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<?xml version="1.0" encoding="UTF-8"?>
<!--
* Add some comments about XML file
-->
<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en_US" xml:id="nyquistfrequencybounds">
<refnamediv>
<refname>nyquistfrequencybounds</refname>
<refpurpose>Computes the frequencies for which the nyquist locus enters and leaves a given rectangle. </refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>[fmin,fmax] = nyquistfrequencybounds(H,bounds)</synopsis>
</refsynopsisdiv>
<refsection>
<title>Parameters</title>
<variablelist>
<varlistentry>
<term>H</term>
<listitem>
<para>
A SISO linear dynamical system.
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>bounds</term>
<listitem>
<para>
A 2 by 2 array: [Rmin Imin;Rmax Imax] that defines a complex-plane rectangle.
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>fmin</term>
<listitem>
<para>
a real: the lowest frequency (Hz) such that the nyquist
locus enters the given rectangle or 0 if the 0 Hz point
lies in the rectangle or [] if the locus is completely
outside the rectangle.
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>fmax</term>
<listitem>
<para>
a real: the highest frequency (Hz) such that the nyquist
locus leaves the given rectangle or %inf if the %inf (hz)
point is in the rectangle or [] if the locus is completely
outside the rectangle.
</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title><para>
Given a C plane rectangle,
<literal>nyquistfrequencybounds</literal> Computes the lowest
frequency for which the nyquist locus enters the rectangle and
the highest frequency for which the nyquist locus leaves the
rectangle.
</para>
This function is useful for high definition zoom of a nyquist locus.
<para>
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
s=%s
num=2+9*s-9*s^2-11*s^3+0.01*s^4;
den=43*s^2+65*s^3+34*s^4+8*s^5+s^6+0.1*s^7
H=syslin('c',num,den)-1
clf;set(gcf(),'axes_size',[805,549])
subplot(221)
nyquist(H)
subplot(222)
bounds=[-2 -2;2 2]
[fmin,fmax]=nyquistfrequencybounds(H,bounds)
nyquist(H,fmin,fmax)
title("bounds:"+sci2exp(bounds,0));
subplot(223)
bounds=[-1.3 -0.3;0 0.3]
[fmin,fmax]=nyquistfrequencybounds(H,bounds)
nyquist(H,fmin,fmax)
title("bounds:"+sci2exp(bounds,0));
subplot(224)
bounds=[-1.1 -0.1;-0.8 0.1]
[fmin,fmax]=nyquistfrequencybounds(H,bounds)
nyquist(H,fmin,1d8)
title("bounds:"+sci2exp(bounds,0));
]]></programlisting>
<para>
<scilab:image>
s=%s
num=2+9*s-9*s^2-11*s^3+0.01*s^4;
den=43*s^2+65*s^3+34*s^4+8*s^5+s^6+0.1*s^7
H=syslin('c',num,den)-1
clf;set(gcf(),'axes_size',[805,549])
subplot(221)
nyquist(H)
subplot(222)
bounds=[-2 -2;2 2]
[fmin,fmax]=nyquistfrequencybounds(H,bounds)
nyquist(H,fmin,fmax)
title("bounds:"+sci2exp(bounds,0));
subplot(223)
bounds=[-1.3 -0.3;0 0.3]
[fmin,fmax]=nyquistfrequencybounds(H,bounds)
nyquist(H,fmin,fmax)
title("bounds:"+sci2exp(bounds,0));
subplot(224)
bounds=[-1.1 -0.1;-0.8 0.1]
[fmin,fmax]=nyquistfrequencybounds(H,bounds)
nyquist(H,fmin,1d8)
title("bounds:"+sci2exp(bounds,0));
</scilab:image>
</para>
</refsection>
<refsection>
<title>See Also</title>
<simplelist type="inline">
<member>
<link linkend="nyquist">nyquist</link>
</member>
</simplelist>
</refsection>
</refentry>
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