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  • Committer: Package Import Robot
  • Author(s): Sylvestre Ledru
  • Date: 2012-08-30 14:42:38 UTC
  • mfrom: (1.4.7)
  • Revision ID: package-import@ubuntu.com-20120830144238-c1y2og7dbm7m9nig
Tags: 5.4.0-beta-3-1~exp1
* New upstream release
* Update the scirenderer dep
* Get ride of libjhdf5-java dependency

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modules/cacsd/help/en_US/damp.xml
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<?xml version="1.0" encoding="UTF-8"?>
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<!--
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 * Add some comments about XML file
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-->
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<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" version="5.0-subset Scilab" xml:lang="en_US" xml:id="damp">
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  <refnamediv>
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    <refname>damp</refname>
8
 
    <refpurpose>Natural frequencies and damping factors. </refpurpose>
9
 
  </refnamediv>
10
 
  <refsynopsisdiv>
11
 
    <title>Calling Sequence</title>
12
 
    <synopsis>
13
 
      [wn,z] = damp(sys)
14
 
      [wn,z] = damp(P [,dt])
15
 
      [wn,z] = damp(R [,dt])
16
 
    </synopsis>
17
 
  </refsynopsisdiv>
18
 
  <refsection>
19
 
    <title>Parameters</title>
20
 
    <variablelist>
21
 
      <varlistentry>
22
 
        <term>sys</term>
23
 
        <listitem>
24
 
          <para>
25
 
            A linear dynamical system (see <link linkend="syslin">syslin</link>).
26
 
          </para>
27
 
        </listitem>
28
 
      </varlistentry>
29
 
      <varlistentry>
30
 
        <term>P</term>
31
 
        <listitem>
32
 
          <para>
33
 
            An array of polynomials.
34
 
          </para>
35
 
        </listitem>
36
 
      </varlistentry>
37
 
      <varlistentry>
38
 
        <term>P</term>
39
 
        <listitem>
40
 
          <para>
41
 
            An array of real or complex floating point numbers.
42
 
          </para>
43
 
        </listitem>
44
 
      </varlistentry>
45
 
      <varlistentry>
46
 
        <term>dt</term>
47
 
        <listitem>
48
 
          <para>
49
 
            A non negative scalar, with default value 0.
50
 
          </para>
51
 
        </listitem>
52
 
      </varlistentry>
53
 
      <varlistentry>
54
 
        <term>wn</term>
55
 
        <listitem>
56
 
          <para>
57
 
            vector of floating point numbers in increasing
58
 
            order: the natural pulsation in rd/s.
59
 
          </para>
60
 
        </listitem>
61
 
      </varlistentry>
62
 
      <varlistentry>
63
 
        <term>z</term>
64
 
        <listitem>
65
 
          <para>
66
 
            vector of floating point numbers: the damping factors.
67
 
          </para>
68
 
        </listitem>
69
 
      </varlistentry>
70
 
    </variablelist>
71
 
  </refsection>
72
 
  <refsection>
73
 
    <title>Description</title>
74
 
    <para>
75
 
      The denominator second order continuous time transfer function
76
 
      with complex poles can be written as <literal>s^2+2*z*wn*s+wn^2</literal> where<literal>z</literal>
77
 
      is the damping factor and <literal>wn </literal>the natural pulsation.
78
 
    </para>
79
 
    <para>
80
 
      If <literal>sys</literal> is a continuous time system,
81
 
      <literal>[wn,z] = damp(sys)</literal> returns in <literal>wn</literal> the natural
82
 
      pulsation <latex>\omega_n</latex>(in rd/s) and in <literal>z</literal> the damping factors
83
 
