# Bill Williams post

[From Bill Powers (2000.09.23.0640 MDT)]

Here is a post from Bill Williams, via Greg Williams (not related), and
edited by me to eliminate double spacing and a few typos. I hope I haven't

Control Theory and Flight Instruction
By Bill Williams

Recently there have been some comments on the net
concerning a connection between control theory and flight
instruction. Most flight instruction is provided by low time
commercial pilots building hours in order to qualify for more
financially rewarding jobs with air carriers. Consequently
the usual standard of instruction suffers.

When I was flying for
a small commuter I did flight instruction on the side. But
I had a genuine interest in flight instruction, in part because
it provided me with a source of volunteer "white rats." They
even paid me, but not very much, to experiment upon them. At
the time I was also learning control theory using an oscilloscope
and experimenting with electronic circuits mainly using Op-Amps,
in simple systems constructed on "bread board" modules. I'd
read Norbert Wiener as a secondary school student, but I didn't
understand the math and wasn't inclined to put the effort into
learning enough math to be confident of comprehending what Wiener
was saying. I didn't have the forsight to anticipate that personal
computers would in the future become cheap and simulations
comparatively easy to program.

So it seemed to me that analog
simulation was the only route which was open to me to obtain
a genuine understanding of the theory behind cybernetics. But
my student pilots were also instructive. It didn't take much
time working with analogue control circuits to convince me
that there was a connection between what the Op-Amp based
circuits did and what I observed students doing in the airplane.
In addition I was convinced that the theory which applied to
the electronic components could be used to improve the methods
employed in flight instruction.

From an instructor's standpoint, perhaps the most awe-inspiring
thing that student pilots do is to go solo and fly away on their
own. Next in order, the most impressive phenomenon that they do is
to generate from time to time what is called a Pilot Induced
Oscillation during an attempt to land. When this phenomena occurs
the oscillation may evolve into a sequence in which the aircraft
alternates between energetically bouncing off the runway followed
by pitching up at an excessive angle risking a stall and an even
more energetic and possible terminal contact between aircraft and
the runway.

The basic control theory explanation of the oscillation
involves an increase in the student's reaction time in which
the transport delay around the loop reaches a critical value
( a 18O degree phase delay ). When this happens efforts to
control the plane ( control in the negative feedback sense )
are transformed into a positive feedback loop and a departure
from controlled flight. The student ordinarily experiences
this transition as an unexpected, and unexplained, complete
loss of control. During a PIO frantic efforts to control the
plane may instead generate oscilations which are of of increasing
amplitude and decreasing period.

In the mid-198O's the PIO
phenomenon was not included as a part of the regular student
training sylabus. Ordinarily, in flight training a student is
given instruction concerning hazzardous situations so that, 1)
they may be avoided, 2) if despite precautions they are encountered
they may be identified, and 3) once identified counter measures
may be applied. At the time, however, none of this ( according
to my recollection ) was part of the regular flight instructional
program. In contrast there is a well organized instructional
sequence concerned with stall avoidance, recognition and recover.
Obviously control is an issue in flying an airplane, and the
has long since been organized ( by regulation and standardized
specifications ) in terms consistent with a control theory
understanding.

Flight training, however, was not so sophisticated,
and the possiblity that a pilot might enter into a situation
in which they might inadvertently generate a PIO was left, in
the absence of a theoretical explaination, to chance. Out of
the many minor accidents that involve light aircraft, it is
unlikely that one in a thousand pilots who have experienced an
accident in which a PIO is a contributing factor would be able
to explain the role which the PIO played in causing the accident.
You could tell them that the transport delay in their reactions
controllers, and they still wouldn't know what had happened
to them. I knew a B-52 pilot who described generating a PIO on
landing returning from mission over North Viet Nam-- and
he didn't know in any genuine sense what had happened or why.
The aircraft commander took the plane away from him after it
was clear that my acquaintance wasn't going to recover by
himself. When the crew deplaned the rear gunner who had
experienced more excitment on landing than during the rest of
the flight was waving a white handkerchief signalling that he
was surrendering.

