<?xml version="1.0" encoding="ISO-8859-1" standalone="no"?>
<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>eng</LANGUAGE>

  <TITLE>black</TITLE>

  <TYPE>Scilab Function</TYPE>

  <DATE>April 1993</DATE>

  <SHORT_DESCRIPTION name="black">Black's diagram (Nichols
  chart)</SHORT_DESCRIPTION>

  <CALLING_SEQUENCE>
    <CALLING_SEQUENCE_ITEM>black( sl,[fmin,fmax] [,step] [,comments]
    )</CALLING_SEQUENCE_ITEM>

    <CALLING_SEQUENCE_ITEM>black( sl,frq [,comments] )</CALLING_SEQUENCE_ITEM>

    <CALLING_SEQUENCE_ITEM>black(frq,db,phi
    [,comments])</CALLING_SEQUENCE_ITEM>

    <CALLING_SEQUENCE_ITEM>black(frq,repf [,comments])</CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>

  <PARAM>
    <PARAM_INDENT>
      <PARAM_ITEM>
        <PARAM_NAME>sl</PARAM_NAME>

        <PARAM_DESCRIPTION>
          <SP>: list ( linear system <VERB>syslin</VERB>)</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>

      <PARAM_ITEM>
        <PARAM_NAME>fmin,fmax</PARAM_NAME>

        <PARAM_DESCRIPTION>
          <SP>: real scalars (frequency bounds)</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>

      <PARAM_ITEM>
        <PARAM_NAME>frq</PARAM_NAME>

        <PARAM_DESCRIPTION>
          <SP>: row vector or matrix (frequencies)</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>

      <PARAM_ITEM>
        <PARAM_NAME>db,phi</PARAM_NAME>

        <PARAM_DESCRIPTION>
          <SP>: row vectors or matrices (modulus, phase)</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>

      <PARAM_ITEM>
        <PARAM_NAME>repf</PARAM_NAME>

        <PARAM_DESCRIPTION>
          <SP>: row vectors or matrices (complex frequency response)</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>

      <PARAM_ITEM>
        <PARAM_NAME>step</PARAM_NAME>

        <PARAM_DESCRIPTION>
          <SP>: real</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>

      <PARAM_ITEM>
        <PARAM_NAME>comments</PARAM_NAME>

        <PARAM_DESCRIPTION>
          <SP>: string</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
    </PARAM_INDENT>
  </PARAM>

  <DESCRIPTION>
    <P>Black's diagram (Nichols'chart) for a linear system <VERB>sl</VERB>.
    <VERB>sl</VERB> can be a continuous-time or discrete-time SIMO system (see
    <VERB>syslin</VERB>). In case of multi-output the outputs are plotted with
    different symbols.</P>

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

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

    <P><VERB>comments</VERB> is a vector of character strings (captions).</P>

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

    <P><VERB>repf</VERB> matrix of complex numbers. One row for each
    response.</P>

    <P>To plot the grid of iso-gain and iso-phase of <VERB>y/(1+y)</VERB> use
    <VERB>chart()</VERB>.</P>

    <P>Default values for <VERB>fmin</VERB> and <VERB>fmax</VERB> are
    <VERB>1.d-3</VERB>, <VERB>1.d+3</VERB> if <VERB>sl</VERB> is
    continuous-time or <VERB>1.d-3</VERB>, <VERB>0.5</VERB> if <VERB>sl</VERB>
    is discrete-time.</P>
  </DESCRIPTION>

  <EXAMPLE><![CDATA[

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))
chart();
sstr='(s^2+2*0.9*10*s+100)/(s^2+2*0.3*10.1*s+102.01)';
black(h,0.01,100,sstr);
h1=h*syslin('c',(s^2+2*0.1*15.1*s+228.01)/(s^2+2*0.9*15*s+225))
clf()
black([h1;h],0.01,100,['h1';'h'])
 
  ]]></EXAMPLE>

  <SEE_ALSO>
    <SEE_ALSO_ITEM>
      <LINK>bode</LINK>
    </SEE_ALSO_ITEM>

    <SEE_ALSO_ITEM>
      <LINK>nyquist</LINK>
    </SEE_ALSO_ITEM>

    <SEE_ALSO_ITEM>
      <LINK>chart</LINK>
    </SEE_ALSO_ITEM>

    <SEE_ALSO_ITEM>
      <LINK>freq</LINK>
    </SEE_ALSO_ITEM>

    <SEE_ALSO_ITEM>
      <LINK>repfreq</LINK>
    </SEE_ALSO_ITEM>

    <SEE_ALSO_ITEM>
      <LINK>calfrq</LINK>
    </SEE_ALSO_ITEM>

    <SEE_ALSO_ITEM>
      <LINK>phasemag</LINK>
    </SEE_ALSO_ITEM>
  </SEE_ALSO>
</MAN>