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Control Systems Mathematica

Worng discription in the Documentation?

Fabian Wiek

Fabian Wiek, University

Posted 9 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 :) Attachments:

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 :)

POSTED BY: Fabian Wiek

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Fabian Wiek

Fabian Wiek, University

Posted 9 years ago

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

Suba Thomas

Suba Thomas, WOLFRAM

Posted 9 years ago

I assume that the revised question is a clarification for the terminology used, as this was left hanging in MSE. Let's start with what `RootLocusPlot` does. It 'plots the location of poles for the closed-loop system for a range of k values.' (quote from the Details and Options section of its ref. page). By default the configuration is as below, where sys is the argument to `RootLocusPlot` and 'sgn' is assumed to be '-'. Thus be default, sys is the open-loop transfer function and the root-locus of the closed-loop system is desired assuming that the feedback sign is negative. As you have done in the nb attachment can do block diagram reduction and simplify sys and the summing junction to one system csys=sys/(1+sys). Now if you give 'csys' as the argument to `RootLocusPlot` it is no longer the default configuration. You have given the closed-loop system directly, and as far as `RootLocusPlot` is concerned it must consider just 'csys' (and it doesn't care if it came as a result of block reduction or otherwise) and no additional summing junction/feedback. Hence `FeedbackType->None`. In summary, `RootLocusPlot` by default considers a system along with a comparator or summing junction. The default assumes that the sign is negative (`FeedbackType->"Negative"`). `FeedbackType->"Positive"` assumes it is a summing junction. `FeedbackType->None` assumes no summing or comparator junction. What `RootLocusPlot` is interested in computing is the closed-loop system, which is sys/(1+sys), sys/(1-sys), and sys respectively. (I'm glad you asked this as a separate question, because my explanation turned out to be rather long for a comment.)

POSTED BY: Suba Thomas

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