In order to study a phenomenon it is almost a neccessity to
encounter it. Ordinarily, aside from minor clumsiness, PIO's as
a well developed event, only occur at considerable intervals.
I found, however, that by using an understanding of control theory,
it was possible to create a situation in which PIOs would occur
more frequently. Fatigue slows down reaction time ( or in more PCT
correct terms it increases the the transport delay time). Therefore,
if you wear a student out by working them hard, their reactions
will slow down and the critical 18O lag may be approached. And,
the aircraft may be configured so that it is less stable. A
power off approach ( less airflow over the tail ) is less stable.
So is loading passengers into the back seats ( moving the center of
gravity back relative to the aerodynamic center helps ). A steep
landing approach is more demanding of precise control during the
roundout and flare for touchdown. And attempting to initiate a
PIO at night benifits from a less accurate visual perception.

In normal flight at altitude fatigue alone is will not be
sufficient to generate a PIO. However, when attempting to
land and the runway is approaching at a threatening rate, students
will sometimes switch from a continuous control mode to a
bang-bang mode of control in which they alternate between
approaching the runway too fast and jerking the nose up, and
with the nose pointing up at too high ( risking a stall and
hard landing ) they would then shove the nose down. My
description of the PIO and the switch from a continous to a
bang-bang control process depends upon inferences on my part,
somewhat informed inferences, but nevertheless inferences.
I don't know of any studies which have systematically characterized
what is taking place, but surely given its importance it has been
characterized somewhere by someone.

If a student recognizes that their flying has entered this
mode of dysfunctional control they can without difficulty escape
the oscilations by adding power when the nose is pointing up
and flying away from the ground rather than shoving the nose
down and continuing with the oscillations. The initial
experience with a PIO however can be so disconcerting that
the pilot doesn't think to abandon the attempt to land and
break the cycle by adding power and flying away from the ground.
Once a pilot has experienced a PIO, subsequent encounters are more
easily recognizable and far less threatening which makes a
successful recovery more likely.

As a result of the flight training syllabus not being developed
from control theory principles there is a vagueness in specifications
as to what perceptions a student pilot should attempt to control
during the touchdown phase of landing. Or rather, instead of being
told what to percieve, a student is typically told "what to do."
The "what to do" instructions are, for the most part in some sense
perceptions to control.

While the structure of control and the strategy that an
experienced, proficient pilot uses in landing an airplane
is, I am confident, of considerable complexity, when instructing
I told new students that they should fly the airplane down
to an altitude of about ten feet over the runway and then
attempt in a relaxed way with small corrections to hold the
airplane steady at ten feet off the runway. ( Now having been
"enlightened" and in order to avoid the PCT police I might say
control for a perception of .... " ) When a student attempted
to hold the plane at a constant 1O foot altitude, the aircraft's
speed would bleed off, and the airplane would gently sag onto
the runway in the proper attitude, with the nose at a slightly
raised angle. To work out well this strategy depended upon the
student not controlling tightly for altitude or doing so with
short transport delay-- an instructor can almost always count
on this being the case. Despite its simplicity this suggestion
worked remarkably well. From the standpoint of the instructor,
approaching landing instruction this way made for a comparatively
relaxed situation in which it was possible to predict with
considerable success early in the touchdown phase how
matters were going to evolve. And poor control, due either to
an inexperienced student pilot, or a very fatigued more
experienced pilot, didn't seem to make much if any difference.

The usual way landing is taught ( without telling a student
what perceptions to control for ) it is left to the student
and trial-and-error learning ( I hadn't yet encountered PCT so
I didn't yet know about reorganization ). When the student is
engaging in trial-and-error experimentation close to the ground,
the result is not a relaxed situation either for the student or
the instructor. ( I don't believe, however, that there are many
instructors who percieve the situation as being especially hazardous.
I would much rather teach someone to fly than to drive. )
In retrospect it seems irresponsible, but I was soloing students
after 4 hours of instruction.

When a student controlled for
holding the aircraft stable over the runway, often the very
first attempt to land worked out quite well. After that,
with a measure of confidence based on having the experience
of making a good landing a student's skills quite often developed
rapidly. Soloing the student was primarily a symbolic event.
But it had real consequences-- after having soloed a student
was more confident and calmed down. This result it seems to me
in retrospect was the result of less random reorganization.
Later on I had to be inventive in order to provoke students
into making less than perfect landings so that they could
learn the skills required to make a recovery from a bad landing.
A gusty twenty knot crosswind was usually so far beyond their
capacity that it provided lots of practice in coping with
attempts to land that had gone sour.

In contrast, efforts
to fly the aircraft to the runway according to what I remember
as being the usual practice, while they might work for a
fresh, experienced pilot, didn't work out nearly so well if
everything wasn't just right. In a situation in which the
windshield is covered by ice, or engine oil, it can be a
should be made in the approach to touch-down so that in
the event of impaired visiblity, it is still possible to
make a successful landing.

