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88 2. Tutorial
In[11]:= NicholPlot[H3[I w], {w, 0.1, 5.}, AspectRatio −> 0.8,
PlotPoints −> 100, PlotRange −> {{−200, −80}, {−15, 2}}]
dB
-2.5
-150 -120 -90 deg
-5
-7.5
-10
-12.5
-15
Out[11]= Graphics
The curve crosses the gain axis at a gain of dB, so we have a gain margin of dB. At the
phase axis intersect we have a phase value of approximately ∘ which is ∘ away from the axis
origin. Hence, the phase margin is ∘ .
NicholPlot Options
Like NyquistPlot, NicholPlot inherits its options from ListPlot. NicholPlot has additional
options like, for example, PhaseDisplay (see Section 2.5.1) and FrequencyScaling (see Section 2.5.2).
2.5.4 Root Locus Plots
Let Hs k denote a rational transfer function whose coefficients depend on the real parameter k. A
root locus plot shows the locus of the poles and zeros of Hs k in the complex plane as k varies
within an interval k k .
To draw a root locus plot use the command RootLocusPlot (Section 3.9.5). The calling format is
RootLocusPlot[tfunc, {k, k , k }]
where tfunc is a transfer function in the frequency variable s and one real parameter k.
Of course, the parameter does not necessarily have to be named k. We can also use any other symbol
to denote the parameter. Below, we define the transfer function H4[s, a] with coefficients which are
functions of the parameter a.
In[12]:= H4[s_, a_] := (a + 2*s + s^2)/(10 + 3*a*s + 4*s^2 + s^3)
Then we graph the root locus of H4 as a varies from to . By default, RootLocusPlot samples
the parameter interval at five equally spaced points. This number can be increased or decreased by