable to the setting of the
reference signal.

The behavioral illusion is seen mainly in terms of changes, changes in
disturbing variables and changes in the action of the system relative to
the background level of action that is going on. Since psychologists have
defined stimuli and responses mainly in terms of changes away from
background levels, the behavioral illusion applies fairly directly. But
there is another illusion operating here, which is the illusion that when
behavior is continuing at some steady background level, nothing is
happening. If you ONLY look at changes, you miss the main show. Stimuli are
always present, behavior is always going on, even if there is nothing
remarkable that stands out from this background.

That, by the way, is another reason I am less than maximally impressed by
Bateson's discussions of differences. Behavior is going on, environmental
variables and action variables have specific values, even when no changes
are occurring. Just standing there is behaving. Just standing there is
controlling. Keeping the car at a steady 60 miles per hour on a level road
under windless conditions is controlling. Since there a re no "differences"
in the variables of interest under such conditions, Bateson would say there
is nothing that makes a difference. But that's just the wrong way to think
about what's going on. If there were no control system, the foot would
relax and the car would slow down to idling speed.

Best,

Bill P.

[From Peter J. Burke UCR 9/26/2002 2:15PM PDT]

from Bill Powers (2002.09.26)

We must also account for the amount of foot
pressure that is applied when the speed is constant, road is level, and the
air is still, and that is ultimately traceable to the setting of the
reference signal.

Not to mention friction between tires and road.

Peter

ยทยทยท

-----Original Message-----
From: Control Systems Group Network (CSGnet)
[mailto:CSGNET@LISTSERV.UIUC.EDU]On Behalf Of Bill Powers
Sent: Thursday, September 26, 2002 4:30 AM
To: CSGNET@LISTSERV.UIUC.EDU
Subject: d, r. and q0

[From Bill Powers (2002.09.26.0425 MDT)]

Rick Marken (2002.09.25) --

I don't have your last post in front of me, since I'm on a different
computer right now. But you asked if I was comfortable with saying that the
steering wheel "caused" the car's path to deviate left and right. Now that
you ask, I have to say no. Causation is just the wrong language -- it
forces us into an either-or mode when we should be talking about how
variables depend on other variables. The steering wheel does not determine
deviations of the path of the car because there are other variables acting
at the same time which also affect the car's path: crosswinds, tilts of
roadbed, I don't have to go through the list again. You can't predict where
the car will end up just by measuring the steering wheel angle.

So while turning the steering wheel may have modestly reliable effects on
the car, our predictions of where the car will go will be increasingly
uncertain as disturbances become larger. And by the same token (this is
what it has taken me some time to put into words), disturbances may have
pretty reliable effects in producing the actions that oppose them (given a
control system), but these effects become increasingly uncertain as
variations in the reference signal become larger. In our analyses, we
typically assume the reference signal to be constant in order to show how
changes in disturbances relate to changes in actions. But in most real
cases, we have to allow for changes in the reference signal to be occurring
at the same time that the disturbance is varying. All we observe is the
composite effect of these two sources of variation; without knowing how
_both_ d and r are varying, we can account for only part of the variance of
qo.

But the real answer to our problem is simpler than that. Consider
controlling the speed of a car. The action variable, qo, we could say is
the force with which the foot presses down on the accelerator. To bring the
car to a reference speed like 60 mph, we find we must press with some
amount of force which is determined by the feedback function that converts
a pressure on the pedal into a speed of the car. The reference speed we
have chosen determines the final speed, and that in turn determines the
required pressure according to the inverse of the feedback function. Of
course we don't need to calculate that inverse; we just keep increasing or
decreasing the foot pressure according to the difference between the
observed speed and the desired speed, and this results in bringing the
speed to the reference level. When that has been achieved, the foot
pressure, obviously, has become what is necessary to maintain that speed.
That pressure happens to correspond to the inverse feedback function of the
reference signal, but it isn't achieved by calculating that inverse.

Now let the car come to a slope and start going upward or downward. The
slope produces a force equal to the weight of the car times the sine of the
angle of ascent or descent, and the car starts to speed up or slow down.
The control system experiences an error between desired and indicated
speed, and adjusts the foot pressure until the error is gone. Now the
_change_ in foot pressure corresponds to the disturbing force that exists,
so the "behavioral illusion" is demonstrated for this relationship between
changes.

However, we must not forget that by far the largest part of the foot
pressure being applied is due to the reference signal, not the disturbance,
unless the slope is extreme. "The behavior" does not consist solely of the
small changes in foot pressure due to changes in slope of the road, or
headwinds, or soft tires. We must also account for the amount of foot
pressure that is applied when the speed is constant, road is level, and the
air is still, and that is ultimately traceable to the setting of the
reference signal.

The behavioral illusion is seen mainly in terms of changes, changes in
disturbing variables and changes in the action of the system relative to
the background level of action that is going on. Since psychologists have
defined stimuli and responses mainly in terms of changes away from
background levels, the behavioral illusion applies fairly directly. But
there is another illusion operating here, which is the illusion that when
behavior is continuing at some steady background level, nothing is
happening. If you ONLY look at changes, you miss the main show. Stimuli are
always present, behavior is always going on, even if there is nothing
remarkable that stands out from this background.

That, by the way, is another reason I am less than maximally impressed by
Bateson's discussions of differences. Behavior is going on, environmental
variables and action variables have specific values, even when no changes
are occurring. Just standing there is behaving. Just standing there is
controlling. Keeping the car at a steady 60 miles per hour on a level road
under windless conditions is controlling. Since there a re no "differences"
in the variables of interest under such conditions, Bateson would say there
is nothing that makes a difference. But that's just the wrong way to think
about what's going on. If there were no control system, the foot would
relax and the car would slow down to idling speed.

Best,

Bill P.

[From Bill Powers (2002.09.28.0920 MDT)]

Peter J. Burke UCR 9/26/2002 2:15PM PDT--

From Bill Powers (2002.09.26)

>We must also account for the amount of foot
>pressure that is applied when the speed is constant, road is level, and the
>air is still, and that is ultimately traceable to the setting of the
>reference signal.

Not to mention friction between tires and road.

Peter

A good point to notice, but forces like those, as well as air resistance,
arise from causing the car to move, not from sources independent of the
car's motion. They aren't disturbances, but part of the environmental
feedback function. The environmental feedback function (EFF) determines how
fast the car will end up traveling for a given amount of foot pressure. The
parameters of the EFF include things like the spring under the pedal, the
effect of the linkage on the carburetor or fuel injector, properties of the
engine, the drive train,the tires, and the aerodynamics of the car's body
in still air. Disturbances would be external variables that can cause
changes in the forces acting on the car independently of the effects of the
accelerator pedal -- that could change the net force acting on the car with
no change in pressure on the pedal.

That's not quite as ironclad a definition as it may seem, because the
properties of the EFF usually depend on other variables, like the alcohol
or water content of the fuel, which can vary independently of the driver's
action. So I guess we have to think of the long-term "normal form" of the
EFF, with disturbances being independent variables that can alter or add to
it over the short term. The main thing is that "real" disturbances have to
be able to vary independently of the driver's action over a relatively
brief period of observation, like ten minutes or an hour.

Best,

Bill P.

Best,

Bill P.