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2.5 Graphics 87
NyquistPlot Options
NyquistPlot inherits its plot options, which are accessible through
Options[NyquistPlot], from Mathematica’s standard function ListPlot. See the Mathematica book
for detailed explanations of these options. NyquistPlot has additional options like, for example
FrequencyScaling which controls the spacing of the frequency points at which the transfer function
is sampled. FrequencyScaling can be set to Linear or Exponential, resulting in equidistant or
exponentially spaced sampling points respectively. The default is Exponential.
2.5.3 Nichol Plots
Yet another method of visualizing frequency responses is Nichol’s chart. A Nichol plot is similar to
a Nyquist plot but shows gain on a logarithmic scale (dB) vs. phase on a linear scale (degrees), with
an axis origin at the point dB ∘ . The advantage of Nichol’s chart is the ease by which gain
and phase margins can be determined graphically. The gain margin is simply the negative value of
the gain axis intersect. The phase margin is equal to the distance between the axis origin and the
phase axis intersect.
Nichol charts are computed by the function NicholPlot (Section 3.9.3). The argument sequence is
the same as for NyquistPlot (Section 3.9.4) or BodePlot (Section 3.9.1).
Let’s use a Nichol chart to determine the gain and phase margins of a system which is characterized
by the following transfer function.
In[9]:= H3[s_] := 20*(3 + s)/(s*(5 + s)*(20 + 5*s + 2*s^2))
We draw a Nichol chart of H3[I w] for an angular frequency Ω varying from sec to sec .
Again, we increase the number of plot points to produce a smooth curve.
In[10]:= NicholPlot[H3[I w], {w, 0.1, 5.},
AspectRatio −> 0.8, PlotPoints −> 100]
dB
15
10
5
-360 -300 -240 -120 -60 0 deg
-5
-10
-15
-20
Out[10]= Graphics
Now, in order to read off the margins better, we zoom in on the part of the curve located in the
fourth quadrant.