It might be instructive to model different strategies
for landing an aircraft based upon controlling different
perceptions. I am confident attempts to land by controlling
for some perceptions would result in a much better control
system for a sucessful landing than the use of other perceptual
clues. It is for example well known that it is more effective
to control an airplane's airspeed indirectly by controlling
the plane's attitude than it is to attempt to control airspeed
by attempting to control directly for airspeed with the throttle.

I've wondered how a simulation of a pilot's behavior as a
stimulus-response process would differ in respect to the pilot
induced oscilation phenomenon. Perhaps there is an opportunity
to demonstrate one more time that a stimulus-response explanation
is not a good model of a living control system.

I would think that when landing an experienced pilot
controls for a complex configuration of perceptions including
among others: a relation between height above the runway, nose
angle to the horizon, and rate of approach to the runway.
A proficient pilot with current experience may also rely in
part upon a knowledge of relationships between a control
displacement at a given airspeed and the aircraft's reaction.
It seems to me likely that there is an element of what in some
sense is an open-loop control process involved. I noticed that
when I checked out airline pilots in a small plane that their
first landing would be somewhat clumsy. It was not that their
control skills were deficient, but, it seemed to me, that they
lacked the sort of "look-up table" which a pilot who was current
in small aircraft could make use of to control the aircraft
more effectively than would be possible through a negative-feed
back process alone. If I had understood this complex nature
of control better at the time, I would have had the students
fly a dipsy-doodle pattern-- quickly raising and lowering the
nose through a much wider angle than is usually experienced.
Flying this pattern would have demonstrated to them that just
because the nose was higher than it should be following a bounce
off the runway didn't mean they had to abruptly shove it way
down setting themselves up for another bounce on the runway.

Returning to the perceptions which ought to be attended to
during an approach to landing, rather than list all the relevant
relationships in the configuration, I would think the complex
perception would be a matter of combination of values for
altitude, and the nose angle, rates of change and rates of
acceleration of these rates. It is, however, not a genuine
option to suggest to a prospective student pilot that they
first take a course in matrix algerbra and the calculus of
variations.

The usual methods used in teaching a student to land when
I was engaged in flight instruction consisted of a-theoretical rules
of thumb, and rules regardomg "What to do." appeared to be considered
satisfactory. In effect, whatever a student was told, in practice
they reorganized until they arrived at a strategy by which they
could make acceptable landings. Aside from the time, anxiety,
and expense the result was in my opinion a fragile, poorly
integrated set of skills that decayed rapidly when not in use.
The absence in the syllabus of instruction regarding PIO's
constitutes an exception to the principle usually followed that
a student pilot should be prepared to recognize, avoid and
counter potential hazards. When the basis of flight instruction
does not include control theory it would not appear to be
possible to provide adaquate instruction with regard to Pilot
Induced Oscillations.

Modelling the PIO phenomena might be a worthwhile CSG project.
However, I'm not entirely confident that simulating the process
on a PC would neccesarily capture the actual phenomena well
enough to be useful. It seemed to me that the entry into the
PIO mode was triggered first by poor control of the approach
generating an excessive rate of closure with the runway, followed
by panic ( a harsh bounce off the runway makes its own very
real contribution here ) followed by a transition to a bang-bang
mode of control with sensory processing being degraded both in
precision and timeliness. The role of panic involved in
initiating an actual PIO may be an important part of the phenomena,
and I doubt whether flying a PC would "induce the emotional effect."

As a starting point, however, it might be interesting to work
with a simulation in which the subject attempted to control a
process with variable degrees of stability, and varying degrees
of lag between control inputs and changes in the vehicle's behavior.
At some point increasing instablities or increasing transport delay
ought to overwhelm a subjects capacity to control the process
effectively. PIOs during landing attempts, however, appear to
involve more than pure ( unconstrained ) instablities or transport
delays, the influence of the nearby runway and the possiblity of
a stall close to the ground might be stimulated by a task of guiding
a marginally stable vehicle with a considerable lag in response
to control inputs on a path between two walls. A transition
between stable control and the PIO sort of phenomena might be
triggered by a random external disturbance, or a abrupt turn of
the path. Familiarity with the input-output relations of control
outputs and vehicle response may also be important.

