[From Bill Powers (920325.2000)]
There's an important point about the open-loop, closed-loop argument that
we've been missing; I really feel slow in not catching it until now, while
reading Rick's comments about SR systems changing into closed-loop systems
and vice versa depending on the circumstances.
THERE ARE NO CLOSED-LOOP BEHAVING SYSTEMS (except those with negative
feedback internal to their nervous systems). The contrast we should be
making is between closed-loop and open-loop _situations_. If, in the
external world, there are connections such that an action by an organism
has an immediate effect on the relevant input to the organism ("immediate"
being defined in terms of the speed of action of the system), then the
situation is closed-loop. If the action has no immediate effect on the
relevant input, the situation is open-loop. You don't have to understand
the organization of the behaving system to distinguish open-loop from
closed-loop situations.
To say that an organism is organized as a control system with respect to
some specific stimulus is to say three things: first, that it subtracts its
input from an internally generated reference signal (or vice versa
depending on the external situation), to establish the effective zero point
of the input. Second, that its action is based on departures of the input
(as analogized in a perceptual signal) from the reference level (normally
specified as a reference signal). Third, that in the environment in which
the behaving system evolved, there is a strong effect of the output on the
input, IF THE NORMAL LINK EXISTS. The sense of this effect will be to
create feedback, the sign of the internal comparison or output process
being chosen for negative, rather than positive, feedback.
If a control system became organized in a specific environment so that a
strong external feedback link normally exists, it will behave in all
respects as a control system, controlling its own input information. The
environment, however, can change.
For example, suppose you're driving down a twisting mountain road and your
car suffers a complete electrical failure, ignition and all. Where you had
been negotiating the curves effortlessly, you now suddenly start making
huge steering efforts, almost more than you can produce, because _your
power steering is gone_. In the environment that normally connects your
steering efforts to the perceived position of the car on the road, the
feedback link has suddenly become much weaker; a given torque applied to
the steering wheel now has far less effect on the lateral motions of the
car.
Your internal system still has the same properties it had before. A given
perceptual error in position of the car still leads to the same increase in
steering effort, in the appropriate direction, as before. But the part of
the loop gain contributed by the external part of the loop has suddenly
dropped by a large factor, so the total loop gain has decreased to a small
fraction of its former value. As a result the error increases greatly,
causing greatly increased steering efforts. But your steering efforts,
large as they now are, control the perceived path of the car far less
effectively.
And what if the steering mechanism broke completely? You would still be
organized the same way inside, appropriately for controlling your
perceptions in a normal environment. But now the car would deviate greatly
from the path you want to see; the error signal would become enormous; your
output efforts would swing back and forth wildly between their maximum
limits in the final moments before the careening car finally went off the
road.
In this last scenario, you are still organized as a control system but
you're no longer in a closed-loop situation. Because the external feedback
link is gone, you are operating open-loop. The extreme actions show that
the error signal is far out of its normal range, and in fact indicate that
you have lost control.
Any organism that has evolved to control its own perceptions in a
particular environment can find itself in an open-loop situation. This can
happen not just through losing the feedback connection, but through
encountering such a large disturbance that your efforts to oppose it
saturate. Once you're producing maximum output to oppose a disturbance, any
further increase in that disturbance affects your input without opposition.
The loop is broken because now changes in the disturbance, which cause
changes in the perception and the error signal, no longer produce matched
opposing changes of output. So the situation has become open loop even
though you're exerting the maximum possible effort to maintain control.
In stimulus-response experiments, most often the applied stimulus is really
just a disturbance of some other input variable undetected by the
experimenter, a disturbance which the test organism can successfully cancel
by altering its actions. This leads, as I have mentioned before, to
illusory stimulus-response laws that really reveal only environmental
properties.
But in some experiments, the experimenter gets hold of the actual input
that's being controlled. Rather than applying disturbing _influences_ to
that input, which the animal can counteract, the experimenter puts his own
vastly more powerful control loop to work and forces the input to change
regardless of the animal's efforts. This is called "varying the independent
variable." Doinhg so effectively puts the animal in an open-loop situation,
because its actions no longer affect its inputs. Now what you see are
strong reactions to the input, because the changes of input directly affect
the error signal, which is usually highly amplified to produce the output.
If the loop were closed, this high amplification would not create large
outputs; it would just keep the error small, the outputs being only what is
necessary to counteract normal disturbances. With the loop open, however,
this amplification creates extremes of output. The system is being operated
in a highly abnormal condition.
