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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_V2.1-en.txt
*
-->
<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" xml:id="sensi">
<refnamediv>
<refname>sensi</refname>
<refpurpose>sensitivity functions</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>[Se,Re,Te]=sensi(G,K)
[Si,Ri,Ti]=sensi(G,K,flag)
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Arguments</title>
<variablelist>
<varlistentry>
<term>G</term>
<listitem>
<para>
standard plant (<literal>syslin</literal> list)
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>K</term>
<listitem>
<para>
compensator (<literal>syslin</literal> list)
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>flag</term>
<listitem>
<para>
character string <literal>'o'</literal> (default value) or <literal>'i'</literal>
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>Se</term>
<listitem>
<para>
output sensitivity function <literal>(I+G*K)^-1</literal>
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>Re</term>
<listitem>
<para>
<literal>K*Se</literal>
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>Te</term>
<listitem>
<para>
<literal>G*K*Se</literal> (output complementary sensitivity function)
</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
<literal>sensi</literal> computes sensitivity functions. If <literal>G</literal> and <literal>K</literal> are
given in state-space form, the systems returned are generically minimal.
Calculation is made by <literal>lft</literal>, e.g.,
<literal>Se</literal> can be given by the commands
<literal> P = augment(G,'S')</literal>, <literal>Se=lft(P,K)</literal>.
If <literal>flag</literal> = <literal>'i'</literal>, <literal>[Si,Ri,Ti]=sensi(G,K,'i')</literal>
returns the input sensitivity functions.
</para>
<programlisting role=""><![CDATA[
[Se;Re;Te]= [inv(eye()+G*K);K*inv(eye()+G*K);G*K*inv(eye()+G*K)];
[Si;Ri;Ti]= [inv(eye()+K*G);G*inv(eye()+K*G);K*G*inv(eye()+K*G)];
]]></programlisting>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
G=ssrand(1,1,3);
K=ssrand(1,1,3);
[Se,Re,Te]=sensi(G,K);
Se1=inv(eye()+G*K); //Other way to compute
ss2tf(Se) //Se seen in transfer form
ss2tf(Se1)
ss2tf(Te)
ss2tf(G*K*Se1)
[Si,Ri,Ti]=sensi(G,K,'i');
w1=[ss2tf(Si);ss2tf(Ri);ss2tf(Ti)]
w2=[ss2tf(inv(eye()+K*G));ss2tf(G*inv(eye()+K*G));ss2tf(K*G*inv(eye()+K*G))];
clean(w1-w2)
]]></programlisting>
</refsection>
<refsection role="see also">
<title>See Also</title>
<simplelist type="inline">
<member>
<link linkend="augment">augment</link>
</member>
<member>
<link linkend="lft">lft</link>
</member>
<member>
<link linkend="h_cl">h_cl</link>
</member>
</simplelist>
</refsection>
</refentry>
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