damp function added in CACSD module 55/3955/8
Serge Steer [Thu, 5 May 2011 15:25:49 +0000 (17:25 +0200)]
Change-Id: Iff9d75c6e9f012ec696967aa8466687410459384

SEP/SEP_058_damp.odt [new file with mode: 0644]
scilab/CHANGES_5.4.X
scilab/modules/cacsd/help/en_US/damp.xml [new file with mode: 0644]
scilab/modules/cacsd/help/images/damp.svg [new file with mode: 0644]
scilab/modules/cacsd/macros/damp.sci [new file with mode: 0644]
scilab/modules/cacsd/tests/unit_tests/damp.dia.ref [new file with mode: 0644]
scilab/modules/cacsd/tests/unit_tests/damp.tst [new file with mode: 0644]

diff --git a/SEP/SEP_058_damp.odt b/SEP/SEP_058_damp.odt
new file mode 100644 (file)
index 0000000..05e6bba
Binary files /dev/null and b/SEP/SEP_058_damp.odt differ
index ed7f458..b4a7528 100644 (file)
@@ -95,6 +95,8 @@ New functions
   "numerically almost equal", i.e. that the relative error is small.
   This automatically fixes the bug #4381.
 
+* The damp function in CACSD modules computes the natural pulsation
+  and damping factor of linear dynamical systems.
 
 Optimization:
 =============
diff --git a/scilab/modules/cacsd/help/en_US/damp.xml b/scilab/modules/cacsd/help/en_US/damp.xml
new file mode 100644 (file)
index 0000000..d30b67b
--- /dev/null
@@ -0,0 +1,187 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Add some comments about XML file
+-->
+<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">
+  <info>
+    <pubdate>$LastChangedDate: 05-05-2011 $</pubdate>
+  </info>
+  <refnamediv>
+    <refname>damp</refname>
+    <refpurpose>Natural frequencies and damping factors. </refpurpose>
+  </refnamediv>
+  <refsynopsisdiv>
+    <title>Calling Sequence</title>
+    <synopsis>
+      [wn,z] = damp(sys)
+      [wn,z] = damp(P [,dt])
+      [wn,z] = damp(R [,dt])
+    </synopsis>
+  </refsynopsisdiv>
+  <refsection>
+    <title>Parameters</title>
+    <variablelist>
+      <varlistentry>
+        <term>sys</term>
+        <listitem>
+          <para>
+            A linear dynamical system (see <link linkend="syslin">syslin</link>).
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>P</term>
+        <listitem>
+          <para>
+            An array of polynomials.
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>P</term>
+        <listitem>
+          <para>
+            An array of real or complex floating point numbers.
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>dt</term>
+        <listitem>
+          <para>
+            A non negative scalar, with default value 0.
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>wn</term>
+        <listitem>
+          <para>
+            vector of floating point numbers in increasing
+            order: the natural pulsation in rd/s.
+          </para>
+        </listitem>
+      </varlistentry>
+      <varlistentry>
+        <term>z</term>
+        <listitem>
+          <para>
+            vector of floating point numbers: the damping factors.
+          </para>
+        </listitem>
+      </varlistentry>
+    </variablelist>
+  </refsection>
+  <refsection>
+    <title>Description</title>
+    <para>
+      The denominator second order continuous time transfer function
+      with complex poles can be written as <literal>s^2+2*z*wn*s+wn^2</literal> where<literal>z</literal>
+      is the damping factor and <literal>wn </literal>the natural pulsation.
+    </para>
+    <para>
+      If <literal>sys</literal> is a continuous time system,
+      <literal>[wn,z] = damp(sys)</literal> returns in <literal>wn</literal> the natural
+      pulsation <latex>\omega_n</latex>(in rd/s) and in <literal>z</literal> the damping factors
+      <latex>\xi</latex> of the poles of the linear dynamical system
+      <literal>sys</literal>. The <literal>wn</literal> and
+      <literal>z</literal> arrays are ordered according to the increasing
+      pulsation order.
