Course Handout - Basics of Cybernetics
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written and published in Wales by Derek J. Smith (Chartered Engineer). It forms
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First published online 14:18 GMT 28th March 2003,
Copyright Derek J. Smith (Chartered Engineer). This
version [2.1 - links to graphics] dated 09:00 30th June 2018
Earlier versions of this material appeared in Smith (1997; Chapter 4). It is simplified
here and supported with hyperlinks.
1 - Control Engineering
(pre-1948)
One
of Humankind's greatest problems is the relative weakness of the human body.
Ever since civilisation began, humans have struggled
to supplement their physical strength by external means wherever possible. They
have used draught animals to pull their ploughs and carts, and variations on
the "mighty five" simple inventions (the lever, the wheel, the
inclined plane, the screw, and the wedge) to move their obstacles and erect
their buildings. But the bigger the weight involved, the greater the risk of
accident and injury. All power sources - be they your own muscles, harnessed
oxen, rushing water, wind, steam, or whatever - require control, and the more
powerful the power source, the finer that control needs to be. The name given
to the resulting technology is control engineering.
In
the early days, of course, control was exercised by the person using the
mechanism in question. For example, when the millers of yesteryear needed to
turn their mills back into the wind every time it shifted, it involved
manhandling several tons of wood and iron. And they had to put up with this for
about 600 years before Edward Lee, in 1745, developed the mill
"fan-tail" to do the job automatically for them [picture]. This
mechanism consisted of a small rotor mounted at the rear of the mill cap, and
set at a horizontal right angle to the main sails. As long as the wind struck
the main sails directly, the fan-tail stood idle. When the wind veered to one
side or the other, however, the fan-tail started to rotate one way or the
other, and drove gears which cranked the mill cap back into the wind again.
There
was a similar problem controlling the speed of rotation of the millstones. If
this got too high, then the driven stone tended to bounce around against the
fixed stone and the quality of the grain suffered as a result. Again,
adjustments could be made manually - a process the millers called tentering - but on a gusty day this would be a
full-time job in itself. This problem was eventually solved by an automatic
control system introduced by Thomas Mead in 1787, and relying upon the use of a
"centrifugal governor" [picture].
This was a double conical pendulum, that is to say, a pair of fly balls
suspended on hinged arms from a spinning base plate (a contrivance known about
for some time previously - but in miniature - to clockmakers). The base plate
was attached to the millstone drive shaft (so that its speed varied with the
millstone speed), and the faster it turned, the further out the fly balls would
fly under the influence of centrifugal force. It remained only to connect the
outward swing of the fly balls to some means of slowing the main drive and you
had a means of making continuous and automatic adjustments to your speed. This
adjustment was achieved either (a) by physically pressing against the turning
millstone, or (b) by variably "reefing" or "feathering" the
slats which made up the sails (or on occasions, indeed, by a combination of the
two).
As
it happened, the textile millers were having similar problems at about the same
time. Theirs came from the fact that the act of spinning requires the tension
on the threads to be very precisely maintained. Yet the steam engines which
were being installed to drive the spinning machines were very difficult to
control. When you put more coal in the furnace they went faster (about twenty
minutes later), and when you put them to work they went slower (because you
used up all the steam). And when they went faster they snapped all the threads,
and when they went slower the quality of the thread became lumpy. The textile
millers had been getting by for some time by employing men to adjust the steam
pressure manually, but this was expensive, and their complaints to the builders
of the engines prompted one of them - the great James Watt himself - to note
how effectively Mead's centrifugal governor had coped with the flour millers'
problem. It took Watt only a year to install a similar device on a steam engine
(1788), and it soon became the control mechanism of choice. As the machine came
under load, the speed decreased, the fly balls dropped, and more steam was
automatically supplied. If the machine got too fast, on the other hand, the
steam supply was just as automatically eased off.
A
good formal definition of this sort of governor is given by the physicist,
James Clerk Maxwell:
"A governor is a part of
a machine by means of which the velocity of the machine is kept nearly uniform,
notwithstanding variations in the driving-power or the resistance." (Maxwell, 1867:270.)
