Output and the Test

[From Bill Powers (970109.1230 MST)]

In talking with Bruce Abbott about modeling of the digestive system, I
realized that we need to talk about the role of a control system's output in
the Test. We have to distinguish between the basic physical chemistry of the
body's "power supply" and the control systems associated with it, and one
way to do this is to look for places where the output of a control system
can alter the basic operation of an otherwise passive physical system.

When you just consider the flow of food into the body, and the subsequent
expulsion of waste, there are big basic chemical systems to consider, in
which processes in one compartment lead to processes in another. There are
flows of material between compartments. If this were a purely passive
process, the flows would be determined by concentrations in the source and
destination compartments, according to the reaction constants and physical
processes like diffusion. However, most of these flows are mediated by
enzymes, and the concentration of enzymes is affected by low-energy
processes of many sorts -- that is, processes which themselves carry little
energy and communicate through low-energy chemical or neural signals. The
places where such enzymes participate are natural control points, where the
outputs of control systems could alter the high-energy processes. The idea
here is similar to the way a low-energy neural signal can vary the flow of
chemical energy into a muscle.

To pick another example of historical interest, consider a steam engine.
Into the engine comes a flow of pressurized steam. The steam causes a piston
to move, which turns a crankshaft and wheel and also operates a valve that
switches the steam back and forth between the ends of the cylinder, keeping
the motion going. The crankshaft drives a pulley which drives a long endless
belt that passes out into the factory and back, passing along the ceiling
over the lathes and drill presses and stamping machines and forge fans. Each
machine can be turned on by tightening a pulley against the moving belt or
tightening another belt around an idler pulley.

So we can trace the process from the boiler to the cylinder and its valves,
through the piston to the crankshaft, through the long belt to the machines
in the factory, and finally to the work that is done in cutting or shaping
metal and wood. This is the "machine" of the 18th Century.

When James Watt came along, he tackled a problem that this big machine had.
When no lathes or drills were being powered, or only a few, the steam engine
would run at a brisk speed. But as more and more loads were added, it would
slow down because of the drags against the long belt and all the machine
tools would run more slowly, or even stall. Furthermore, as the fire under
the boiler burned faster or slower or as the water level changed the steam
pressure varied, which also cause the speed of the steam engine and the belt
to change.

Before Watt came up with his invention, there used to be a human being who
stood beside the machine and operated the steam valve at the input to keep
the belt speed from changing too much. The steam valve could be turned by a
moderate effort, but it caused large variations in the transmission of much
larger forces through the system. The steam valve was a place where the
output of a low-energy control system could alter the normal sequence of
processes that connected the fire under the boiler to the speed of a lathe
in the factory.

With the engineer acting, the steam pressure could rise and fall and the
loads on the long belt could vary, while the belt speed was held essentially
constant by the engineer. But if the engineer went to sleep or fell ill, the
belt speed would simply vary with the steam pressure and the load; machines
would jam and the factory would come to a halt. What was needed was an
automatic way of operating the steam valve at that natural control point in
the system.

We all know what the solution was: a flyball governer that sensed the speed
of the crankshaft and converted any errors into the action of a small piston
on the main steam valve, borrowing a smidgen of steam to power the gadget.

But we're considering the output of this gadget, not the input. What would
make someone suspect that a control system is at work here? First, anyone
looking for a control system would have to analyze the whole system as it
would operate if there were no control. The analysis would be essentially
what was described above: a causal sequence in which each process depended
on the process before it and acted on the next process in line. Every step
is understandable in physical cause-effect terms. From this analysis we
could predict how fast the system would run with various loads and various
steam pressures.

One factor in a complete analysis would be the constriction on the inlet
flow of steam at the point where it passed through the inlet pipe. If the
flow were highly constricted the system would run slowly; if the pipe were
large and unobstructed, the system would run much faster (for a given load).
A valve in this inlet pipe would provide a variable constriction, so to
compute the speed of the system one would have to know the setting of the valve.

