Learning, Detecting Control -Reply

[Hans Blom, 960222b]

(Rick Marken (960220.1100))

One of the first things that control engineering students learn is
how to reduce expressions of form (2) into expressions of form (1).

(1) effect = f(cause)
(2) effect = f(cause, effect)

They learn to analyze a closed loop system as though it were open
loop? Why?

In order to get a global picture of what goes on rather than a local
one; this moves the analysis up a level, one could say. Note that, if
there is any noise or uncertainty in the system, an expression like
effect = f(cause, effect) forces the analysis to be local to the
point in time where the effect occurs. This is maybe clearer when the
expression is rewritten as effect (t) = f (cause (t-1), effect (t-1))
where the time is made explicit. This local analysis makes answering
higher level questions like "what is the ultimate effect of a cause"
difficult, which is readily answerable from (1).

So to say that there is a "fundamental difference" between the two
"types of causality" will not be appreciated by many control
engineers.

But do _you_ appreciate it? (My guess: no)

Sometimes. Depends on the type of question that needs an answer. When
considering stability, for instance, an expression of type (2) is
more helpful. From

    effect := constant_cause + 2 * effect

I see immediately that we have an unstable system. Sometimes an
expression of type (1) is more helpful. From

    effect := 2 * cause

I see immediately that the underlying control system (if there is
one) is stable, and that there is a linear relation between cause and
effect. Form (1) has the advantage that it is a "higher level" view
which does not contain unnecessary detail anymore.

Greetings,

Hans

ยทยทยท

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Eindhoven University of Technology Eindhoven, the Netherlands
Dept. of Electrical Engineering Medical Engineering Group
email: j.a.blom@ele.tue.nl

Great man achieves harmony by maintaining differences; small man
achieves harmony by maintaining the commonality. Confucius