2 - Control Loops and Feedback
In
the preceding examples, the overriding principle is that of control, and to have
control you have to be able to manipulate information. Specifically, you need
to transmit information on how you want your mechanism to perform in the first
place, then you need to receive information on how things are currently going
(in order to keep that performance within tightly preset limits of
acceptability), and then you need to transmit information whenever you want to
make the necessary adjustments. This gives you two types of control
information. The transmitted information is feedforward - the
information which instructs a mechanism or process on what needs to be done,
and the received information is feedback - information coming back from
that mechanism or process, and telling you how things are progressing.
These
two fundamental types of information then circulate in a very special way in
what is known as a control loop. This is a mechanism (such as Lee's or
Mead's) for detecting deviations from some preset standard, and for taking
appropriate corrective action. The elements of a typical control loop are as
follows:
(a) Standard Setting: This is where a planned action is
initiated in a given device by giving it a flow of initial command information
(the feedforward described above). This sets the level of required
performance. In a thermostat, for example, it is where the dial on the wall
is turned to the desired temperature, in a steam engine it is where the
centrifugal governor is adjusted to deliver a given output r.p.m.,
and in a single-handed yacht it is where the automatic steering gear is set to
maintain a certain angle to the wind while the yachtsperson goes below to get
some sleep. The unit which stores this standard is called the "comparator".
(b) Output Monitoring: This is where the ongoing
progress is somehow measured, to make sure that things are going to plan. The
unit which carries this process out is called the "sensor",
and the information it senses is "fed back" to the comparator for
evaluation.
(c) Comparison: This is where actual performance
is compared with required performance. It takes place in the comparator,
and generates, in turn, what is called an error signal. The error signal
shows the extent of the divergence of actual away from required performance,
and is the basis of the corrective action which then needs to be taken. In our
thermostat, for example, the error signal might be saying that the room you
wanted kept at 65o was actually at 62o.
(d) Compensation: This is where remedial action is
taken by the device controller to reduce the error signal. This remedial
action can take many forms. It might simply be to switch a process on or off in
its entirety (which is what your living room thermostat does to your central
heating boiler). Or it might involve something slightly more complicated, such
as fractionally turning a device up or down. Or it might involve something even
more complicated still, such as arranging for the resulting corrections to be
roughly proportional to the size of the error signal. It is also possible to
reduce the error signal by asking for the standard to be adjusted, but this
requires extremely complicated logic.
(e) "Hunting": This is an inability on the
part of a control system to establish a smooth level of performance. It is
where output "pulsates" above and below the required performance level,
typically as a result of "shortcomings in the governor or other speed
control systems" (Chambers Science and Technology Dictionary). It
occurs because there is always a time-lag between the detection of an error and
the application of the correction. Moreover, if the correction is not carefully
applied it is easy to over-compensate. Thus, if you need to steer left but
overdo it, you will have to correct to the right; whereupon you might overdo it
again and have to go left a second time; and so on, and so on, until either you
learn to steer more gently or you end up hitting something.
Figure
1 shows these elements at work in a simple control system. Look for
feedforward, feedback, and the various elements of the control loop, and note
especially that the whole process is self-regulating - you switch everything
on, set the standard, and then leave it to look after itself.
Figure 1 - A
Simple Control System: The
standard, or "required", level of performance is stored in the comparator
(shaded, lower centre). Performance is then regularly sampled by the sensor
(shaded, right), and compared with the stored standard. If a discrepancy is
detected, an error signal is passed to the device controller
(shaded, upper centre), and suitable corrective action taken. Note the
generally clockwise direction of the feedforward and feedback aspects of the
cycle. Note also how important it is to distinguish the occasional external
manual elements of the process (beyond the left system boundary) from the
continuous internal automatic ones (between the system boundaries). A
considerably more sophisticated version of this system is shown in Figure 2. If this diagram fails to load automatically,
it may be accessed separately at |
Enhanced from a black-and-white original in Smith (1997; Figure 4.2). This version Copyright © 2003, Derek J. Smith. |
3 - Negative vs Positive Feedback
In
fact, two types of feedback need to be identified, namely negative and
positive. Negative feedback is where corrective action is taken to reduce,
or "damp", the amount of an error. This is the sort of
feedback which gives us the classic "closed loop" control system
described above. It also gives us the feedback we are already familiar with in
biology under the name homeostasis (Cannon, 1927). Positive Feedback,
by contrast, is where the correction is made in the same direction as
that of the original displacement. Each pass around the feedback cycle thus magnifies
the displacement instead of diminishing it. This means that we can no longer
refer to the displacement as an "error", because not only do we want
it to be there for some reason, but we also want it to be bigger than it
already is. Positive feedback is only needed in control systems if the amplification
of a signal is needed. Indeed, neurophysiology itself only started to make real
advances with the coming of positive feedback electrical amplification systems
capable of sufficiently magnifying the very small neural currents involved.