If the PIO phenomenon could be model convincingly, it might
attract some significant attention in the flight training community.
While I'm not familiar with recent developments in flight instruction,
it seems likely that PIOs during landing attempts would continue
to be neglected. I would think that an increasing concern with
liablity exposure would mandate that this would be the case
for instruction based upon actually provoking PIOs. However,
if an effective simulation could be developed, then the same
liablity considerations might be a very strong selling point
for such a program.

More friviously it ought to be noted that flight simulator
programs are among the best selling games.

[From Bruce Gregory (2000.0923.1115)]

Bill Powers (2000.09.23.0640 MDT)

As a result of the flight training syllabus not being developed
from control theory principles there is a vagueness in specifications
as to what perceptions a student pilot should attempt to control
during the touchdown phase of landing. Or rather, instead of being
told what to percieve, a student is typically told "what to do."
The "what to do" instructions are, for the most part in some sense
perceptions to control.

The FAA has gotten a little better at this, admittedly without recognizing
that their recommendations are consistent with a control theory approach.
Getting to the runway with the right airspeed can rather easily be
translated into control terms. Keep the numbers a "few inches" above the
cowling on the windshield. The location of "the spot" can be demonstrated
by the instructor while making the correct approach and having the student
notice that the numbers appear to remain stationary and where the numbers
appear to be on the windscreen. Such a "constant attitude" approach requires
that the airspeed be controlled by the throttle. (True using the stick to
control airspeed results in better control, but makes the task of
controlling attitude much more difficult.)

The most direct way I know to keep PIO's from occurring is for the pilot to
control his or her perception of how she or he is moving the stick. In the
words of my flight check instructor, "Hold it steady, or pull back. Never
push forward." This ensures that the pilot does not reduce the angle of
attack and hence the lift. Reducing lift in the flair is an excellent way to
initiate an oscillation.

I agree that telling the student what to pay attention to rather than what
to do is a major step forward. It's an excellent way to apply PCT to the
real world.

(Ten feet is quite an altitude to stall at. I aim for something more like
one foot. Rotate at 10 feet but hold it off at one, is my script.)

BG

[From Bruce Abbott (2000.09.23.2305 EST)]

Bill Powers (2000.09.23.0640 MDT) --

Here is a post from Bill Williams . . .

From an instructor's standpoint, perhaps the most awe-inspiring
thing that student pilots do is to go solo and fly away on their
own. Next in order, the most impressive phenomenon that they do is
to generate from time to time what is called a Pilot Induced
Oscillation during an attempt to land. When this phenomena occurs
the oscillation may evolve into a sequence in which the aircraft
alternates between energetically bouncing off the runway followed
by pitching up at an excessive angle risking a stall and an even
more energetic and possible terminal contact between aircraft and
the runway.

The basic control theory explanation of the oscillation
involves an increase in the student's reaction time in which
the transport delay around the loop reaches a critical value
( a 18O degree phase delay ). When this happens efforts to
control the plane ( control in the negative feedback sense )
are transformed into a positive feedback loop and a departure
from controlled flight.

Flying is not the only situation in which such human-induced oscillations
occur, as I unwittingly demonstrated myself some years ago while having my
car towed home by my Dad's car, by means of a short cable. When it came
time to stop (at a red light, for example, I would ease on the brakes enough
to keep tension on the cable. On one occasion, however, I began to brake
while the cable evidently was fairly slack, resulting in the cable snapping
taught and then acting like a spring to launch my car forward at a speed
fast enough to slacken the cable once again. As my car was now about to ram
my Dad's, I pressed the brakes again, causing the whole sequence to repeat,
only harder this time, then again, and again. As I fought to regain control
before the cable snapped or the two cars collided, in occurred to me that I
had to get on (and off) the brakes a bit sooner in the cycle so as to dampen
out the oscillation. It took me a few more cycles to get timing right but
the tactic did work and both cars came safely to a stop without damaging
anything other than my pride.

Bruce A.

[From Bill Powers (2000.09.24.0339 MDT)]

Bruce Abbott (2000.09.23.2305 EST)--

Bill Williams:

The basic control theory explanation of the oscillation
involves an increase in the student's reaction time in which
the transport delay around the loop reaches a critical value
( a 18O degree phase delay ). When this happens efforts to
control the plane ( control in the negative feedback sense )
are transformed into a positive feedback loop and a departure
from controlled flight.

There are two aspect of the situation that determine whether oscillations
will occur. One is the properties of the airplane, the other is the
properties of the controlling person.

