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

Thanks for your thoughts.  I will probably head in this direction of
talking about different sine waves and compare their frequencies and fft
plots and such.

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


On Mon, Sep 6, 2021 at 11:10 AM Clarence W. Rowley <cwr...@pr...>
wrote:

> 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...> 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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