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In order to see some details on a Nyquist Diagram I have used the function NyquistPlot that comes with Mathematica v8 and v9.

NyquistPlot[
  TransferFunctionModel[(30000*(s + 3)^2)/(s*(s + 0.5)^2*(s + 20)^2), s], 
  Automatic, 
  PlotPoints -> 1000, ImageSize -> Medium]

Mathematica graphics

The first thing one can see is that there is a discontinuity (not in the actual diagram). Note that the dashed lines are departing from the wrong position of the branches.

I have tried to adjust the range of frequencies so as to see "more" of the diagram but to no avail.

One info: there are three crossings on the negative real axis (x-axis): -3.7, -56.5, -1074. I wonder whether there is a way to see them all.

Any ideas?

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1 Answer

The default plot range needs a little help:

p = NyquistPlot[
       TransferFunctionModel[(30000*(s + 3)^2)/(s*(s + 0.5)^2*(s + 20)^2), s], 
       PlotRange -> {{-1500, 200}, {-100, 100}}]

enter image description here

The three crossings can be seen better as follows:

Show[p, PlotRange -> {{-1200, 10}, {-100, 100}}, 
        PlotRangePadding -> 0, Ticks->Automatic]

enter image description here

Show[p, PlotRange -> {{-60, 10}, {-10, 10}}, 
        PlotRangePadding -> 0, Ticks->Automatic]

enter image description here

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Many thanks - I have noticed that one has to be very careful when using the functions on the control package. –  Ed Mendes Feb 19 '13 at 22:35
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