Consider just the roll axis. The airplane's control hookup converts a stick
or wheel deflection into an angle of the ailerons, which imparts a torque
to the airplane. If this torque is greater than the restoring torque due to
wing dihedral angle, the airplane will commence a roll, and this roll will
simply continue as long as the control is deflected. The airplane will go
into a barrel roll, slow or fast, which will continue until it hits the
ground.

To turn the airplane, the stick or wheel must be deflected and held until
the wings roll to some desired angle. As they do so, the plane begins
turning in the direction in which it is banked (whether or not the rudder
is used). When it is turning at the desired rate (so many degrees per
second, or minutes per complete turn depending on which instruments you
have) the controls must be returned nearly to neutral (stick or wheel
centered), to keep the angle of bank from increasing any further. The
airplane then continues to turn at the same rate, around and around. To
make the turn stop, the controls must be used to level the wings,
eliminating the angle of bank.

The situation is just as complicated for going up and down in straight
flight. The controls (stick or wheel plus, now, throttle) produce rates of
change of altitude, and these changes must be started by one adjustment and
stopped by the opposite adjustment of the controls. These are the basic
means of control that have to be learned, and each of them requires
learning a control system before the overall control can be mastered.

What Bill W. says about reaction time is important, but once a pilot has
learned all the right coordinations, the reaction times are probably about
as short as they can get, and remain fairly constant. They _could_ become
longer, and that _could_ explain any oscillatins that occur, but there is
another factor at work: the sensitivity of the pilot's actions to error. I
think this is much more subject to change.

Suppose the pilot's output sensitivity were such that a pitch change of 45
degrees led to a change in fore-and-aft stick angle of 1 degree per second:
one degree of pitch angle error produces 1/45 degree per second of stick
angle change. Would this be enough to bring the plane back to level?
Possibly: if the plane were diving, this gradual backward movement might
get the plane back to level before it hit the ground. Note that this lag is
an integral lag; it's different from a reaction time. But ignore that if it
means nothing to you.

At some rate of change of stick movement, the dive would be corrected
before it ever got as large as a 45-degree angle. This might require a
somewhat higher output sensitivity of, say, 5 degrees per second of stick
movement per 45 degrees of pitch angle, or 1/9 degree of stick movement per
degree of pitch angle.

But what would happen if the output sensitivity got as high as 20 degrees
of stick movement per degree of pitch angle? Twenty degrees of stick
movement is a very drastic movement; it would cause the plane to increase
or decrease its pitch very rapidly. But that would cause even more violent
changes in stick movement, so the result would be very much like what Bill
William calls "bang-bang" control: the stick would move violently forward,
the plane would pitch downward, and stick would move violently backward,
the plane would pitch upward, and so on. If, during the downward movement,
the wheel were to contact the ground, the pilot would probably pull back
hard on the stick and the plane would be bounced violently upward, leading
to an even more violent push forward on the stick, another bounce and so
on. Even without any change in the pilot's basic reaction time, the
oscillations would be sustained by the excessive gain in the pilot's part
of the control loop.

All the suggested remedies have the same effect: to reduce the gain in the
pilot's output function. Take it easy, move more slowly, don't try to
correct every little error, just hold the plane level and let it settle in,
don't overcontrol, and so on. If the pilot understood control theory, all
you'd have to say is "lower the gain."

There's more to it than this, of course; this is a dynamic system with
built-in lags, and the control system has to be designed right to keep the
lags from making the whole loop inherently unstable. This can be done by
using hierarchical control, as in my demo of the inverted pendulum.

The first thing the pilot should be taught is the difference between
position control and force control of the wheel or stick. You can control
either way: position control involves controlling the sense of stick angle,
and force control involves controlling the sense of skin pressure and
effort as the hand presses against the stick. What is needed for good
piloting is force control (right, Bill W and Bruce G?).

When you apply a force to the wheel or stick, the wheel or stick moves the
control linkages and control surfaces until wind force is in equilibrium
with applied force. In effect, you're feeling and controlling a force
proportional to the actual forces acting on the airplane in pitch, roll,
and yaw. The actual amount of stick or wheel movement is irrelevant; it
simply moves until you feel the intended amount of force reflected from the
control surfaces. It won't move much at cruising speed. When you're flying
slowly, it will move more to achieve a given force, but you ignore the
movement; it's the force that moves the airplane.

