1 <?xml version="1.0" encoding="UTF-8"?>
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13 <refentry version="5.0-subset Scilab" xml:id="black" xml:lang="en"
14 xmlns="http://docbook.org/ns/docbook"
15 xmlns:xlink="http://www.w3.org/1999/xlink"
16 xmlns:svg="http://www.w3.org/2000/svg"
17 xmlns:ns5="http://www.w3.org/1999/xhtml"
18 xmlns:mml="http://www.w3.org/1998/Math/MathML"
19 xmlns:db="http://docbook.org/ns/docbook">
21 <pubdate>$LastChangedDate: 2008-03-26 09:50:39 +0100 (Wed, 26 Mar 2008)
26 <refname>black</refname>
28 <refpurpose>Black-Nichols diagram of a linear dynamical system</refpurpose>
32 <title>Calling Sequence</title>
35 black( sl,[fmin,fmax] [,step] [,comments] )
36 black( sl,frq [,comments] )
37 black(frq,db,phi [,comments])
38 black(frq,repf [,comments])
43 <title>Parameters</title>
50 <para>a continuous or discrete time SIMO linear dynamical
51 system ( see: <link linkend="syslin">syslin</link>).</para>
56 <term>fmin,fmax</term>
59 <para>real scalars (frequency bounds)</para>
67 <para>row vector or matrix (frequencies)</para>
75 <para>row vectors or matrices (modulus, phase)</para>
83 <para>row vectors or matrices (complex frequency response)</para>
106 <title>Description</title>
108 <para>Black's diagram (Nichols'chart) for a linear system ( see: <link linkend="syslin">syslin</link>). <literal>sl</literal> can be a continuous-time or
109 discrete-time SIMO system. In case of
110 multi-output the outputs are plotted with different colors.</para>
112 <para>The frequencies are given by the bounds
113 <literal>fmin</literal>,<literal>fmax</literal> (in Hz) or by a row-vector
114 (or a matrix for multi-output) <literal>frq</literal>.</para>
116 <para><literal>step</literal> is the ( logarithmic ) discretization step.
117 (see <link linkend="calfrq">calfrq</link> for the choice of default value).</para>
119 <para><literal>comments</literal> is a vector of character strings
122 <para><literal>db,phi</literal> are the matrices of modulus (in Db) and
123 phases (in degrees). (One row for each response).</para>
125 <para><literal>repf</literal> matrix of complex numbers. One row for each
128 <para>To plot the grid of iso-gain and iso-phase of
129 <literal>y/(1+y)</literal> use <link
130 linkend="nicholschart">nicolschart()</link>.</para>
132 <para>Default values for <literal>fmin</literal> and
133 <literal>fmax</literal> are <literal>1.d-3</literal>,
134 <literal>1.d+3</literal> if <literal>sl</literal> is continuous-time or
135 <literal>1.d-3</literal>, <literal>0.5</literal>/sl.dt (nyquist frequency)
136 if <literal>sl</literal> is discrete-time.</para>
140 <title>Examples</title>
142 <programlisting role="exemple"><![CDATA[
145 sl=syslin('c',5*(1+s)/(.1*s^4+s^3+15*s^2+3*s+1))
146 clf();black(sl,0.01,10);
151 <imagedata fileref="../images/black1.svg"/>
155 <programlisting role="example"><![CDATA[
156 //Black diagram with Nichols chart as a grid
158 Plant=syslin('c',16000/((s+1)*(s+10)*(s+100)));
159 //two degree of freedom PID
161 PID=syslin('c',(1/(2*xsi*tau*s))*(1+2*xsi*tau*s+tau^2*s^2));
163 black([Plant;Plant*PID ],0.01,100,["Plant";"Plant and PID corrector"]);
164 //move the caption in the lower rigth corner
165 ax=gca();Leg=ax.children(1);
166 Leg.legend_location="in_lower_right";
167 nicholschart(colors=color('light gray')*[1 1])
173 <imagedata fileref="../images/black2.svg"/>
180 <title>See Also</title>
182 <simplelist type="inline">
183 <member><link linkend="nicholschart">nicholschart</link></member>
184 <member><link linkend="bode">bode</link></member>
185 <member><link linkend="nyquist">nyquist</link></member>
187 <member><link linkend="syslin">syslin</link></member>
188 <member><link linkend="calfrq">calfrq</link></member>
189 <member><link linkend="datatips">datatips</link></member>