[Martin Taylor 950523 10:30]
Bill Powers (950519.1700 MDT)
You:
In a model that simulates a continuous waveform, you cannot represent
a step function legitimately.Hans:
Why should a model only simulate continuous waveforms? Our models were
discrete, and the can adequately handle even square waves, as my demo
shows.You:
Because implicit in all the modelling is the notion that the models
simplify control that occurs in real live systems that have to work
in a continuously changing world.But that isn't an answer to Hans' point. Actually, you can apply any
disturbance you like to a control system; we've happily applied step-
disturbances to human beings doing tracking. All that happens is that
the step causes a large error to appear, and the control system corrects
it as fast as its design will permit.
It is an answer to Hans' point, which is a question about MODELLING, not
about what disturbances one can apply to what kinds of control systems. One
can apply any kind of disturbance to any kind of control system, if you
have the physical means to do so. The question is: if you apply disturbance
A to a control system of type X, will a control system of type Y behave
the same way when you apply the analogue of disturbance A to it.
Specifically, if you apply a step disturbance to a control system in a
discrete model, will the modelled continuous system behave in the same way
when a step disturbance is applied to it?
Hans said that you can apply step disturbances in a discrete control
system. Yes you can. You say you can apply step disturbances to a
continuous system. To a reasonable approximation, so you can. Neither
statement is relevant to whether what happens in one system can be safely
used as a description of what would happen in the other if it were to be
tried. And that's the function of a model.
···
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(Response to private message)
Bill,
I'm sorry, but I printed out your code before leaving on Friday, and then
left it on the printer, so I haven't examined it.
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Hope granddaughter was worth every minute of the trip!
Martin