      <latex>\xi</latex> of the poles of the linear dynamical system
84
 
      <literal>sys</literal>. The <literal>wn</literal> and
85
 
      <literal>z</literal> arrays are ordered according to the increasing
86
 
      pulsation order.
87
 
    </para>
88
 
    <para>
89
 
      If <literal>sys</literal> is a discrete time system
90
 
      <literal>[wn,z] = damp(sys)</literal> returns in
91
 
      <literal>wn</literal> the natural pulsation
92
 
      <latex>\omega_n</latex>(in rd/s) and in <literal>z</literal> the
93
 
      damping factors <latex>\xi</latex> of the continuous time
94
 
      equivalent poles of <literal>sys</literal>. The
95
 
      <literal>wn</literal> and <literal>z</literal> arrays are
96
 
      ordered according to the increasing pulsation order.
97
 
    </para>
98
 
    <para>
99
 
      <literal>[wn,z] = damp(P)</literal>  returns in
100
 
      <literal>wn</literal> the natural pulsation
101
 
      <latex>\omega_n</latex>(in rd/s) and in <literal>z</literal> the
102
 
      damping factors <latex>\xi</latex> of the set of roots of the polynomials
103
 
      stored in the <literal>P</literal> array.  If
104
 
      <literal>dt</literal> is given and non 0, the roots are first
105
 
      converted to their continuous time equivalents.
106
 
      
107
 
      The <literal>wn</literal> and <literal>z</literal> arrays are ordered
108
 
      according to the increasing pulsation order.
109
 
    </para>
110
 
    <para>
111
 
      <literal>[wn,z] = damp(R)</literal>  returns in
112
 
      <literal>wn</literal> the natural pulsation
113
 
      <latex>\omega_n</latex>(in rd/s) and in <literal>z</literal> the
114
 
      damping factors <latex>\xi</latex> of  the set of roots stored in the
115
 
      <literal>R</literal> array. 
116
 
      
117
 
      If <literal>dt</literal> is given and non 0, the roots are first
118
 
      converted to their continuous time equivalents.
119
 
      <literal>wn(i)</literal> and <literal>z(i)</literal> are the the
120
 
      natural pulsation and damping factor of <literal>R(i)</literal>.
121
 
    </para>
122
 
  </refsection>
123
 
  <refsection>
124
 
    <title>Examples</title>
125
 
    <programlisting role="example"><![CDATA[
 
2
<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" version="5.0-subset Scilab" xml:lang="en_US" xml:id="damp">
 
3
    <refnamediv>
 
4
        <refname>damp</refname>
 
5
        <refpurpose>Natural frequencies and damping factors. </refpurpose>
 
6
    </refnamediv>
 
7
    <refsynopsisdiv>
 
8
        <title>Calling Sequence</title>
 
9
        <synopsis>
 
10
            [wn,z] = damp(sys)
 
11
            [wn,z] = damp(P [,dt])
 
12
            [wn,z] = damp(R [,dt])
 
13
        </synopsis>
 
14
    </refsynopsisdiv>
 
15
    <refsection>
 
16
        <title>Parameters</title>
 
17
        <variablelist>
 
18
            <varlistentry>
 
19
                <term>sys</term>
 
20
                <listitem>
 
21
                    <para>
 
22
                        A linear dynamical system (see <link linkend="syslin">syslin</link>).
 
23
                    </para>
 
24
                </listitem>
 
25
            </varlistentry>
 
26
            <varlistentry>
 
27
                <term>P</term>
 
28
                <listitem>
 
29
                    <para>
 
30
                        An array of polynomials.
 
31
                    </para>
 
32
                </listitem>
 
33
            </varlistentry>
 
34
            <varlistentry>
 
35
                <term>P</term>
 
36
                <listitem>
 
37
                    <para>
 
38
                        An array of real or complex floating point numbers.
 
39
                    </para>
 
40
                </listitem>
 
41
            </varlistentry>
 
42
            <varlistentry>
 
43
                <term>dt</term>
 
44
                <listitem>
 
45
                    <para>
 
46
                        A non negative scalar, with default value 0.
 
47
                    </para>
 
48
                </listitem>
 
49
            </varlistentry>
 
50
            <varlistentry>
 
51
                <term>wn</term>
 
52
                <listitem>
 
53
                    <para>
 
54
                        vector of floating point numbers in increasing
 
55
                        order: the natural pulsation in rd/s.
 
56
                    </para>
 
57
                </listitem>
 
58
            </varlistentry>
 
59
            <varlistentry>
 
60
                <term>z</term>
 
61
                <listitem>
 
62
                    <para>
 
63
                        vector of floating point numbers: the damping factors.
 
64
                    </para>
 
65
                </listitem>
 
66
            </varlistentry>
 
67
        </variablelist>
 
68
    </refsection>
 
69
    <refsection>
 
70
        <title>Description</title>
 
71
        <para>
 
72
            The denominator second order continuous time transfer function
 
73
            with complex poles can be written as <literal>s^2+2*z*wn*s+wn^2</literal> where<literal>z</literal>
 
74
            is the damping factor and <literal>wn </literal>the natural pulsation.
 
75
        </para>
 
76
        <para>
 
77
            If <literal>sys</literal> is a continuous time system,
 
78
            <literal>[wn,z] = damp(sys)</literal> returns in <literal>wn</literal> the natural
 
79
            pulsation <latex>\omega_n</latex>(in rd/s) and in <literal>z</literal> the damping factors
 
80
            <latex>\xi</latex> of the poles of the linear dynamical system
 
81
            <literal>sys</literal>. The <literal>wn</literal> and
 
82
            <literal>z</literal> arrays are ordered according to the increasing
 
83
            pulsation order.
 
84
        </para>
 
85
        <para>
 
86
            If <literal>sys</literal> is a discrete time system
 
87
            <literal>[wn,z] = damp(sys)</literal> returns in
 
88
            <literal>wn</literal> the natural pulsation
 
89
            <latex>\omega_n</latex>(in rd/s) and in <literal>z</literal> the
 
90
            damping factors <latex>\xi</latex> of the continuous time
 
91
            equivalent poles of <literal>sys</literal>. The
 
92
            <literal>wn</literal> and <literal>z</literal> arrays are
 
93
            ordered according to the increasing pulsation order.
 