Without positive feedback we would never have had the EEG nor
the microelectrode.
4 - The Servomechanism
Another
important control concept emerged with the development of power-assisted
steering for ships. Here, too, the essence of the problem was that muscle power
alone was not enough. The earliest sailing ships, for example, were steered by
trailing an oar over the stern. It then occurred to people to fix this oar in
place on "hinges" so that it became a rudder (Pliny attributes this
invention to Tiphys, helmsman of the Argo, and
a member, therefore, of Jason's famous argonauts),
and this arrangement was then improved by linking the rudder by pulleys and
ropes to a steering wheel placed more conveniently up on the bridge of the
vessel. The turning of all such rudders required considerable manual effort
especially in high seas, and in vessels of any size block-and-tackle systems
had to be used to "gear down" a lot of turns on the helm (ie. the steering wheel) to a small displacement of the
rudder itself.
With
the coming of steam, came the opportunity for steering systems to be power
assisted. This allowed greater speed of response to the helm, and thus greater manoeuverability and safety. The first steam-powered
steering system was patented by Gray in 1866, and installed in the SS Great
Eastern. The essence of the invention was that when the helm was moved to a
new position no direct attempt was made to move the rudder. Instead, the helm
moved a steam valve which powered a gear-train which moved the rudder. A manual
pressure on the helm of just a few kilograms applied a fully controlled and
highly demand-sensitive pressure on the rudder bar of many tons. And the clever
part came in shutting that power off automatically when the rudder reached the
desired position (at which time the physical displacement of the rudder had
"caught up" with the steersman's intent).
In
1868, the French engineer Jean Joseph Farcot patented
improvements to this sort of control machinery, and in 1873 published a book
entitled Le Servo-Moteur, thus introducing the
word servomechanism into the control engineer's vocabulary. Here is a
formal definition:
"The 'servo' notion
implies that heavy work is done by a strong slave under the direction of a
master, who by virtue of this assistance need exert no effort beyond that of
formulating commands." (Roberts, 1978:116.)
Servomechanisms
(or "servos", or "slave systems") are important because
they allow a small control system to control pieces of far heavier machinery.
Thus the helmsmen of the late twentieth century can easily have one-finger
control over the steering of a supertanker - an amplification factor of about
1:1 billion. And much the same sort of thing happens in biology, because our
brains are small control systems and our bodies are pieces of far heavier
machinery. In fact, neurons weighing in the order of 0.00000001 gm can control
a body weighing around 100,000 gm - a amplification
factor of 1:1,000 billion. (Or even more, should the neuron happen to be
controlling the finger which is steering the supertanker!) This being so, it
helps if we are able to recognise servomechanisms
"hidden" away inside more complex systems, because it will give
insight into the modular organisation of those
systems. There are seven distinctive features to look for when doing this:
* A servomechanism's control standard is set from some
distance away.
* A servomechanism has local access to the power it needs
to do its job.
* A servomechanism can hold indefinitely to a given
setting, but .....
* ..... ideally, it
should be able to "interrupt" its higher controller should it start
to experience significant difficulties in holding that setting.
* Ideally, it is sensitive, quick to respond, and
properly damped, so that it responds smoothly and without hunting (see earlier
this chapter).
* Ideally, when told to seek a new setting it applies its
changes proportionately to the size of the change required, that is to say, big
changes are implemented at a greater rate of change than small changes.
* Ideally, it is "user friendly", that is to
say, it is richly equipped with built-in safeguards.
It
is also useful to study the distribution and use of memory resources in a
control system. We have already mentioned that a comparator cannot actually do
its job at all without some sort of memory capability, and things get worse in
servo-assisted systems due to the physical separation of servo and controller.