As the inverted pendulum model shows, this makes the lowest loop, which
controls angular acceleration, completely stable and very fast.

The next higher loop monitors the immediate effect of controlling angular
acceleration: the velocity with which pitch, roll, or yaw changes. Again,
if the pilot now learns to control angular velocity by altering the
controlled angular acceleration (stick pressure), he will have very fast
and stable control of the rate of roll, rate of pitch, and rate of yaw. The
instructor takes the pilot up high and tells him to change all these angles
slowly and rapidly, back and forth and up and down and this way and that
way, until he can make them change either fast or slowly, any way he likes.
The instructor keeps the plane right-side up by whatever means are necessary.

The final step is to use the angular velocity control system to control
pitch, roll, and yaw at particular angles. You now have stable control over
the airplane's attitude, and you can start learning how to fly straight and
level, or change course, or ascend and descend.

That's how I would teach new pilots to control an airplane's attitude.

The interesting thing about hierarchical control is that anticipation
occurs automatically, in an interesting way. Suppose one loop, not the top
one, has a bit of a lag in it. This means that the feedback will lag
changes in the reference signal. During that lag a change in the reference
signal will be converted directly to error just as if there were no
negative feedback. This gives the effect of a large initial burst of output
that declines quickly to the normal level -- and that is precisely what is
required by the next higher level of control to compensate for the lag! It
gives exactly the effect of anticipation that is needed.

I don't know whether that kind of anticipation is teachable, or whether it
simply falls out of learning to control hierarchically (if there is a
choice of learning to control any other way). We often tell ourselves
stories about what we're doing without the story in any way helping or
hindering; it could be that learning to anticipate simply happens because
it results in stability. But we tell ourselves that we are _deciding_ to
anticipate -- at just about the same time it starts to happen.

Best,

Bill P.

[From Richard Kennaway (2000.09.24.1351 BST)]

Bill Powers (2000.09.24.0339 MDT):

There's more to it than this, of course; this is a dynamic system with
built-in lags, and the control system has to be designed right to keep the
lags from making the whole loop inherently unstable. This can be done by
using hierarchical control, as in my demo of the inverted pendulum.

the parameters of the control loops in that demo, and I think your
answer was that you played around with them until it worked. I've been
looking at that system in terms of classical linear control theory, and
applying the Routh-Hurwitz stability criterion, which produces several
inequalities relating the gains of the five control loops. The system
is stable if and only if the inequalities are satisfied. I doubt you
had those inequalities in mind, but somehow you picked values that
worked. Physical intuition?

I'm in London at a conference right now (The Perl and Raku Conference NA)
with only pen and paper to think with, but when I get back I'll try
plugging in different values for the gains and check out the R-W
prediction.

-- Richard Kennaway, jrk@sys.uea.ac.uk, http://www.sys.uea.ac.uk/~jrk/
School of Information Systems, Univ. of East Anglia, Norwich, U.K.

[From Bruce Abbott (2000.09.24.1230 EST)]

Bill Powers (2000.09.24.0339 MDT) --

The interesting thing about hierarchical control is that anticipation
occurs automatically, in an interesting way. Suppose one loop, not the top
one, has a bit of a lag in it. This means that the feedback will lag
changes in the reference signal. During that lag a change in the reference
signal will be converted directly to error just as if there were no
negative feedback. This gives the effect of a large initial burst of output
that declines quickly to the normal level -- and that is precisely what is
required by the next higher level of control to compensate for the lag! It
gives exactly the effect of anticipation that is needed.

Interesting! However, this cannot be the whole story with respect to
anticipation. I am reminded of Parnelli Jones' report on the experience of
driving the first turbine car at Indy. The turbine engine had such a lag in
response to accelerator input the Jones had to learn to mash down on the
accelerator _before_ entering a turn, at just the right moment to assure
that acceleration would begin as the car emerged from the turn.

It seems to me that this sort of anticipation could not be driven by lag in
a lower system. The lag in engine response to accelerator depression would
not produce an exaggerated error until the driver depressed the accelerator
while exiting the turn. As a result of this larger error the driver would
mash down the accelerator more rapidly than otherwise, but by this time it
is already too late for this compensation to be of much help.

I would propose instead that in this case compensation must occur based on
learning to coordinate accelerator action with certain visual inputs. One
varies the timing of accelerator depression with respect to perceived
distance from (or into) the curve the means of creating a match between the
perceptions of exiting the curve and feeling the acceleration begin. (This
is just another control system at work, of course.)

