[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
inserted any errors, but admit to them in advance.
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
theory of aircraft design in regard to handling characteristics
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
had reached the critical 18O degree point, and talk about bang-bang
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
correct, but not as helpful as would be instructions about what
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
distinct advantage to know systematically what adjustments
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.