This point can be particularly clearly seen in systems which make use of efference copy and reafference
- terms introduced by Von Holst and Mittelstaedt
(1950) to describe a clever way of coping with the potentially excessive
feedback found in most biological systems. The problem is that motor activity -
efference - does not just induce movement, but
also affects what is picked up by the senses. As soon as you start moving,
proprioceptors will tell you about limb position and balance, cutaneous
receptors will tell you about changes in touch, pain, temperature, and
pressure, homeostatic systems will signal requests for blood pressure and blood
glucose maintenance, and special senses (eyes and ears) will detect the changing
visual and auditory shape of the world. The senses, in short, are
involved every bit as much in motor activity as are the motor pathways.
What
efference copy systems do, therefore, is subtract
what you expect your senses to tell you next from what they actually tell you
next. This gives zero if things are going to plan, but a non-zero error signal
if they are not. This comparison is achieved by momentarily storing an image of
the main motor output - the efference copy
- and by then monitoring what is subsequently received back from the senses -
the reafference. The principal benefit, of
course, comes when the two flows totally cancel each other out, because this
leaves the higher controller free to get on with more important things. Every
now and then, however, the system encounters some sort of external obstacle, or
"perturbation". This causes the reafference
not to match the efference copy, and this, in
turn, causes the higher controller to be interrupted with requests for
corrective action. And because the sensors in an efference
copy system thereby become capable of confirming for themselves that the
effectors are working to plan, this is a highly efficient way of reducing
unnecessary network traffic. Here are the formal definitions:
"[Efference
copy is] basically a copy of the motor output [and] in some way represents the
expected pattern of sensory messages that would be produced in the absence of
external interference with the action of the effectors. [Reafference
is] the message returned to the nervous system, in consequence of the issue of
the command." (Roberts, 1978:141.)
An
even more advanced way to make use of past experience is to develop some form
of predictive control system, that is to say, a system where the efference at every level of the control hierarchy is
prepared well ahead of actual need (up to seconds ahead in many cases, but
hours or even days ahead in the case of more "strategic"
predictions). Indeed, there is considerable insight to be gained (even as
non-technologists) by considering the problems faced by robotics engineers. Maravall, Mazo, Palencia, Perez,
and Torres (1990), for example, are among the many research teams working in
this area, and have obtained good results with robots capable of constantly
making guesses at what is coming next. Figure 2 shows these advanced concepts
at work in a schematised servo-assisted system.
Figure 2 - A
More Sophisticated Control System: This
is a more powerful version of the control system shown in Figure 1. The three
original modules are still there (albeit the internal logic is no longer
shown), only now they have to support multiple muscle groups (top
right), which, properly coordinated, allows the organism to develop
significantly more complex behaviours such as swimming, running, flying, etc.
There are also several important new modules (and important new memory
resources to go with them). (1) a higher order
controller (far left) replaces the external manual source of command
information. This means that there is no longer any high-side system
boundary, making the new layout self-controlling. That is to say, it is now
capable of willed behaviour, or "praxis"
(for more on which see Chapter 6). (2) multiple
sensor devices (bottom right) allow more complex sensory monitoring of
the outside world, but only at the price of having (3) some sort of categorising
process (bottom centre) to prevent the higher order controller being
overloaded. At the same time, an important subset of the output devices has
to be devoted to sensor orienting (4), that is to say, to keeping the
sensory devices pointed in the right direction for maximum sensitivity. The
output devices need also to be equipped with a contention scheduler
(5) (top centre) to prevent different devices working at crossed purposes.
Fortunately, an efference copy system
(6) (at hub) allows traffic from right to left to be minimised. Predictive
control is provided by components at all levels. The higher order controller "thinks
ahead" (7), the device controllers deploy a repertoire of prelearned skills (8), and the peripheral
systems know from their efference copy what is
expected next (9). Note that this diagram, if redrawn to Yourdon notation and
rotated 90o to the right (so that the system boundary is at the
bottom), has many points of congruence with Frank's organogramm and Smith's (1993, 1996) six-module model of cognition. Note especially that Denmark Technical
University's Rodney Cotterill (eg. Cotterill,
2001) is building a convincing theory of consciousness based around the
brain's efference copy system - for more on this,
see our e-paper on
Short-Term Memory Concepts in Computing and Artificial Intelligence, Part 5
(Section 3.12). If this diagram fails to load automatically,
it may be accessed separately at |
Enhanced from a black-and-white original in Smith (1997; Figure 4.3). This version Copyright © 2003, Derek J. Smith. |
5 - Cybernetics
It
does not often fall to an individual scientist to be the creator of a new
science, but in 1948 the engineer Norbert Wiener gave a name to the emerging
science of control. The name he chose was cybernetics, an anglicisation of kybernetes,
the Greek word for "steersman". (Which,
incidentally, is also - via the Latin gubernator - the root of the
English word governor, making it doubly appropriate for Mead's
centrifugal governor to have been called what it was.) The key
publication was Norbert Wiener's 1948 book "Cybernetics, or Control and
Communication in the Animal and the Machine" (although Wiener actually
credits the French physicist André Ampère with having discussed cybernétique principles as early as 1834). By its
nature, Wiener's new science automatically embraced the concepts of feedback,
control loops, servo-mechanisms, information, communication
channels, and systems theory. Porter (1969) provides a decent formal
definition:
"Cybernetics is concerned
with the communication and manipulation of information and its use in
controlling the behaviour of biological, physical,
and chemical systems. It is the basic science underlying the processes of behaviour in biological systems." (Porter, 1969:vii; emphasis added.)