94
        </para>
 
95
        <para>
 
96
            <literal>[wn,z] = damp(P)</literal>  returns in
 
97
            <literal>wn</literal> the natural pulsation
 
98
            <latex>\omega_n</latex>(in rd/s) and in <literal>z</literal> the
 
99
            damping factors <latex>\xi</latex> of the set of roots of the polynomials
 
100
            stored in the <literal>P</literal> array.  If
 
101
            <literal>dt</literal> is given and non 0, the roots are first
 
102
            converted to their continuous time equivalents.
 
103
            
 
104
            The <literal>wn</literal> and <literal>z</literal> arrays are ordered
 
105
            according to the increasing pulsation order.
 
106
        </para>
 
107
        <para>
 
108
            <literal>[wn,z] = damp(R)</literal>  returns in
 
109
            <literal>wn</literal> the natural pulsation
 
110
            <latex>\omega_n</latex>(in rd/s) and in <literal>z</literal> the
 
111
            damping factors <latex>\xi</latex> of  the set of roots stored in the
 
112
            <literal>R</literal> array. 
 
113
            
 
114
            If <literal>dt</literal> is given and non 0, the roots are first
 
115
            converted to their continuous time equivalents.
 
116
            <literal>wn(i)</literal> and <literal>z(i)</literal> are the the
 
117
            natural pulsation and damping factor of <literal>R(i)</literal>.
 
118
        </para>
 
119
    </refsection>
 
120
    <refsection>
 
121
        <title>Examples</title>
 
122
        <programlisting role="example"><![CDATA[
126
123
    s=%s;
127
124
    num=22801+4406.18*s+382.37*s^2+21.02*s^3+s^4;
128
125
    den=22952.25+4117.77*s+490.63*s^2+33.06*s^3+s^4
129
126
    h=syslin('c',num/den);
130
127
    [wn,z] = damp(h)
131
128
    ]]></programlisting>
132
 
    <para>
133
 
      The following example illustrates the effect of the damping factor on
134
 
      the frequency response of a second order system.
135
 
    </para>
136
 
    <programlisting role="example"><![CDATA[
 
129
        <para>
 
130
            The following example illustrates the effect of the damping factor on
 
131
            the frequency response of a second order system.
 
132
        </para>
 
133
        <programlisting role="example"><![CDATA[
137
134
   s=%s;
138
135
   wn=1;
139
136
   clf();
149
146
   legend('$\xi='+string(Z)+'$')
150
147
   plot(wn/(2*%pi)*[1 1],[0 70],'r') //natural pulsation
151
148
   ]]></programlisting>
152
 
    <para>
153
 
      It produces this plot:
154
 
    </para>
155
 
    <para>
156
 
      <inlinemediaobject>
157
 
        <imageobject>
158
 
          <imagedata fileref="../images/damp.svg"/>
159
 
        </imageobject>
160
 
      </inlinemediaobject>
161
 
    </para>
162
 
    <para>
163
 
      Computing the natural pulsations and daping ratio for a set of roots:
164
 
    </para>
165
 
    <programlisting role="example"><![CDATA[
 
149
        <para>
 
150
<scilab:image>
 
151
   s=%s;
 
152
   wn=1;
 
153
   clf();
 
154
   Z=[0.95 0.7 0.5 0.3 0.13 0.0001];
 
155
   for k=1:size(Z,'*')
 
156
     z=Z(k)
 
157
     H=syslin('c',1+5*s+10*s^2,s^2+2*z*wn*s+wn^2);
 
158
     gainplot(H,0.01,1)
 
159
     p=gce();p=p.children;
 
160
     p.foreground=k;
 
161
   end
 
162
   title("$\frac{1+5 s+10 s^2}{\omega_n^2+2\omega_n\xi s+s^2}, \quad \omega_n=1$")
 
163
   legend('$\xi='+string(Z)+'$')
 
164
   plot(wn/(2*%pi)*[1 1],[0 70],'r') //natural pulsation
 
165
</scilab:image>
 
166
        </para>
 
167
        <para>
 
168
            Computing the natural pulsations and daping ratio for a set of roots:
 
169
        </para>
 
170
        <programlisting role="example"><![CDATA[
166
171
    [wn,z] = damp((1:5)+%i)
167
172
    ]]></programlisting>
168
 
  </refsection>
169
 
  <refsection>
170
 
    <title>See Also</title>
171
 
    <simplelist type="inline">
172
 
      <member>
173
 
        <link linkend="spec">spec</link>
174
 
      </member>
175
 
      <member>
176
 
        <link linkend="roots">roots</link>
177
 
      </member>
178
 
    </simplelist>
179
 
  </refsection>
 
173
    </refsection>
 
174
    <refsection>
 
175
        <title>See Also</title>
 
176
        <simplelist type="inline">
 
177
            <member>
 
178
                <link linkend="spec">spec</link>
 
179
            </member>
 
180
            <member>
 
181
                <link linkend="roots">roots</link>
 
182
            </member>
 
183
        </simplelist>
 
184
    </refsection>
180
185
</refentry>