[Hans Blom, 931117]
(Martin Taylor 931110 19:00)
I have been suggesting
that there is value in an INITIAL open-loop component when reference
signals change ...
This is a "trick" similar to one that is often employed in servo-systems:
------------------ ------- -------------- ----------
> > > > > > > >
----->| precompensator |--->|+ |---->| controller |--->| system |---
set- | | | - | | | | | |
point ------------------ ------- -------------- ---------- |
/|\ |
···
---------------------------------------
The precompensator often makes the controller simpler and easier to
design. It is especially helpful when the controller has no or negligible
delay but the system to be controlled or the feedback link has. A similar
design has the precompensator in parallel with the controller. The pre-
compensator can give the system an initial "kick" to get it going, and so
the overall system can avoid time delays that are inherent in biological
systems.
--------------
--------------->| precompens.|------
> -------------- |
> \|/
> ------- -------------- ------ ----------
> > > > > > + | | |
----->|+ |---->| controller |-->|+ |-->| system |---
set- | - | | | | | | | |
point ------- -------------- ------ ---------- |
/|\ |
-----------------------------------------------
This diagram corresponds to what Bill describes:
Feedforward implies supplying a path that bypasses part of the
normal control process in the forward (efferent) direction -- for
example, by routing a copy of the reference signal directly to
the output function, as in the Lang-Ham proposition.
Note that when the precompensator has a high paass filter characteristic,
it only comes into action on changes of the setpoint.
(Rick Marken (921111.2100))
1. Feedforward refers to efferent connections from brain to output.
In a control loop, feedforward is a direct connection from a reference
signal to an output function, bypassing the comparator. In an open loop
system (one in which there is no effect of output on input) all efferent
connections are feedforward.
This refers to the second diagram above. The first diagram shows a
feedforward path (the precompensator) in a different position. In a
hierarchical control system composed of components like diagram 1,
feedforward paths would exist WITHIN an overall feedback structure.
2. Bill Powers has posted two mathematical descriptions of the dubious
benefits of adding a feedforward connection to an "ordinary" control
loop. I used the spreadsheet simulation to compare the behavior of the
standard control model to a control model with feedforward; the model
with feedforward did a teensey bit better than the feedback-only model
when there were no disturbances. Otherwise, it was a wash. Feedforward
might improve the performance of a standard control loop -- but not by
much, and probably not at all.
Re the "dubious benefits of adding a feedforward connection to an
"ordinary" control loop": in engineering, feedforward does NOT have a
dubious status. It solves a number of problems that pure feedback cannot
solve, or it enhances the effect of feedback. Evolution seems, in the long
run, to strongly favor organisms that do "a teensey bit better".
3. A feedforward connection is certainly a possible augmentation of the
pure feedback model. But at the present time, given the data that is
available, feedforward mechanisms do not improve the ability of the
feedback model to act like a living control system. So feedforward
does not improve our ability to simulate control behavior.
Not even "a teensey bit" in some cases?
6. PCT maintains a strong SHOW ME attitude regarding the possible
existence of behaviors that are generated by feedforward processes
ONLY. PCT does not rule out the possibility that feedforward might
be ADDED to feedback to improve performance but the bias would be
to have the feedforward be there ALL THE TIME. But mathematical
analysis (see 2) suggests that the benefits of feedforward to a
control system are small, if they are beneficial at all.
I have trouble with your requirement that "the feedforward be there ALL
THE TIME". Does that refer to the CONNECTION or to the EFFECT? In the
diagrams above, the connection is there all the time. The effect of the
connection may be temporary: in the diagrams, the EFFECT of the feed-
forward connection (compared to a straight-through connection in diagram
1, and compared to no connection in diagram 2) may be observable only
briefly after abrupt changes of the reference level. So the effect may be
difficult to measure and may be unmeasurably small in (almost) steady
state conditions. Yet the effect may be large if you consider the system's
settling time, i.e. the time required before the system's output is stable
again after a step change of the reference level. In other words: feed-
forward does not help in compensating against disturbances; it does help
in speeding up the system's response.
7. Conventional models of living systems view virtually ALL behavior
as SOLELY a result of feedforward processes.
Yes, and PCT provides a much needed additional perspective.
PCT shows that this estimate
of the probable prevalence of feedforward based behavior has been
GREATLY EXAGGERTAED.
