Re: [python-control-discuss] pedagogical controls question

[Clarence W. R. <cwr...@pr...>]

Hi Ryan,

This is something I've struggled with in my own teaching.  I don't have a great answer, but I'll tell you how I typically answer it.

Students usually understand that, for a linear system, if the input is a sinusoid at frequency w, then the output is a sinusoid at frequency w (and the amplitude and phase are given by the transfer function G(iw)).

It's true more generally that if the input is an exponential exp(st) then the output is also an exponential G(s) exp(st), where G(s) is the transfer function.  This holds whether s is real or complex.  So if s is real, you just have an exponentially growing (or decaying) input, and the output is also exponentially growing (or decaying) with a gain of G(s).  And if s is pure imaginary, then you are back to the case of sinusoids.

Best regards,
Clancy


==================

Clancy Rowley

Professor, Mechanical and Aerospace Engineering

Affiliated faculty, Program in Applied and Computational Math

Princeton University

On Sep 6, 2021, at 10:21 AM, Ryan Krauss <kra...@gv...<mailto:kra...@gv...>> wrote:

Not sure if this list is still active or if there is a good answer to my question.  I teach a junior level intro to dynamic systems course for manufacturing engineers who don't take dynamics.  There are some unique challenges based on whether or not skipping dynamics indicates a lack of conceptual understanding about more theoretical things.

Every year I get questions like "what is s?" or "what is the frequency domain?".  They seem to want some kind of an analogy that is very concrete (not abstract).  I have tried various things.  I think I can do a decent job explaining the frequency domain from a fourier standpoint, but how do you talk about the frequency domain when s has a real component (i.e. is not purely imaginary like in Fourier analysis)?

Any suggestions are welcome.

Thanks,
Ryan

--
Dr. Ryan Krauss
Associate Professor
Product Design and Manufacturing Engineering
Grand Valley State University
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