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<?xml version="1.0" encoding="UTF-8"?>
<!--
 * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
 * Copyright (C) INRIA
 * 
 * This file must be used under the terms of the CeCILL.
 * This source file is licensed as described in the file COPYING, which
 * you should have received as part of this distribution.  The terms
 * are also available at    
 * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
 *
 -->
<refentry version="5.0-subset Scilab" xml:id="nyquist" xml:lang="en"
          xmlns="http://docbook.org/ns/docbook"
          xmlns:xlink="http://www.w3.org/1999/xlink"
          xmlns:svg="http://www.w3.org/2000/svg"
          xmlns:ns5="http://www.w3.org/1999/xhtml"
          xmlns:mml="http://www.w3.org/1998/Math/MathML"
          xmlns:db="http://docbook.org/ns/docbook">
  <info>
    <pubdate>$LastChangedDate: 2008-03-26 09:50:39 +0100 (Wed, 26 Mar 2008)
    $</pubdate>
  </info>

  <refnamediv>
    <refname>nyquist</refname>

    <refpurpose>nyquist plot</refpurpose>
  </refnamediv>

  <refsynopsisdiv>
    <title>Calling Sequence</title>

    <synopsis>nyquist( sl,[fmin,fmax] [,step] [,comments] )
nyquist( sl, frq [,comments] )
nyquist(frq,db,phi [,comments])
nyquist(frq, repf [,comments])</synopsis>
  </refsynopsisdiv>

  <refsection>
    <title>Parameters</title>

    <variablelist>
      <varlistentry>
        <term>sl</term>

        <listitem>
          <para> <literal>syslin</literal> list (SIMO linear system in
          continuous or discrete time )</para>
        </listitem>
      </varlistentry>

      <varlistentry>
        <term>fmin,fmax</term>

        <listitem>
          <para>real scalars (frequency bounds (in Hz))</para>
        </listitem>
      </varlistentry>

      <varlistentry>
        <term>step</term>

        <listitem>
          <para>real (logarithmic discretization step)</para>
        </listitem>
      </varlistentry>

      <varlistentry>
        <term>comments</term>

        <listitem>
          <para>string vector (captions).</para>
        </listitem>
      </varlistentry>

      <varlistentry>
        <term>frq</term>

        <listitem>
          <para>vector or matrix of frequencies (in Hz) (one row for each
          output of <literal>sl</literal>).</para>
        </listitem>
      </varlistentry>

      <varlistentry>
        <term>db,phi</term>

        <listitem>
          <para>real matrices of modulus (in Db) and phases (in degree) (one
          row for each output of <literal>sl</literal>).</para>
        </listitem>
      </varlistentry>

      <varlistentry>
        <term>repf</term>

        <listitem>
          <para>matrix of complex numbers. Frequency response (one row for
          aech output of <literal>sl</literal>)</para>
        </listitem>
      </varlistentry>
    </variablelist>
  </refsection>

  <refsection>
    <title>Description</title>

    <para>Nyquist plot i.e Imaginary part versus Real part of the frequency
    response of <literal>sl</literal>.</para>

    <para>For continuous time systems <literal>sl(2*%i*%pi*w)</literal> is
    plotted. For discrete time system or discretized systems
    <literal>sl(exp(2*%i*%pi*w*fd)</literal> is used ( <literal>fd=1</literal>
    for discrete time systems and <literal>fd=sl('dt')</literal> for
    discretized systems )</para>

    <para><literal>sl</literal> can be a continuous-time or discrete-time SIMO
    system (see <literal>syslin</literal>). In case of multi-output the
    outputs are plotted with different symbols.</para>

    <para>The frequencies are given by the bounds <literal>fmin,fmax</literal>
    (in Hz) or by a row-vector (or a matrix for multi-output)
    <literal>frq</literal>.</para>

    <para><literal>step</literal> is the ( logarithmic ) discretization step.
    (see <literal>calfrq</literal> for the choice of default value).</para>

    <para><literal>comments</literal> is a vector of character strings
    (captions).</para>

    <para><literal>db,phi</literal> are the matrices of modulus (in Db) and
    phases (in degrees). (One row for each response).</para>

    <para><literal>repf</literal> is a matrix of complex numbers. One row for
    each response.</para>

    <para>Default values for <literal>fmin</literal> and
    <literal>fmax</literal> are <literal>1.d-3</literal>,
    <literal>1.d+3</literal> if <literal>sl</literal> is continuous-time or
    <literal>1.d-3</literal>, <literal>0.5</literal>/sl.dt (nyquist frequency)
    if <literal>sl</literal> is discrete-time.</para>

    <para>Automatic discretization of frequencies is made by
    <literal>calfrq</literal>.</para>
  </refsection>

  <refsection>
    <title>Examples</title>

    <programlisting role="example"><![CDATA[ 
clf();
s=poly(0,'s');
h=syslin('c',(s^2+2*0.9*10*s+100)/(s^2+2*0.3*10.1*s+102.01));
comm='(s^2+2*0.9*10*s+100)/(s^2+2*0.3*10.1*s+102.01)';
nyquist(h,0.01,100,comm);
h1=h*syslin('c',(s^2+2*0.1*15.1*s+228.01)/(s^2+2*0.9*15*s+225))
clf();
nyquist([h1;h],0.01,100,['h1';'h'])
clf();nyquist([h1;h])
 ]]></programlisting>
  </refsection>

  <refsection>
    <title>See Also</title>

    <simplelist type="inline">
      <member><link linkend="bode">bode</link></member>

      <member><link linkend="black">black</link></member>

      <member><link linkend="calfrq">calfrq</link></member>

      <member><link linkend="freq">freq</link></member>

      <member><link linkend="repfreq">repfreq</link></member>

      <member><link linkend="phasemag">phasemag</link></member>
    </simplelist>
  </refsection>
</refentry>