1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
|
<?xml version="1.0" encoding="UTF-8"?>
<!--
* Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
* Copyright (C) INRIA - F.D
* Revised July 2011, S. Steer, 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="pfss">
<refnamediv>
<refname>pfss</refname>
<refpurpose>partial fraction decomposition</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>elts=pfss(Sl)
elts=pfss(Sl,rmax)
elts=pfss(Sl,cord)
elts=pfss(Sl,rmax,cord)
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Arguments</title>
<variablelist>
<varlistentry>
<term>Sl</term>
<listitem>
<para>
A linear dynamical system in state-space or transfer
function representation (see <link linkend="syslin">syslin</link>).
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>rmax</term>
<listitem>
<para>
A real number controlling the conditioning of block
diagonalization (see <link linkend="bdiag">bdiag</link>).
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>cord</term>
<listitem>
<para>
A character string with possible values <literal>'c'</literal>
or <literal>'d'</literal>.
</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
Partial fraction decomposition of the linear system <literal>Sl</literal>.
</para>
<para>
<literal>elts</literal> is the list of linear systems which add up to <literal>Sl</literal>
i.e. <literal>elts=list(S1,S2,S3,...,Sn)</literal> with:
</para>
<para>
<literal>Sl = S1 + S2 +... +Sn</literal>.
</para>
<para>
Each <literal>Si</literal> contains some poles of <literal/>
Saccording to the
block-diagonalization of the <literal>A</literal> matrix of <literal>S</literal>.
</para>
<para>
For non proper systems the polynomial part of <literal>Sl</literal> is put
in the last entry of <literal>elts</literal>.
</para>
<para>
If <literal>Sl</literal> is given in transfer form, it is first
converted into state-space by <link linkend="tf2ss">tf2ss</link>
and each subsystem <literal>Si</literal> is then converted in
transfer form by <link linkend="ss2tf">ss2tf</link>.
</para>
<para>
The A matrix is of the state-space is put into block diagonal form
by function <link linkend="bdiag">bdiag</link>. The optional parameter
<literal>rmax</literal> is sent to <literal>bdiag</literal>,
<literal>rmax</literal> should be set to a large number to enforce
block-diagonalization.
</para>
<para>
If the optional flag <literal>cord='c'</literal> is given the elements in <literal>elts</literal>
are sorted according to the real part (resp. magnitude if <literal>cord='d'</literal>)
of the eigenvalues of A matrices.
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
W=ssrand(1,1,6);
elts=pfss(W);
W1=0;for k=1:size(elts), W1=W1+ss2tf(elts(k));end
clean(ss2tf(W)-W1)
]]></programlisting>
<programlisting role="example"><![CDATA[
num=22801+4406.18*s+382.37*s^2+21.02*s^3+s^4;
den=22952.25+4117.77*s+490.63*s^2+33.06*s^3+s^4
h2=syslin('c',num/den);
]]></programlisting>
</refsection>
<refsection role="see also">
<title>See Also</title>
<simplelist type="inline">
<member>
<link linkend="pbig">pbig</link>
</member>
<member>
<link linkend="bdiag">bdiag</link>
</member>
<member>
<link linkend="coffg">coffg</link>
</member>
<member>
<link linkend="dtsi">dtsi</link>
</member>
</simplelist>
</refsection>
</refentry>
|
