[Hans Blom, 960214b]
(Martin Taylor 960212 15:30)
To me, at least, the heavyweight distinction between equilibrium and
control systems is that a control system needs a power source
_independent_ of the disturbance source.Is this necessarily so?
I think so, yes. A refrigerator is not a perpetual motion machine.
Any action in the world increases the overall entropy of the system that
includes the actor, and that includes control systems. A control system
reduces the entropy of the CEV--or at least maintains it against a
disturbance-induced increase. The action of the control system must include
a compensating increase in entropy. What this implies is a transfer of energy
through the acting system from a source to a sink. That sink is not the CEV.
The implication is that side-effects of control are unavoidable.
Remember that physicists sometimes call
thermal energy "free energy", with the connotation that it can be
_used_, at least if something is clever enough to have invented a
method to do so. Plants have, in that they rely on the "free energy"
of light; some bacteria do something similar.
UV photons have a high energy. They can break some biological molecules,
and in so doing the energy is absorbed (or at least some of it is) and can
be converted into chemical storage. Infra-Red photons aren't so useful. Their
energy is largely reflected from living plants (which may be why we don't
see infra-red--we'd be permanently dazzled). The light from the sun is
going from a high-energy source to the outer-space sink, by way of the
plant.
Control theory, at
least the PCT version of it, usually disregards power sources, power
conversion and power consumption, being more concerned with analysis
of the informational aspects of "the loop". I consider that an
oversight. As you note, an autonomous control system needs energy.
Where does it come from?
Food, usually. In other words, chemically stored energy from the sun,
on its way to outer space.
Usually, in what we are concerned with in PCT, the energetic aspects aren't
of much interest. There's enough to do the job, and the heating properties
of the side effects are negligible compared to the effects on the CEV of
other sources of disturbance. Besides, the side effects may well be carried
well away from the control system that generates them. Only when we are
concerned with starvation conditions and the lassitude (reduction in control
gain?) that goes with them is PCT much concerned with the energetics.
Consider Bill P's example of the hot bath (80 C, which would be enough to
injure a human). No human would control a bath at this temperature if the
sensor had to be an immersed finger. The sensor is, from the human's viewpoint,
a distance sensor--looking at the steam, immersing a hardware-store
thermometer... The human stays away from contact with it.
The effector is a heater, whose heat goes into the bath, but thence into
the atmosphere (or into the disturbing refrigerator). The act of controlling
the bath heats the room more than if the bath were simply brought to 80 C
and heavily insulated to stay at that temperature.
A control system is a cooling device.
Replace "is" with "can be viewed as", and I'm with you.
Sorry, I'll stick with "is." Of course, I'll grant that it's all perception,
and "is" applies to the real world out there, so that "can be viewed as"
is strictly speaking more accurate. But I want it to be clear that there
is more to this than that: "Similar formula's apply, and similar theoretical
considerations can describe either control or cooling." I want to claim
that _any_ control system is a kind of refrigerator.
Remember the degrees of freedom problem. The one degree of freedom that
a scalar control system cools is negligible numerically in comparison to
the Avogadro's number of degrees of freedom in a mole of gas or liquid.
(What is A's number, which I will call A? 10^24 or something like that?)
But is it non-zero, and when the world is viewed from the viewpoint of
the control system, that one degree of freedom is all there is. It sees
the cooling effect as macroscopic, whereas the heating effect of its side
effects, partitioned equally among Avogadro's number of molecules, is only
1/A in any single degree of freedom, including the one being controlled.
For all practical purposes one can ignore heat-like distribution
of side effects. Where one has to worry about them is when they retain a
low-entropy configuration so that they can affect the control degree of
freedom appreciably. And for those cases one doesn't need thermodynamics.
When there are a lot of scalar control systems operating together, then
one begins to worry about these kinds of thermodynamic consideration. If,
as you suggested a few days ago, one might contemplate controlling all N
degrees of freedom in the perceptible universe, one would find that a
refrigerator cannot do without its heat sink. And when the side-effects
are not dispersed among uncontrolled degrees of freedom, the same happens.
That's why I mentioned a few days ago the "hint" about reorganization and
efficiency in terms of control being cooling and side-effects being heating.
Even though side-effects are unavoidable, they can be minimized, and with
luck well dispersed. But that means efficiency, and the more efficient,
the better control. So even without competition and resource limitation,
control systems should ordinarily evolve to greater efficiency.
Martin