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1 <?xml version="1.0" encoding="UTF-8"?>
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16 <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="ja" xml:id="csim">
17     <refnamediv>
18         <refname>csim</refname>
19         <refpurpose>線形システムのシミュレーション (時間応答)</refpurpose>
20     </refnamediv>
21     <refsynopsisdiv>
22         <title>呼び出し手順</title>
23         <synopsis>[y [,x]]=csim(u,t,sl,[x0 [,tol]])</synopsis>
24     </refsynopsisdiv>
25     <refsection>
26         <title>引数</title>
27         <variablelist>
28             <varlistentry>
29                 <term>u</term>
30                 <listitem>
31                     <para>関数, リストまたは文字列 (制御入力)</para>
32                 </listitem>
33             </varlistentry>
34             <varlistentry>
35                 <term>t</term>
36                 <listitem>
37                     <para>
38                         時間を指定するための実数ベクトルで、<literal>t(1)</literal> は
39                         初期時間 (<literal>x0=x(t(1))</literal>)を表す.
40                     </para>
41                 </listitem>
42             </varlistentry>
43             <varlistentry>
44                 <term>sl</term>
45                 <listitem>
46                     <para>
47                         連続時間系の<literal>syslin</literal>リスト (SIMO線形システム)
48                     </para>
49                 </listitem>
50             </varlistentry>
51             <varlistentry>
52                 <term>y</term>
53                 <listitem>
54                     <para>
55                         <literal>y=[y(t(i)]</literal>, i=1,..,n となる行列
56                     </para>
57                 </listitem>
58             </varlistentry>
59             <varlistentry>
60                 <term>x</term>
61                 <listitem>
62                     <para>
63                         <literal>x=[x(t(i)]</literal>, i=1,..,n となる行列
64                     </para>
65                 </listitem>
66             </varlistentry>
67             <varlistentry>
68                 <term>tol</term>
69                 <listitem>
70                     <para>2つの要素 [atol rtol] からなるベクトルであり、それぞれ
71                         ODEソルバ(ode参照)の絶対許容誤差および相対許容誤差を定義する
72                     </para>
73                 </listitem>
74             </varlistentry>
75         </variablelist>
76     </refsection>
77     <refsection>
78         <title>説明</title>
79         <para>
80             線形制御系 <literal>sl</literal>のシミュレーションを行います.
81             ただし,<literal>sl</literal>は,
82             <literal>syslin</literal>リストで表された連続時間システムとします.
83         </para>
84         <para>
85             <literal>u</literal> は制御入力,<literal>x0</literal> は状態量初期値です.
86         </para>
87         <para>
88             <literal>y</literal> は出力,<literal>x</literal> は状態量です.
89         </para>
90         <para>
91             制御入力は以下のいずれかとすることができます:
92         </para>
93         <para>
94             1. 関数 : <literal>[inputs]=u(t)</literal>
95         </para>
96         <para>
97             2. リスト : <literal>list(ut,parameter1,....,parametern)</literal>. 
98             ただし、<literal>inputs=ut(t,parameter1,....,parametern)</literal> (<literal>ut</literal> は関数)
99         </para>
100         <para>
101             3. インパルス応答の計算を表す文字列 <literal>"impuls"</literal>
102             (ここで,<literal>sl</literal>の入力は単一で<literal>x0=0</literal>が必要).
103             直達項を有する系の場合, t=0における無限インパルスは無視されます.
104         </para>
105         <para>
106             4. ステップ応答の計算を表す文字列 <literal>"step"</literal> 
107             (ここで、<literal>sl</literal>の入力は単一で,<literal>x0=0</literal>が必要)
108         </para>
109         <para>
110             5. t の各値に対応する u の値を指定するベクトル.