At the lowest levels of the hierarchy, that is true. As Bill has shown,
however, the higher levels of the hierarchy must necessarily be slower.
Here, feedforward will show its greatest contribution. Most "conventional
models of living systems" study these higher levels of the hierarchy...
In fact, there is no evidence that ANY behavior
is generated by feedforward processes.
Do you have evidence to support this claim?
(Bill Powers (931111.0830 MST))
Your description of the tracking experiment is a little
confusing. Are you visualizing a target that moves horizontally
while it traces out a sine or triangle wave vertically? That
would imply a two-dimensional control task, and would be
difficult to implement on a computer screen because the screen is
only 25 cm wide.
My description was confusing. I apologize. Let me try to be clearer. I
propose the following display on the computer's screen: The target's
movement in time goes from the top of the screen to the bottom (that way
you can use the normal scrolling if you use a text screen). The target
therefore traces out a vertical sine or triangle wave or what have you.
"Now" corresponds with the bottom of the screen. The other screen lines
show the most recent history of the target. Whenever the target is
invisible, you print an empty line rather than a line containing the
asterisk (or whatever) that indicates the target's position. The position
of the handle and its history (mouse, joystick) are plotted similarly, but
with a different symbol; the handle position and its history are visible
at all times. So, if the target is a sine wave, you will see a vertical
sine wave of asterisks that shows gaps, and another noisy vertical sine
wave of x's or so around it that is continuous. If both symbols coincide,
show only the handle's symbol. This is a "quick 'n dirty" version; you can
undoubtedly think of nicer (graphic) displays. Is this clearer?
I hope you realize that if you haven't
actually done experiments like these with human subjects, your
statements about how people would behave under various
circumstances would be considerably weakened. They would be
reduced from observations to predictions from a theory that has
not yet been supported by experiment.
I have done some of these experiments, but that was a long time ago: in
the early 70's. That research came under the name of "modelling the human
operator". We attempted to characterize the human operator's "transfer
function" in terms of gain, delay time, dominant time constants and such.
That research was predominantly a failure. Reproducible results were
obtained only if the target to be tracked was pure (low pass filtered)
noise. As soon as the target was more or less predictable, the operator
soon learned to make use of the regularities. This resulted in ridiculous
results like zero or even negative delay times.
After that, we did many experiments, in which we compared the performance
of a human operator with that of control systems that we designed, mostly
in simulation studies that were based on a model of part of a patient's
physiology. Those models allow you to design many different mock-up
patients, including worst cases that test the limits of what the con-
troller can do. We still do these studies whenever we test new controller
designs or improve old ones.
We also did some experiments in which we compared the performance of
automatic control systems with physicians (anaesthetists). In these
experiments, we discovered some of the rules of when to use feedforward
and when not. If a drug has a vary variable effect, DO NOT use feedfor-
ward; anaethetists often predict what the effects of, say, a surgical
action will be and try to precompensate for it, occasionally with almost
disastrous results because they have an inappropriate knowledge of the
patient's sensitivity to a drug. If a drug has an almost constant effect -
- inter- and intra-individually -- you can use feedforward. Some drugs
(several anaesthetics, for instance) are, indeed, used in a feedforward-
only regime, because appropriate sensors are not available.
Also, some degree of feedforward is required in systems that must be as
fast as possible. A blood pressure controller for the intensive care unit
is different from one that is used in the operating room -- only because a
surgeon's time is extremely costly and surgeons get in a very bad mood
when they have to wait for what they consider an unnecessary minute.
You assume here that there ARE periodic signals that a human
being could "easily handle after one minute's training." This
implies that you have already done this experiment. If you have,
why not just report the results?
The results are confusing and do not generalize, as I indicated above.
The fact that humans pick up regularities so quickly is the confounding
factor.
I suspect, if you'll forgive my skepticism, that any
"experiments" that have been done have been mathematical, not
using real human subjects.
Are you satisfied now?
Warping of the time scale can, of course, remove phase errors
very nicely, if you don't want to admit that phase errors
occurred. Tom Bourbon has data to show that open-loop phase
errors do not average to zero. You would just have to keep
warping and warping without limit to make the data fit the
theory.