We would begin to suspect the existence of a control system if the belt
speed did not vary nearly as much as we would predict on the basis of our
analysis, when the steam pressure or the load varied. This is how the Test
for the controlled variable is usually described: we begin by looking for an
effect of a disturbance, an effect which should occur but doesn't.

Once we see that such a lack of effect is occurring, we can start asking why
it doesn't occur. Obviously, something in the chain of processes between
fire and lathe is changing. But it's not just the change that is
significant, because there are always changes in the intermediate processes
as pressure and load vary; what's significant is that the change is of just
the right kind to cancel the effects of varying loads and pressures on belt
speed. Something that we took as a constant of the system when we analyzed
it is actually a variable.

Eventually, we will discover that the "variable constant" is the
constriction due to the setting of the valve in the inlet pipe. We find that
as the belt speed tends to slow down, the valve opens a bit more, lessening
the constriction, and when the belt tends to speed up, the valve closes a
bit, increasing the constriction. We find this whether it is Watt's gadget
or the stationary engineer that is doing the controlling.

At any one setting of the valve, the whole system works exactly as always in
a purely cause-effect manner. But we discover that the setting of the valve
is not a constant any more; it varies along with steam pressure and loads,
and does so quickly and sensitively enough to change the entire character of
the overall cause-effect process. In fact, it seems to _reverse_ cause and
effect. If we see the belt slow down a bit due to an increased load, we find
that the steam pressure at the inlet actually falls, as if the load is
somehow acting on the boiler, backward through the causal chain. Of course
we know now that this is due to the increased opening of the inlet valve, so
steam is being drawn from the boiler at a faster rate.

So we have discovered the place where the _output_ of the control system is
acting. It is acting upstream from the place where we found the variable
(belt speed) that should have changed but didn't, or at least didn't change
as much as it should have according to our initial analysis.

Once we know where the output is acting we can start backtracking. What is
causing the steam valve to change its setting? This leads very quickly to
James Watt's little gadget, which we find perched on top of the steam
engine. We find the small piston and linkage that moves the main steam
valve, and going still further backward the small valve that operates that
piston using a little of the inlet steam, and then the spinning flyball
mechanism which, as the balls separate and come together, moves the lever
that operates the small valve. And what determines how fast the flyballs are
spinning? The crankshaft speed, which is directly linked to belt speed. We
are finally led by this backtracking process to the device that senses
exactly the variable we found to be unnaturally stable, downstream from the
place where the output acts. The final step, of course, is to show that the
variations in belt speed that do occur are a joint effect of steam pressure,
load, and valve setting. The dependency on valve setting closes the loop.

In this way of applying the Test, we look for the output effect first, and
then backtrack from there to discover, last, what the controlled perception
is. The principle is simply that for every effect we observe (like the
opening of the main steam valve) there must be something causing it (like
the movement of a link attached to a small piston). And when we find that
cause, we treat it as another effect, and look for _its_ cause. This leads
us backward around the closed loop until we have accounted for everything.

In this way of looking at control, we start with a physical process that can
be explained entirely in causal terms, or in terms of normal physical laws.
We detect control by observing a departure from the processes that we would
deduce entirely on physical grounds. Then we look for the "constant" in the
physical process which is actually a variable, and backtrack systematically
to explain why that variable is changing exactly as it does. This leads us
backward around the loop until we find that the ultimate cause of the
variation with which we began is the same variation.

The last step of all is to invent control theory to explain how this strange
closed loop of causation can possibly behave as it does.

Somewhere in my files I have a woodcut picture showing a panoramic view of
the inside of the Great Hall of Industry at the Columbian Exposition of
1895. The hall is full of machinery, and in the foreground is the giant
steam engine that powers all the exhibits through a long moving belt. Just
discernible at the top of the steam engine is a little cluster of objects,
with a flyball governer at the top, a tiny object in this hall of monstrous
devices. If you didn't know it was there, you could easily overlook it. But
we now know that this small decorative object is what really controlled the
speed of every machine in that huge hall. A tiny cluster of brain cells in
the body of a dinosaur.

I wonder if William James ever saw that exhibition.


Bill P.