Bruce A.

[From Bill Powers (2000.09.24.1216 MDT)]

Richard Kennaway (2000.09.24.1351 BST)--

I've been
looking at that system in terms of classical linear control theory, and
applying the Routh-Hurwitz stability criterion, which produces several
inequalities relating the gains of the five control loops. The system
is stable if and only if the inequalities are satisfied. I doubt you
had those inequalities in mind, but somehow you picked values that
worked. Physical intuition?

Or luck. Actually I started with the lowest loop and raised the gain until
it started getting unstable, then backed off about 50 percent. Same for the
others -- just cut-and-try reorganization. I'm really excited about your
investigation of formal stability criteria -- that could make the model
publishable in serious literature. Want to write a paper on it with me?

Best,

Bill P.

[From Bill Powers (2000.09.24.1245 MDT)]

Bruce Abbott (2000.09.24.1230 EST)--

It seems to me that this sort of anticipation could not be driven by lag in
a lower system. The lag in engine response to accelerator depression would
not produce an exaggerated error until the driver depressed the accelerator
while exiting the turn.

A higher-level system could, of course, choose an earlier time in the
process at which to hit the accelerator (a true anticipation).

As a result of this larger error the driver would
mash down the accelerator more rapidly than otherwise, but by this time it
is already too late for this compensation to be of much help.

Yes.

I would propose instead that in this case compensation must occur based on
learning to coordinate accelerator action with certain visual inputs. One
varies the timing of accelerator depression with respect to perceived
distance from (or into) the curve the means of creating a match between the
perceptions of exiting the curve and feeling the acceleration begin. (This
is just another control system at work, of course.)

I think that's a good proposal. I would say that what is controlled is a
perceived relationship between the perception of pressing the accelerator
pedal and the perception of a certain point while exiting the curve. A
fairly dangerous situation, since with such a large lead time, disturbances
that occur during it can't be opposed (such as another car cutting in ahead
of you just after you have mashed the accelerator, when it's too late to
cancel the surge of engine power that will follow).

The problem with all true anticipations is that they are extremely
sensitive to timing. If they occur too late, they fail to correct errors;
if they occur too soon, they cause errors. I think that most useful
anticipations are more of the nature of getting a hand or foot into the
right position or bracing the body to receive an impact whenever it occurs.

Best,

Bill P.

[From Bruce Gregory (2000.0925.1119)]

Bill Powers (2000.09.24.0339 MDT)

The first thing the pilot should be taught is the difference between
position control and force control of the wheel or stick. You
can control
either way: position control involves controlling the sense
of stick angle,
and force control involves controlling the sense of skin pressure and
effort as the hand presses against the stick. What is needed for good
piloting is force control (right, Bill W and Bruce G?).

Ideally, you are trimming away forces. (I used to land a Mooney using
the electric trim and so had no perception of force at all.) I think
almost all my references are visual. Are you aware of the forces you
exert in a tracking experiment? I don't think I am.

BG

[From Bill Powers (2000.09.25.1650 MDT)]

Bruce Gregory (2000.0925.1119)--

Ideally, you are trimming away forces. (I used to land a Mooney using
the electric trim and so had no perception of force at all.) I think
almost all my references are visual. Are you aware of the forces you
exert in a tracking experiment? I don't think I am.

The forces you sense are primarily those involved in changing the attitude
of the airplane away from straight and level flight, as when making a turn.
Of course they aren't the highest level of controlled variable, so one who
is very used to flying may not pay attention to them any more. With my
measley 100 hours, I never got to that point. And I certainly wasn't flying
Mooneys! Is this "let them eat cake" day?

Best,

Bill P.

[From Bruce Gregory (2000.0926.1014)]

Bill Powers (2000.09.25.1650 MDT)

And I certainly
wasn't flying
Mooneys! Is this "let them eat cake" day?

It's been many years since I flew a Mooney. In those days it was a
little less upscale that it is now. The Mooney I flew had the infamous
Johnson bar that required you to lower and raise the landing gear by
swinging the a large "pipe." (The designer had apparently never heard of
mechanical advantage.) It was quite a scene in the cockpit, but I'll bet
few Mooney pilots of that era forgot to lower the gear! (Naturally, it
was considerably harder to raise the gear than to lower it. Once you
lowered the gear, you were not inclined to raise it again to comply with
some request from Air Traffic control.)

BG