111         </para>
112     </refsection>
113     <refsection>
114         <title>例</title>
115         <programlisting role="example"><![CDATA[
116 s=poly(0,'s');
117 rand('seed',0);
118 w=ssrand(1,1,3);
119 w('A')=w('A')-2*eye();
120 t=0:0.05:5;
121 //impulse(w) = step (s * w)
122 plot2d([t',t'],[(csim('step',t,tf2ss(s)*w))',0*t'])
123 ]]></programlisting>
124         <scilab:image>
125             s=poly(0,'s');
126             rand('seed',0);
127             w=ssrand(1,1,3);
128             w('A')=w('A')-2*eye();
129             t=0:0.05:5;
130             plot2d([t',t'],[(csim('step',t,tf2ss(s)*w))',0*t'])
131         </scilab:image>
132         <programlisting role="example"><![CDATA[
133 s=poly(0,'s');
134 rand('seed',0);
135 w=ssrand(1,1,3);
136 w('A')=w('A')-2*eye();
137 t=0:0.05:5;
138 plot2d([t',t'],[(csim('impulse',t,w))',0*t'])
139 ]]></programlisting>
140         <scilab:image>
141             s=poly(0,'s');
142             rand('seed',0);
143             w=ssrand(1,1,3);
144             w('A')=w('A')-2*eye();
145             t=0:0.05:5;
146             plot2d([t',t'],[(csim('impulse',t,w))',0*t'])
147         </scilab:image>
148         <programlisting role="example"><![CDATA[
149 s=poly(0,'s');
150 rand('seed',0);
151 w=ssrand(1,1,3);
152 w('A')=w('A')-2*eye();
153 t=0:0.05:5;
154 //step(w) = impulse (s^-1 * w)
155 plot2d([t',t'],[(csim('step',t,w))',0*t'])
156 ]]></programlisting>
157         <scilab:image>
158             s=poly(0,'s');
159             rand('seed',0);
160             w=ssrand(1,1,3);
161             w('A')=w('A')-2*eye();
162             t=0:0.05:5;
163             plot2d([t',t'],[(csim('step',t,w))',0*t'])
164         </scilab:image>
165         <programlisting role="example"><![CDATA[
166 s=poly(0,'s');
167 rand('seed',0);
168 w=ssrand(1,1,3);
169 w('A')=w('A')-2*eye();
170 t=0:0.05:5;
171 plot2d([t',t'],[(csim('impulse',t,tf2ss(1/s)*w))',0*t'])
172 ]]></programlisting>
173         <scilab:image>
174             s=poly(0,'s');
175             rand('seed',0);
176             w=ssrand(1,1,3);
177             w('A')=w('A')-2*eye();
178             t=0:0.05:5;
179             plot2d([t',t'],[(csim('impulse',t,tf2ss(1/s)*w))',0*t'])
180         </scilab:image>
181         <programlisting role="example"><![CDATA[
182 s=poly(0,'s');
183 rand('seed',0);
184 w=ssrand(1,1,3);
185 w('A')=w('A')-2*eye();
186 t=0:0.05:5;
187 //時間関数で定義された入力
188 deff('u=timefun(t)','u=abs(sin(t))')
189 clf();plot2d([t',t'],[(csim(timefun,t,w))',0*t'])
190 ]]></programlisting>
191         <scilab:image>
192             s=poly(0,'s');
193             rand('seed',0);
194             w=ssrand(1,1,3);
195             w('A')=w('A')-2*eye();
196             t=0:0.05:5;
197             deff('u=timefun(t)','u=abs(sin(t))')
198             clf();plot2d([t',t'],[(csim(timefun,t,w))',0*t'])
199         </scilab:image>
200     </refsection>
201     <refsection role="see also">
202         <title>参照</title>
203         <simplelist type="inline">
204             <member>
205                 <link linkend="syslin">syslin</link>
206             </member>
207             <member>
208                 <link linkend="dsimul">dsimul</link>
209             </member>
210             <member>
211                 <link linkend="flts">flts</link>
212             </member>
213             <member>
214                 <link linkend="ltitr">ltitr</link>
215             </member>
216             <member>
217                 <link linkend="rtitr">rtitr</link>
218             </member>
219             <member>
220                 <link linkend="ode">ode</link>
221             </member>
222             <member>
223                 <link linkend="impl">impl</link>
224             </member>
225         </simplelist>
226     </refsection>
227 </refentry>