I know that open-loop phase errors usually do not average to zero. In
long-duration cave experiments, the "diurnal clock" starts to tick for 25-
hour days on average, with extremes ranging from 12 to 36 hours. I presume
that other "clocks" have similar deviations. Besides drift, there is noise
(short-term fluctuations). The basic problem is, however, how to measure
errors. What is your criterium? Do you just pick a "standard" test -- and
if so, which one? I proposed to start with using qualitative common sense
judgment before starting to "measure". You do the same when you initially
judge a new control system design. The first questions are: Is it stable?
Is it fast enough? Is it accurate? Only after that do you start to "fine-
tune" and measure.
One point we should be very clear on: the fact that open-loop
control might suffice in a given circumstance does NOT indicate
that the behaving system is operating open-loop. The open-loop
design is a solution looking for a problem.
For control engineering, this is not true. Why would it be true for
biological systems?
The fact is that the [feedforward] models are inadequate for good
control over any prolonged time.
That depends -- see my anaesthetics example above. If sensors are not
available or if sensors fail, feedforward is all you can do, even over
long time periods. It does not matter all that much whether a patient is
sedated 80%, 100% or 120%. The 80% can be picked up from secundary signs
(a rising blood pressure or heart rate after an incision), the 120% only
results in a slightly longer stay in the recovery room.
I remember best the instances where my hand feels the [light]
switch on the first try [in the dark].
Funny. I remember best the instances where I fail. How could that be?
Sometimes there is no feedback signal, either because it just
isn't there, or because you do not pay attention to it.
Perhaps I am misreading this sentence, but to me this implies
that attention is required to make a feedback signal operative in
a control system, and I disagree with that.
If, in your tracking experiments, your subject is not paying attention to
the position of the target but to the fly that crawls across the screen,
his tracking performance will deteriorate or tracking will cease. More was
not meant.
(Bill Powers (931112.0815 MST))
The main issue we have to clear up is whether a purely open-loop
model is EVER a plausible representation of the mechanisms of
behavior.
I wonder whether this is a tautology. Don't we correlate "behavior" with
organisms, and don't we correlate the organisms that we consider with
having at least SOME feedback control?
When I look at the behavior of an organism, I don't look around
for events in its environment, or into its history, to explain
what I see. I wonder "How can this organism possibly be doing
what I see it doing right here in front of me?" I don't care how
it got its organization. I just want to know what that
organization is.
When *I* look at the behavior of an organism, I DO look around for events
in its environment and in its history, to explain what I see now that I
did not see before. I wonder "How can this organism possibly be doing what
I see it doing right here in front of me where it could not do that
before?" I DO care how its clever organization came into being after its
initial stupidity or naivete, because I see learning as a process that
continues from day to day, hour to hour, minute to minute, moment to
moment; because I see learning as the acquisition of skills/tools that my
future behavior will be based upon. I want to know how I can fine-tune
those skills, and I wonder what the underlying processes are, and which
are the ways in which I can optimize my learning process. I don't only
want to get there, I want to get there FASTER.
Explanations that are nothing more than naming behaviors by their
outcomes, that explain outcomes in terms of reinforcement,
evolution, social influences, childhood trauma, chemical
imbalances, mental quirks or conditions, or general scientific
principles like thermodynamics all beg the only question about
organisms worth answering: what is behavior and how does it work?
Whereas for me the central question is: what is behavior and how do skills
improve over time? Isn't that a question worth answering?
(Rick Marken (931113.1000))
But the discussion has suggested a useful point that should be
included in the PCT repetoire of demonstrations, experiments and
models. The point is that a heirarchicy of feedback control systems
can "survive" for some time intermittant losses of sensory input
about controlled variables.
That is not a new result. When your room thermostat breaks down, you won't
notice it for some time. The point is whether a system with (also) feed-
forward might not "survive" better or longer.
I am planning to do a version of the experiment suggested by Hans and
Bill P. -- tracking a predictable target and having the corsor disappear
for periods of time that can be adjusted by the experimenter. I plan to
compare the behavior of subjects to that of a control system model AND
an open loop model.
Great! Designing a purely open loop model that can track a periodic signal
and that is trained by processing the difference between its output with
the observations -- whenever the latter are available -- would be entirely
feasible and a valuable exercise in feedforward control. You might find
some useful references in the signal processing literature or in the
textbook reference that I give below.
(Bob Clark (931113.1715 EST))
If the value of the controlled variable is to be determined at a
later time, some form of "anticipation" or "prediction" is implied.