+    </para>
+    <para>
+      If <literal>sys</literal> is a discrete time system
+      <literal>[wn,z] = damp(sys)</literal> returns in
+      <literal>wn</literal> the natural pulsation
+      <latex>\omega_n</latex>(in rd/s) and in <literal>z</literal> the
+      damping factors <latex>\xi</latex> of the continuous time
+      equivalent poles of <literal>sys</literal>. The
+      <literal>wn</literal> and <literal>z</literal> arrays are
+      ordered according to the increasing pulsation order.
+    </para>
+    <para><literal>[wn,z] = damp(P)</literal>  returns in
+      <literal>wn</literal> the natural pulsation
+      <latex>\omega_n</latex>(in rd/s) and in <literal>z</literal> the
+      damping factors <latex>\xi</latex> of the set of roots of the polynomials
+      stored in the <literal>P</literal> array.  If
+      <literal>dt</literal> is given and non 0, the roots are first
+      converted to their continuous time equivalents.
+
+      The <literal>wn</literal> and <literal>z</literal> arrays are ordered
+      according to the increasing pulsation order.
+    </para>
+    <para><literal>[wn,z] = damp(R)</literal>  returns in
+      <literal>wn</literal> the natural pulsation
+      <latex>\omega_n</latex>(in rd/s) and in <literal>z</literal> the
+      damping factors <latex>\xi</latex> of  the set of roots stored in the
+      <literal>R</literal> array. 
+
+      If <literal>dt</literal> is given and non 0, the roots are first
+      converted to their continuous time equivalents.
+      <literal>wn(i)</literal> and <literal>z(i)</literal> are the the
+      natural pulsation and damping factor of <literal>R(i)</literal>.
+    </para>
+  </refsection>
+  <refsection>
+    <title>Examples</title>
+    <programlisting role="example"><![CDATA[
+    s=%s;
+    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
+    h=syslin('c',num/den);
+    [wn,z] = damp(h)
+    ]]></programlisting>
+    <para>
+The following example illustrates the effect of the damping factor on
+the frequency response of a second order system.
+ </para>
+    <programlisting role="example"><![CDATA[
+   s=%s;
+   wn=1;
+   clf();
+   Z=[0.95 0.7 0.5 0.3 0.13 0.0001];
+   for k=1:size(Z,'*')
+     z=Z(k)
+     H=syslin('c',1+5*s+10*s^2,s^2+2*z*wn*s+wn^2);
+     gainplot(H,0.01,1)
+     p=gce();p=p.children;
+     p.foreground=k;
+   end
+   title("$\frac{1+5 s+10 s^2}{\omega_n^2+2\omega_n\xi s+s^2}, \quad \omega_n=1$")
+   legend('$\xi='+string(Z)+'$')
+   plot(wn/(2*%pi)*[1 1],[0 70],'r') //natural pulsation
+   ]]></programlisting>
+    <para>
+   It produces this plot:
+ </para>
+    <para>
+      <inlinemediaobject>
+        <imageobject>
+          <imagedata fileref="../images/damp.svg"/>
+        </imageobject>
+      </inlinemediaobject>
+    </para>
+    <para>
+Computing the natural pulsations and daping ratio for a set of roots:
+ </para>
+    <programlisting role="example"><![CDATA[
+    [wn,z] = damp((1:5)+%i)
+    ]]></programlisting>
+  </refsection>
+  <refsection>
+    <title>See Also</title>
+    <simplelist type="inline">
+      <member>
+        <link linkend="spec">spec</link>
+      </member>
+      <member>
+        <link linkend="roots">roots</link>
+      </member>
+    </simplelist>
+  </refsection>
+  <refsection>
+    <title>Authors</title>
+    <simplelist type="vert">
+      <member>Serge Steer, INRIA</member>
+    </simplelist>
+  </refsection>
+</refentry>
diff --git a/scilab/modules/cacsd/help/images/damp.svg b/scilab/modules/cacsd/help/images/damp.svg
new file mode 100644 (file)
index 0000000..02e4ed1
--- /dev/null
@@ -0,0 +1,330 @@
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+     width="612px" height="458px" viewBox="0 0 612 458"
+     style="stroke:none">
+<title>Figure n°0</title>
+<desc>
+Creator: GL2PS 1.3.2, (C) 1999-2006 Christophe Geuzaine (geuz@geuz.org)
+For: Scilab
+CreationDate: Thu May  5 16:36:45 2011
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diff --git a/scilab/modules/cacsd/macros/damp.sci b/scilab/modules/cacsd/macros/damp.sci
new file mode 100644 (file)
index 0000000..0baba91
--- /dev/null
@@ -0,0 +1,97 @@
+function [wn,z,p] = damp(R,dt1)
+//Natural frequency and damping factor for continuous systems.