Footnote: I will never forget reading of an experiment in which the
researchers were trying to control for every possible interference and get
a reliable response to a stimulus out of a rat. They strapped the rat into
a narrow box and sewed its eyelids open so it couldn't avoid seeing the
stimulus light. They got the same response (from a leg, I think), after
conditioning, something like 80 per cent of the time, and gave up. They
were studying this rat in a totally open-loop situation -- how they thought
they would get any data about normal behavior escaped me then and escapes
me now.
When an organism that normally acts as a control system experiences an
open-loop situation, it becomes hyper-responsive to changes in its input
because those changes are no longer counteracted; they show up directly as
error signals. There will be hyperresponsivity to changes in reference
signals, too, because the reference signal also shows up directly as a
change in error signal. Normally the perceptual signal would immediately
catch up and the error would be kept from getting large. But with the loop
open, the perceptual signal no longer changes because of the output, and
the error signal remains large.
If the loop is opened by denervation, usually only lower levels of control
are affected. Given time, the higher level systems that normally use those
lower-level systems as means of action will reorganize to compensate for
the overresponse of the lower systems now running open-loop. The initial
instability caused by too high a loop gain gradually disappears as
reorganization lowers the gain in the superordinate control systems.
Nothing can be done about lower-level feedback dynamics that serve to
stabilize limbs; the higher systems are too slow to compensate fully for
dynamical effects. But higher-level control of a sort will be restored.
This is what is meant when researchers who use denervation methods say that
denervation shows that feedback is not necessary for "normal" behavior.
···
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While there are no closed-loop systems, there are open-loop systems,
systems containing no provision for their actions to affect sensitive
sensory inputs, so that all situations are open loop.
Organisms have evolved to take advantage of the fact that their outputs
affect their own sensory inputs. In fact they have evolved elaborate
sensory systems specifically designed to detect the effects of essentially
every possible action, external and internal to the body.
But what of systems so organized that there are no such effects in any
environment? How do these systems have to be organized in order to have
reliable objective effects on their environments? It is possible in
principle for such systems to evolve, even among organisms, strictly on the
basis that the objective effects of their actions affect their survival to
the age of reproduction. The question is, what properties must evolve so
that the resulting actions will counteract external influences that
interfere with surviving to reproduce?
First, the actions must be protected from external disturbances that could
change their effects, or else must be produced by such a massive mechanism
that normal disturbances are incapable of altering the effects, or else
must somehow be compensated without feedback (see below).
Second, the actions must be produced in a uniform way, so that the output
calibration of the system in terms of external outcomes will never change
enough to alter the critical effector outputs or their objective
consequences.
Third, if the actions are based on sensory inputs, the calibration of the
sensory inputs must also remain absolutely stable, so that the same
external situation will always result in the same effective stimulus.
Fourth, if significant disturbances remain possible, then the sensory
system must detect each separate possible cause of a disturbance, convert
its state reliably into a calculated effect on the outcome, and inject a
compensating stimulus into the system that opposes the effect on the
outcome, adjusted to include the behaving system's own properties, all
dynamical effects, all nonlinearities, all changes in the relationship of
the potential disturbance to the outcome, and all changes in the link
between effectors and outcome.
If this set of requirements doesn't seem beyond meeting, there are more. In
most behaviors, the critical outcome doesn't depend directly on the
effector output, but on other variables that depend, often loosely, on the
effector output. When we consider locomotion, the arrival of an organism at
a particular place, or even the placement of its limbs in a particular
orientation, results from the application of muscle forces to limbs, and
the subsequence effects of limb forces on other objects. To go from forces
to positions requires two time integrations, nonlinear ones when jointed
limbs are involved. Time integrations are notoriously sensitive --
hypersensitive -- not only to initial conditions, but to very small errors
of computation. In living systems we have to add the fact that even an
accurately computed output can't be translated accurately into output
forces by real neurons and muscles; these inaccuracies, too, contribute to
the error in the final integrated result. While a simple brief movement
might come somewhere near the necessary result, a long series of movements
occurring serially, such as walking across a room to a source of food,
would begin each new movement with all the accumulated errors of the
previous movements. These errors would remain undetected, because of the
absence of feedback information. The only way of detecting failure would be
to fail and die.
I think the only reasonable conclusion is that no behavior of even moderate
complexity and short duration can be counted on to produce a reliable
effect in an open-loop situation. Given the wonders of electronics and
incredibly accurate mechanical constructions, and environments free of
unpredictable disturbances, open-loop systems can produce reliable results
far into the future, requiring only occasional mid-course corrections. But
this is not even remotely possible for living organisms whose input
sensitivites vary, whose muscles fatigue, and which live in environments
where disturbances are ubiquitous and mostly hidden from the senses.