Key Concept -
Cybernetics: In fact, cybernetics has both a strict definition and
a variety of looser usages. Very strictly speaking, it is the science of
guidance. Less strictly speaking, it is the science of control in general.
It thus has applications in a variety of areas, such as sociology and commerce
(not relevant to this course) and biology (directly relevant to this course -
see Chapter 2, etc.). Generally speaking, however, it is anything remotely
connected with computing or robotics, and because it sounds such a nice word it
is especially popular with writers of science fiction. Thus we have the cybermen in "Dr
Who", cyberspace in "Red Dwarf", the cyborgs in
the "Terminator" movies, etc. ad nauseam.
And
why does all this matter? Because cybernetics tells us
how to control complex, hierarchical, and distributed systems, and because the
biological nervous system is a complex, hierarchical, and distributed system.
The following organisational rules, for example,
apply to all sophisticated control systems, including biological ones:
* There will be peripheral and central modules. The
peripheral ones - the sensory and motor systems - are those which interact
directly with the environment, and the central ones
are those which do not.
* Many of the peripheral modules will be involved in some
form of servomechanism.
* Many of the central modules will be controllers (of the
peripheral ones).
* The trade-off between modular complexity and network
complexity will need delicate tuning.
* As many decisions as possible will need to be made
within the servomechanisms, thus avoiding unnecessary traffic to and from the
controller. There will therefore be especially heavy traffic between sensory
and motor devices at the periphery (just as with the physiological spinal
reflexes).
* There will be coordination of the controllers (by some
sort of "super"-controller). (Remember that Chapter 6 is dedicated to
hierarchical control systems of this sort.)
* There will be integration of the action of the
servomechanisms, in order to prevent different devices working at crossed
purposes. (Consider what happens if, in your car, you press the accelerator and
brake pedals simultaneously!)
* Comparator processes will require memory to hold efference copy instructions pending the
arrival of the reafference.
* Control processes will require memory to allow efference instructions to be packaged up into skills.
* Supercontrol processes will
require memory to allow continuity of purpose at the behavioural
planning level.
References
Cannon, W.B. (1927). The James-Lange theory of
emotion: A critical examination and an alternative theory. American Journal
of Psychology, 39:106-124.
Cotterill, R.M.J. (2001).
Cooperation of the basal ganglia, cerebellum, sensory cerebrum, and
hippocampus: Possible implications for cognition, consciousness, intelligence,
and creativity. Progress in Neurobiology, 64(1):1-33.
Maravall,
D., Mazo, M., Palencia, V., Perez, M.M., and Torres,
C. (1990). Guidance of an autonomous vehicle by visual feedback.
Cybernetics and Systems, 21:257-266.
Maxwell, J.C. (1867). On governors.
Proceedings of the Royal Society, 16:270-283.
Porter, A. (1969). Cybernetics Simplified.
London: English Universities Press.
Roberts, T.D.M. (1978). Neurophysiology
of Postural Mechanisms (2nd Ed.). London: Butterworths.
Smith, D.J. (1997). Human
Information Processing. Cardiff: UWIC. [ISBN: 1900666081]
Von Holst, E. and Mittelstaedt, H. (1950). Das Reafferenzprinzip.
Naturwiss., 37:464-476.
Wiener, N. (1948). Cybernetics.
Cambridge, MA: MIT Press.
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