+//   [Wn,Z,P] = damp(R) returns vectors Wn and Z containing the
+//   natural frequencies and damping factors of R.
+//   The variable R  must be a real or complex array of roots, a
+//   polynomial array or  a linear dynamical system
+
+  if argn(2)<1 then
+    error(msprintf(_("%s: Wrong number of input arguments: %d or %d expected.\n"),"damp",1,2))
+  end
+  //handling optionnal argument dt1
+  if argn(2)==1 then
+    dt1=[];
+  else
+    if type(dt1)==1 then
+      if size(dt1,'*')<>1|dt1<0 then
+        error(msprintf(_("%s: Wrong type for input argument #%d: Real non negative scalar expected.\n"),..
+                       "damp",2))
+      end
+    elseif type(dt1)==10 then
+      if dt1=="c" then
+        dt1=0
+      elseif dt1=="d" then
+        dt1=1
+      else
+        error(msprintf(_("%s: Wrong value for input argument #%d: Must be in the set {%s}.\n"),..
+                       "damp",2,"""c"", ""d"""))
+      end
+    else
+      error(msprintf(_("%s: Wrong type for input argument #%d: Scalar or string expected.\n"),..
+                     "damp",2))
+    end
+  end
+
+  toBeOrdered=%t;dt=[];
+  select typeof(R)
+  case "polynomial" then //polynomial array
+    p=[];
+    for k=1:size(R,'*')
+      p=[p;roots(R(k),"e")];
+    end
+  case "rational" then
+    dt=R.dt
+    if dt=="c" then
+      dt=0
+    elseif dt=="d" then
+      dt=1
+    end
+    p=roots(lcm(R.den))
+  case "state-space" then
+    dt=R.dt
+    if dt=="c" then
+      dt=0
+    elseif dt=="d" then
+      dt=1
+    end
+    p=spec(R.A)
+  case "constant" then
+    p=R;
+    toBeOrdered=%f
+  else
+    error(msprintf(_("%s: Wrong type for input argument #%d: Array of floats or Polynomial expected.\n"),..
+                   "damp",1))
+  end
+  if dt==[] then
+    //R does not furnish time domain
+    if dt1==[] then
+      //no user time domain specified, continuuous time assumed
+      dt=0
+    else
+      //user time domain specified
+      dt=dt1
+    end
+  elseif dt1<>[] then
+    warning(msprintf(_("%s: Input argument #%d ignored.\n"),"damp",2))
+  end
+  // Initialize
+  wn=zeros(p);
+  z=-ones(p);
+  im=ieee();ieee(2);//to allow inf and nan's
+  if dt>0 then // Discrete  time case
+    ind=find(abs(p-1)>10*%eps)
+    s=p(ind);
+    s=log(s)/dt;
+  else //continuous time case
+    ind=find(p<>0)
+    s=p(ind);
+  end
+  wn(ind)=abs(s)
+  z(ind)=-real(s)./abs(s)
+  ieee(im)
+  if toBeOrdered then
+    [wn,k]=gsort(wn,'g','i');
+    z=z(k);
+    p=p(k)
+  end
+endfunction
diff --git a/scilab/modules/cacsd/tests/unit_tests/damp.dia.ref b/scilab/modules/cacsd/tests/unit_tests/damp.dia.ref
new file mode 100644 (file)
index 0000000..99be97b
--- /dev/null
@@ -0,0 +1,93 @@
+// =============================================================================
+// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+// Copyright (C) 2001 - INRIA - Serge Steer
+//
+//  This file is distributed under the same license as the Scilab package.
