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Worng discription in the Documentation?

Posted 10 years ago

In the documentation "ref/RootLocusPlot" -> "Options" -> "FeedbackType" it's written:

Root loci of an open-loop system with positive feedback:

RootLocusPlot[TransferFunctionModel[{{{k (34 + 10 s + s^2)}}, 
   12 + 26 s + 22 s^2 + 9 s^3 + s^4}, s], {k, 0, 30}, 
 FeedbackType -> "Positive"]

and

A closed-loop system:

RootLocusPlot[TransferFunctionModel[{{{k s}}, 1 + s + k s^2 + s^3}, 
  s], {k, 0, 2}, FeedbackType -> None]

Also in documentation's FeedbackType in details there is

The following settings can be used: "Negative" system with negative feedback "Positive" system with positive feedback None closed-loop system or system with no feedback

I always thought a system with feedback is a closed loop system (positive or negative) and the open loop variant has no feedback (none), no?

A little test shows:

num = s^2 a1 + s a2 + a3;
denom = s^3 b1 + s^2 (b2 + F b3) + s F b4 + b5;
constants = {a1 -> 3421.02, a2 -> 0.760227 F, a3 -> 21524.5, 
   b1 -> 5592, b2 -> 3421, b3 -> 1.242, b4 -> 0.760, b5 -> 21524};
tfm = TransferFunctionModel[num/denom, s]

RootLocusPlot[tfm /. constants, {F, 0, 20000}, 
 FeedbackType -> "Negative", PlotLabel -> "FeedbackType->Negative", 
 AspectRatio -> 1/GoldenRatio]

and

RootLocusPlot[
 SystemsModelFeedbackConnect[tfm, "Negative"] /. constants,
 {F, 0, 20000}, FeedbackType -> None,
 PlotLabel -> "ClosedLoop->Negative,FeedbackType->None", 
 AspectRatio -> 1/GoldenRatio]

give the same root locus plot. I might just be confused this morning :)

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POSTED BY: Fabian Wiek
2 Replies
POSTED BY: Suba Thomas

Thank you for this answer, I understand how RootLocusPlot works. What I was trying to mention was that I was confused of how to use FeedbackType by just reading the documentation. It's not very intuitive. Especially the two examples for FeedbackType in RootLocusPlot. I think with an extra line defining the systems by itself and writing "This is an open/closed loop system" there it would be easier to understand the RootLocusPlot in the next line. That the system by itself is closed loop and needs no "extra" feedback therefor.

I think that was the TOs problem on MSE, too.

POSTED BY: Fabian Wiek
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