Even with a small number of current observations, future values can
be estimated by various methods. Accuracy can be improved by adding
more observations, and by increasing their accuracy.
When application to the physical world is considered, there are
methods (at least in principle) for accomplishing these results.
Physical sensors are known that can detect, and, combined with other
devices, can predict the path of an incoming object. Similarly, if
the initial conditions are specified, the path of an out-going object
is predictable.
Right on.
Instead of computing the needed predictions, the predictions could be
based on recorded observations of similar situations. Given a modest
library of such recordings, selection could begin with a preliminary
match, followed up with more accuracy as data accumulate. "A first
approximation, improved by iterating the process."
Selection need not play a role. The process is more like building up a
"running average" that improves (whose standard deviation becomes smaller)
as more observations arrive. Another example is the averaging process by
which an auditory evoked potential gradually becomes lifted above the
noise when more and more responses are recorded, despite the much greater
amplitude of the background EEG. Even though the signal-to-noise ratio is
terrible, the wanted information can be acquired because it repeats and
because we can observe many of those repeats. This is my basic paradigm
for learning, if I have to explain it in a hurry.
(Tom Bourbon [931115.1309])
Hans, it is clear that many of us on the net think the topics you raised
are important. It is equally clear that, absent additional information
from you about what *you* think, not what *we* (including Martin) think
you think, the tone of the discussion is taking a rather nasty turn.
I hope that this and my previous post have cleared up any remaining
uncertainties about what I mean -- although probably not on the signi-
ficance of feedforward processes in humans where we seem to have staunch
defenders of "feedback only". By the way, Martin interprets me correctly,
although he doesn't always agree with me.
(Martin Taylor, 16-NOV-1993 18:20:18.56)
A single mechanism can
contain both, such as the Lang-Ham model. Better models have been
proposed, however. Indeed, a complete theory is now available to
design "optimal" systems.
Do you know of any reference that might be technically accessible to
me on this question--i.e. one that goes into the intuitive structures
rather than the complex mathematical details? I once was an engineer
considering graduate work in control theory, but that was several decades
ago, and my mathematical processes have rusted solid since then. I'm
just now trying to recover some Laplace transform understanding, but
anything beyond that might give me trouble.
A good reference textbook might be "Self-tuning Systems in Control and
Signal Processing" by P.E. Wellstead and M.B. Zarrop; Wiley, 1991. It is
not "deep"; its mathematics is not overwhelming and it is a nice intro-
duction that presents a much needed unification between signal processing
and control, which have much more in common than is often thought. The
disadvantage of not being "deep" is, however, that it presents a "toolbox"
of methods, without showing how these methods relate at a higher level of
abstraction. But that would require more math than you seem to be inclined
to.
(Rick Marken (931116.1300))
In my view, feedforward has an important place in
control, and is most fruitfully combined with feedback control.
You make this claim even though you have presented NO evidence (other
than the notorius "walk in the dark" anecdotes) that feedforward is
needed to explain any aspect of human behavior.
What is "needed"? Your models show that, at a low level of the hierarchy,
you can get away with feedback only. In the past, and now again, I have
given you both examples and theory that show that feedforward can IMPROVE
control, and that the improvement can mainly be found in an increased
speed of response -- when feedback information is available -- and in a
tolerance against missing obsevations -- when it is not. At higher --
slower -- levels of the hierarchy you will start to NEED feedforward.
And what is "explain"? When you "explain" a system, you reduce it to
simpler concepts/components and their interactions. If you allow feedback
components only, feedforward will never be able to "explain" anything.
But don't assume that successful application of feedforward in
engineering means that feedforward MUST be a part of models of
living systems. Wait for the behavioral data.
Don't forget that feedforward is the only mechanism for motion available
to those simple organisms (viri, some bacteria) that do not have their own
locomotor apparatus. So at least in these cases feedforward MUST be a part
of models of living systems. Or is that sophistry?
(Gary Cziko 931116.2200 GMT)
It might be interesting to consider why the VOR gets away with feed-
forward. Little or no disturbances? Muscles which don't have to work
very hard and therefore do not usually tire? The spherical shape of
eyeballs which makes their movement more or less independent of gravity?
That is a very nice summation of conditions under which a feedforward-only
system (with slow recalibrations) might work sufficiently accurately.
Greetings,
Hans