+// =============================================================================
+//Vector of complex numbers
+R=[2 1+%i  2-3*%i];
+[wn,zeta]=damp(R);
+assert_checkequal (wn,abs(R));
+assert_checkequal (zeta,-real(R)./wn);
+dt=1;
+[wn,zeta]=damp(R,dt);
+Rd=log(R)/dt;
+assert_checkequal (wn,abs(Rd));
+assert_checkequal (zeta,-real(Rd)./wn);
+R=0;
+[wn,zeta]=damp(R);
+assert_checkequal (wn,0);
+assert_checkequal (zeta,-1);
+R=0;dt=1;
+[wn,zeta]=damp(R,dt);
+assert_checkequal (wn,%inf);
+assert_checkequal (zeta,%nan);
+R=1;dt=1;
+[wn,zeta]=damp(R,dt);
+assert_checkequal (wn,0);
+assert_checkequal (zeta,-1);
+R=1;
+[wn,zeta]=damp(R);
+assert_checkequal (wn,1);
+assert_checkequal (zeta,-1);
+//Polynomial and Polynomial array
+P=real([poly([2 1+%i 1-%i  2-3*%i 2+3*%i],'s'),poly(0,'s'),poly(1,'s')]);
+[wn,zeta]=damp(P);
+wnref=[0;1;sqrt(2);sqrt(2);2;sqrt(13);sqrt(13)];
+zetaref=[-1;-1;-sqrt(2)/2;-sqrt(2)/2;-1;-2/sqrt(13);-2/sqrt(13)];
+assert_checkalmostequal (wn,wnref);
+assert_checkalmostequal (zeta,zetaref);
+[wn,zeta]=damp(prod(P));
+wnref=[0;1;sqrt(2);sqrt(2);2;sqrt(13);sqrt(13)];
+zetaref=[-1;-1;-sqrt(2)/2;-sqrt(2)/2;-1;-2/sqrt(13);-2/sqrt(13)];
+assert_checkalmostequal (wn,wnref);
+assert_checkalmostequal (zeta,zetaref);
+dt=1;
+[wn,zeta]=damp(P,dt);
+t1=log(1+%i)/dt;
+t2=log(2-3*%i)/dt;
+wnref=[0;log(2);abs(t1);abs(t1);abs(t2);abs(t2);%inf];
+zetaref=[-1;-1;-real(t1)/abs(t1);-real(t1)/abs(t1);-real(t2)/abs(t2);-real(t2)/abs(t2);%nan];
+assert_checkalmostequal (wn,wnref);
+assert_checkalmostequal (zeta,zetaref);
+dt=1;
+[wn,zeta]=damp(prod(P),dt);
+t1=log(1+%i)/dt;
+t2=log(2-3*%i)/dt;
+wnref=[0;log(2);abs(t1);abs(t1);abs(t2);abs(t2);%inf];
+zetaref=[1;-1;-real(t1)/abs(t1);-real(t1)/abs(t1);-real(t2)/abs(t2);-real(t2)/abs(t2);%nan];
+assert_checkalmostequal (wn,wnref);
+assert_checkalmostequal (zeta,zetaref);
+//transfer function
+[wn,zeta]=damp(syslin('c',ones(1,3),P));
+wnref=[0;1;sqrt(2);sqrt(2);2;sqrt(13);sqrt(13)];
+zetaref=[-1;-1;-sqrt(2)/2;-sqrt(2)/2;-1;-2/sqrt(13);-2/sqrt(13)];
+assert_checkalmostequal (wn,wnref);
+assert_checkalmostequal (zeta,zetaref);
+dt=1;
+[wn,zeta]=damp(syslin(dt,ones(1,3),P));
+t1=log(1+%i)/dt;
+t2=log(2-3*%i)/dt;
+wnref=[0;log(2);abs(t1);abs(t1);abs(t2);abs(t2);%inf];
+zetaref=[1;-1;-real(t1)/abs(t1);-real(t1)/abs(t1);-real(t2)/abs(t2);-real(t2)/abs(t2);%nan];
