Article: Measuring Frequency Response

For embedded closed-loop control systems.

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Comments welcome (particularly if I made some stupid mistake).

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Tim Wescott
Wescott Design Services
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Tim Wescott
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Hi Tim,

Yummy, thanks.

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Christopher R. Carlen
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Chris Carlen

Note to self: make sure that it's clear that I'm doing swept-sine measurements.

The sweep is exponential, and some extremely vague handwaving in there about making it slow enough -- I should think about how to clarify that.

Generally the method as I use it, with the exponential sweep, moves things slowly enough that the transient response doesn't cause a great deal of difficulty -- particularly if you have the system operating in closed-loop, which generally causes the transient to settle out much faster than the initial sine wave.

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Tim Wescott
Wescott Design Services
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Tim Wescott

in article snipped-for-privacy@corp.supernews.com, Tim Wescott at snipped-for-privacy@wescottnospamdesign.com wrote on 03/25/2005 16:08:

just a first impression, i can't tell from the body of the article, but it appears in the code that you are doing swept frequency measurements. are you, or am i reading the code wrong ("startF", "stopF").

if you are doing *linearly* swept frequency measurements and your sweep rate is not slow enough, you might want to review:

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it's just to show what the apparent frequency response is and then how to correct for any deterministic error.

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Reply to
robert bristow-johnson

Hi,

you may want to consider adding a brief discussion about interpreting the results. For example the amount and location of peaking in the closed loop response can give a rough idea of the loop bandwidth and the stability margin ( From the closed loop peaking, can you tell the gain and phase margin separately or not??). Also I'm sure you are familiar with Venabale which uses some similar techniques.

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Mark

Reply to
Mark

I think you may have a typo in your discussion of eq. 7. You refer to a ­"Pi/2 term" which I don't see.

Reply to
Gary Richardson

Tim,

I just did a quick read and it looks like you've covered the topic pretty well. Not much I'd add, actually.

Well organized, stated pretty simply, well explained. I think you could expect a red or blue ribbon at the science fair. ;)

Eric Jacobsen Minister of Algorithms, Intel Corp. My opinions may not be Intel's opinions.

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Eric Jacobsen

Figure 5 etc would be better if the Right hand scale showed the 45, 90 and

180 degree points directly.

The font on the equations is a bit small.

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Reply to
Ken Smith

It works for any stability problem that can be made into ratios of polynomials with contiguous regions of stability -- so it works for z, s, w = (z-1)/(z+1), etc.

I have a mission to make software engineers comfortable with control theory, so I cast it entirely in terms of the z transform -- I should probably note that it'll work in the s domain, but then I'd have to explain how to do sampled-time measurements and convert them to continuous-time conclusions.

When I'm doing design for discrete-time control I _always_ do the analysis in the z domain, and if frequency response measurements are appropriate I nearly always do them in the context of the controller, rather than trying to make continuous-time measurements and translate.

Well, _I_ call it a Bode plot when I do it in the z domain. You can't construct it with a pencil and a ruler like you can in the s domain, but you interpret it exactly the same way so it seems appropriate.

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Tim Wescott
Wescott Design Services
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Tim Wescott

A nice discussion, Tim. You put it in terms of z-domain transfer function, but surely s-domain would be at least as appropriate for most of the paper. Is there a z-domain Bode plot?

Jerry

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Reply to
Jerry Avins

Hi,Tim

Your article makes clear many things for me. I think it very good except its long line which is bad for printing.

Thomas Atmel ShangHai

Tim Wescott wrote:

Reply to
wt70707

[snip stuff that doesn't matter]

Thanks, but this is a web page with figures interspersed. The web page is fine but hard to print nicely. A formatted version with imbedded images would be the solution. I tried to convert it but I was reporting on my failure to generate one with free or available tools.

Maybe someone else has better success. Otherwise, the web page has all the information, and I found a way to locally print the content. I just tried (and failed) to make an easily printable version for download.

Thanks, again, to Tim for writing and sharing the web page.

Reply to
xray

Not top-posting in this reply...

What kind of browser are you using? When I do a print preview with Firefox, the page fills nicely but getting page breaks not to split images is another issue.

Great to share this stuff, Tim, but a link to printable format like pdf or doc would be nice.

I know... looking the gift horse, etc. But if you could find a way to present in a printable format that you like, even better.

Thanks for sharing either way.

Reply to
xray

You missed this thread a couple of weeks back about virtual print drivers (3 options):

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Reply to
JeffM

For what it's worth, I converted your pages into a doc file and tried to use that with GhostView to create a pdf. Apparently my old veraion of Word is inadequate. Seems the pictures were not imbedded and I haven't found a setting to change that. Dang!

I tried.

Reply to
xray

Did you try printing the web page with something like PDF995? Not always pretty, but it will print the pictures along with the text. Its a shell for ghostscript.

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Michael A. Terrell
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Michael A. Terrell

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