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So open-loop systems can exist. Even control systems, in an open-loop
situation, will behave like open-loop systems: inaccurately and unreliably,
if they are living systems rather than marvels of mechanical engineering
and stable precision electronics. In the competition for survival, open-
loop systems which can't detect the consequences of their actions directly,
while they are being brought about, don't stand a chance when their
competitors are control systems equipped to sense the outcomes of their own
actions and control them.
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Gary Cziko asked what I meant by "tight coupling" in a recent reply to
Randy Beer. In one case presented by Beer, there was an output that was
sensed and in fact controlled, but the real "controlled" variable was some
other effect of the output, not sensed. I said that if this other variable
were tightly coupled to the controlled output, it might well be unaffected
by disturbances, and so effectively be controlled by the system.
Suppose the controlled output of the "plant" is a motor, and that the
controlled aspect of the motor output is rotational velocity. A tachometer
will provide a signal representing angular velocity. This signal will be
compared with the input signal specifying desired angular velocity, and the
error will be amplified and used to drive the motor. The result will be
that disturbances like varying loads on the motor will have little effect
on the speed of the motor. With a sensitive control system, the effects of
varying loads can be made undetectable.
Now suppose that the real controlled variable is to be the rotational
velocity of a wheel. If the motor has a thick short shaft on which the
wheel is directly mounted, then applying braking forces to the wheel will
not be able to slow the wheel, because slowing the wheel would entail
slowing the motor, and the tachometer signal would drop very slightly,
raising the drive to the motor enough to prevent any significant drop in
speed. This is "tight coupling."
On the other hand, suppose there is a fluid-drive transmission between the
motor and the wheel whose speed is to be "controlled" in this way. If a
braking or accelerating torque is applied to the wheel, the wheel will
begin to turn slower or faster than the motor. The motor itself will
continue to turn at a constant speed, because its speed is controlled. But
the wheel will slip or advance relative to the motor, because of the "loose
coupling" through which it is driven. The fluid drive mechanism will apply
some corrective force, but the speed of the wheel will not be controlled
nearly as well as that of the motor.
If we now imagine the shaft connecting the motor to the wheel as a quarter-
inch diameter steel rod 100 feet long, it's clear that the wheel's angular
position can easily be disturbed relative to the motor shaft's angular
position. We would probably stop the wheel by hand, briefly, while the
motor put a twist into the long shaft. The motor itself would continue to
spin at an inexorably-controlled speed, but the wheel could easily be
disturbed in angular position and momentary speed over a wide range of
variation. That would be very loose coupling.
In both of the loose-coupling conditions, accurate control could be
restored (mostly) by moving the tachometer to the position of the wheel, so
it measures directly the speed of the wheel. In the case of the long shaft,
some dynamical filtering would be needed for stable control, but in the end
the wheel would resist braking or accelerating torques with great precision
(even if it might respond a little more slowly to sudden torques than the
tightly-coupled wheel would).
Of course now the motor shaft speed would become uncontrolled. A braking
force applied to the wheel would cause the motor to speed up -- permanently
in the case of the fluid-drive coupling, temporarily for the long shaft,
while the motor quickly wound up the shaft to create the necessary opposing
torque.
In "control-of-output" interpretations, it's always assumed that the
controlled output variable is tightly, nay rigidly, coupled to the position
where the feedback sensor is located.
Note that there is no way for an open-loop system to control a motor's
shaft speed without sensing the braking or accelerating forces applied to
the shaft by outside agencies. And then the control (actually,
compensation, which is not control) will only be as good as the
calibration, linearity, and constancy of the sensors and the motor's
response to driving signals.
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If any CSGer wants to have the kind of nauseating experience that Rick
likes to celebrate, read the opening main article in Science for 20 March,
1992.
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From Mary Powers:
[from Mary Powers]
Gary Cziko (920325) asks if Bill knows of anyone who understood
PCT well who has abandoned it.
Well, these are the people he ISN'T in touch with - with his full
plate it's hard to notice what's missing (or who).
I would suppose that a reasonable group to look into would be
people who came to at least two meetings of the CSG but are not
current CSG members. If you are really interested, I could
probably dig out the lists of attendees at CSG meetings (good
motive to do some filing I've been avoiding). What sort of
questions would you ask the drop-outs?
Mary P.
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Best to all from both of us
Bill P.