+assert_checkalmostequal (wn,wnref);
+assert_checkalmostequal (zeta,zetaref);
+//state-space
+[wn,zeta]=damp(tf2ss(syslin('c',1,prod(P))));
+wnref=[0;1;sqrt(2);sqrt(2);2;sqrt(13);sqrt(13)];
+zetaref=[-1;-1;-sqrt(2)/2;-sqrt(2)/2;-1;-2/sqrt(13);-2/sqrt(13)];
+assert_checkalmostequal (wn,wnref);
+assert_checkalmostequal (zeta,zetaref);
+dt=1;
+[wn,zeta]=damp(tf2ss(syslin(dt,1,prod(P))));
+t1=log(1+%i)/dt;
+t2=log(2-3*%i)/dt;
+wnref=[0;log(2);abs(t1);abs(t1);abs(t2);abs(t2);%inf];
+zetaref=[1;-1;-real(t1)/abs(t1);-real(t1)/abs(t1);-real(t2)/abs(t2);-real(t2)/abs(t2);%nan];
+assert_checkalmostequal (wn,wnref) ;
+assert_checkalmostequal (zeta,zetaref) ;
+//invalid calls
+assert_checkfalse(execstr("[wn,zeta]=damp()","errcatch")==0);
+assert_checkfalse(execstr("[wn,zeta]=damp(%t)","errcatch")==0);
+assert_checkfalse(execstr("[wn,zeta]=damp(P,1:3)","errcatch")==0);
+assert_checkfalse(execstr("[wn,zeta]=damp(P,%t)","errcatch")==0);
diff --git a/scilab/modules/cacsd/tests/unit_tests/damp.tst b/scilab/modules/cacsd/tests/unit_tests/damp.tst
new file mode 100644 (file)
index 0000000..20aa3a7
--- /dev/null
@@ -0,0 +1,108 @@
+// =============================================================================
+// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+// Copyright (C) 2001 - INRIA - Serge Steer
+//
+//  This file is distributed under the same license as the Scilab package.
+// =============================================================================
+//Vector of complex numbers
+
+R=[2 1+%i  2-3*%i];
+[wn,zeta]=damp(R);
+assert_checkequal (wn,abs(R));
+assert_checkequal (zeta,-real(R)./wn);
+
+dt=1;
+[wn,zeta]=damp(R,dt);
+Rd=log(R)/dt;
+assert_checkequal (wn,abs(Rd));
+assert_checkequal (zeta,-real(Rd)./wn);
+
+R=0;
+[wn,zeta]=damp(R);
+assert_checkequal (wn,0);
+assert_checkequal (zeta,-1);
+
+R=0;dt=1;
+[wn,zeta]=damp(R,dt);
+assert_checkequal (wn,%inf);
+assert_checkequal (zeta,%nan);
+
+R=1;dt=1;
+[wn,zeta]=damp(R,dt);
+assert_checkequal (wn,0);
+assert_checkequal (zeta,-1);
+
+R=1;
+[wn,zeta]=damp(R);
+assert_checkequal (wn,1);
+assert_checkequal (zeta,-1);
+
+//Polynomial and Polynomial array
+P=real([poly([2 1+%i 1-%i  2-3*%i 2+3*%i],'s'),poly(0,'s'),poly(1,'s')]);
+[wn,zeta]=damp(P);
+wnref=[0;1;sqrt(2);sqrt(2);2;sqrt(13);sqrt(13)];
+zetaref=[-1;-1;-sqrt(2)/2;-sqrt(2)/2;-1;-2/sqrt(13);-2/sqrt(13)];
+assert_checkalmostequal (wn,wnref);
+assert_checkalmostequal (zeta,zetaref);
+
+[wn,zeta]=damp(prod(P));
+wnref=[0;1;sqrt(2);sqrt(2);2;sqrt(13);sqrt(13)];
+zetaref=[-1;-1;-sqrt(2)/2;-sqrt(2)/2;-1;-2/sqrt(13);-2/sqrt(13)];
+assert_checkalmostequal (wn,wnref);
+assert_checkalmostequal (zeta,zetaref);
+
+dt=1;
+[wn,zeta]=damp(P,dt);
+t1=log(1+%i)/dt;
+t2=log(2-3*%i)/dt;
+wnref=[0;log(2);abs(t1);abs(t1);abs(t2);abs(t2);%inf];
+zetaref=[-1;-1;-real(t1)/abs(t1);-real(t1)/abs(t1);-real(t2)/abs(t2);-real(t2)/abs(t2);%nan];
+assert_checkalmostequal (wn,wnref);
+assert_checkalmostequal (zeta,zetaref);
+
+dt=1;
+[wn,zeta]=damp(prod(P),dt);
+t1=log(1+%i)/dt;
+t2=log(2-3*%i)/dt;
+wnref=[0;log(2);abs(t1);abs(t1);abs(t2);abs(t2);%inf];
+zetaref=[1;-1;-real(t1)/abs(t1);-real(t1)/abs(t1);-real(t2)/abs(t2);-real(t2)/abs(t2);%nan];
+assert_checkalmostequal (wn,wnref);
+assert_checkalmostequal (zeta,zetaref);
+
+//transfer function
+[wn,zeta]=damp(syslin('c',ones(1,3),P));
+wnref=[0;1;sqrt(2);sqrt(2);2;sqrt(13);sqrt(13)];
+zetaref=[-1;-1;-sqrt(2)/2;-sqrt(2)/2;-1;-2/sqrt(13);-2/sqrt(13)];
+assert_checkalmostequal (wn,wnref);
+assert_checkalmostequal (zeta,zetaref);
+
+dt=1;
+[wn,zeta]=damp(syslin(dt,ones(1,3),P));
+t1=log(1+%i)/dt;
+t2=log(2-3*%i)/dt;
+wnref=[0;log(2);abs(t1);abs(t1);abs(t2);abs(t2);%inf];
+zetaref=[1;-1;-real(t1)/abs(t1);-real(t1)/abs(t1);-real(t2)/abs(t2);-real(t2)/abs(t2);%nan];
+assert_checkalmostequal (wn,wnref);
+assert_checkalmostequal (zeta,zetaref);
+
+//state-space
+[wn,zeta]=damp(tf2ss(syslin('c',1,prod(P))));
+wnref=[0;1;sqrt(2);sqrt(2);2;sqrt(13);sqrt(13)];
+zetaref=[-1;-1;-sqrt(2)/2;-sqrt(2)/2;-1;-2/sqrt(13);-2/sqrt(13)];
+assert_checkalmostequal (wn,wnref);
+assert_checkalmostequal (zeta,zetaref);
+
+dt=1;
+[wn,zeta]=damp(tf2ss(syslin(dt,1,prod(P))));
+t1=log(1+%i)/dt;
+t2=log(2-3*%i)/dt;
+wnref=[0;log(2);abs(t1);abs(t1);abs(t2);abs(t2);%inf];
+zetaref=[1;-1;-real(t1)/abs(t1);-real(t1)/abs(t1);-real(t2)/abs(t2);-real(t2)/abs(t2);%nan];
+assert_checkalmostequal (wn,wnref) ;
+assert_checkalmostequal (zeta,zetaref) ;
+
+//invalid calls
+assert_checkfalse(execstr("[wn,zeta]=damp()","errcatch")==0);
+assert_checkfalse(execstr("[wn,zeta]=damp(%t)","errcatch")==0);
+assert_checkfalse(execstr("[wn,zeta]=damp(P,1:3)","errcatch")==0);
+assert_checkfalse(execstr("[wn,zeta]=damp(P,%t)","errcatch")==0);