← Back to branch summary

~ubuntu-branches/ubuntu/hoary/scilab/hoary

« back to all changes in this revision

Viewing changes to man/fr/control/obscont.xml

  • Committer: Bazaar Package Importer
  • Author(s): Torsten Werner
  • Date: 2005-01-09 22:58:21 UTC
  • mfrom: (1.1.1 upstream)
  • Revision ID: james.westby@ubuntu.com-20050109225821-473xr8vhgugxxx5j
Tags: 3.0-12
http://bugs.debian.org/255869
changed configure.in to build scilab's own malloc.o, closes: #255869

Show diffs side-by-side

added added

removed removed

Lines of Context:
man/fr/control/obscont.xml
 
1
<?xml version="1.0" encoding="ISO-8859-1" standalone="no"?>
 
2
<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
 
3
<MAN>
 
4
  <LANGUAGE>eng</LANGUAGE>
 
5
  <TITLE>obscont</TITLE>
 
6
  <TYPE>Scilab Function</TYPE>
 
7
  <DATE>April 1993</DATE>
 
8
  <SHORT_DESCRIPTION name="obscont"> observer based controller</SHORT_DESCRIPTION>
 
9
  <CALLING_SEQUENCE>
 
10
    <CALLING_SEQUENCE_ITEM>[K]=obscont(P,Kc,Kf)  </CALLING_SEQUENCE_ITEM>
 
11
    <CALLING_SEQUENCE_ITEM>[J,r]=obscont(P,Kc,Kf)  </CALLING_SEQUENCE_ITEM>
 
12
  </CALLING_SEQUENCE>
 
13
  <PARAM>
 
14
    <PARAM_INDENT>
 
15
      <PARAM_ITEM>
 
16
        <PARAM_NAME>P</PARAM_NAME>
 
17
        <PARAM_DESCRIPTION>
 
18
          <SP>: <VERB>syslin</VERB> list (nominal plant) in state-space form, continuous  or discrete time</SP>
 
19
        </PARAM_DESCRIPTION>
 
20
      </PARAM_ITEM>
 
21
      <PARAM_ITEM>
 
22
        <PARAM_NAME>Kc</PARAM_NAME>
 
23
        <PARAM_DESCRIPTION>
 
24
          <SP>: real matrix, (full state) controller gain</SP>
 
25
        </PARAM_DESCRIPTION>
 
26
      </PARAM_ITEM>
 
27
      <PARAM_ITEM>
 
28
        <PARAM_NAME>Kf</PARAM_NAME>
 
29
        <PARAM_DESCRIPTION>
 
30
          <SP>: real matrix, filter gain</SP>
 
31
        </PARAM_DESCRIPTION>
 
32
      </PARAM_ITEM>
 
33
      <PARAM_ITEM>
 
34
        <PARAM_NAME>K</PARAM_NAME>
 
35
        <PARAM_DESCRIPTION>
 
36
          <SP>: <VERB>syslin</VERB> list (controller)</SP>
 
37
        </PARAM_DESCRIPTION>
 
38
      </PARAM_ITEM>
 
39
      <PARAM_ITEM>
 
40
        <PARAM_NAME>J</PARAM_NAME>
 
41
        <PARAM_DESCRIPTION>
 
42
          <SP>: <VERB>syslin</VERB> list (extended controller)</SP>
 
43
        </PARAM_DESCRIPTION>
 
44
      </PARAM_ITEM>
 
45
      <PARAM_ITEM>
 
46
        <PARAM_NAME>r</PARAM_NAME>
 
47
        <PARAM_DESCRIPTION>
 
48
          <SP>: 1x2 row vector</SP>
 
49
        </PARAM_DESCRIPTION>
 
50
      </PARAM_ITEM>
 
51
    </PARAM_INDENT>
 
52
  </PARAM>
 
53
  <DESCRIPTION>
 
54
    <P><VERB>obscont</VERB>  returns the observer-based controller associated with a 
 
55
    nominal plant <VERB>P</VERB> with matrices <VERB>[A,B,C,D]</VERB> (<VERB>syslin</VERB> list).</P>
 
56
    <P>
 
57
    The full-state control gain is <VERB>Kc</VERB> and the filter gain is <VERB>Kf</VERB>.
 
58
    These gains can be computed, for example, by pole placement.</P>
 
59
    <P><VERB>A+B*Kc</VERB> and <VERB>A+Kf*C</VERB> are (usually) assumed stable.</P>
 
60
    <P><VERB>K</VERB> is a state-space representation of the 
 
61
    compensator <VERB> K: y-&gt;u</VERB> in:</P>
 
62
    <P>
 
63
      <VERB> xdot = A x + B u,  y=C x + D u, zdot= (A + Kf C)z -Kf y +B u, u=Kc z</VERB>
 
64
    </P>
 
65
    <P><VERB>K</VERB> is a linear system (<VERB>syslin</VERB> list) with matrices given by:
 
66
     <VERB>K=[A+B*Kc+Kf*C+Kf*D*Kc,Kf,-Kc]</VERB>.</P>
 
67
    <P>
 
68
    The closed loop feedback system <VERB> Cl: v -&gt;y</VERB> with
 
69
    (negative) feedback <VERB>K</VERB> (i.e. <VERB>y = P u, u = v - K y</VERB>, or <VERB>xdot
 
70
    = A x + B u, y = C x + D u, zdot = (A + Kf C) z - Kf y + B u, u = v -F z</VERB>)
 
71
    is given by <VERB>Cl = P/.(-K)</VERB></P>
 
72
    <P>
 
73
    The poles of <VERB>Cl</VERB> (<VERB> spec(cl('A')) </VERB>) are located at the eigenvalues of <VERB>A+B*Kc</VERB>
 
74
    and <VERB>A+Kf*C</VERB>.</P>
 
75
    <P>
 
76
    Invoked with two output arguments <VERB>obscont</VERB> returns a
 
77
    (square) linear system <VERB>K</VERB> which parametrizes all the stabilizing
 
78
    feedbacks via a LFT.</P>
 
79
    <P>
 
80
    Let <VERB>Q</VERB> an arbitrary stable linear system of dimension <VERB>r(2)</VERB>x<VERB>r(1)</VERB>
 
81
    i.e. number of inputs x number of outputs in <VERB>P</VERB>.
 
82
    Then any stabilizing controller <VERB>K</VERB> for <VERB>P</VERB> can be expressed as
 
83
    <VERB>K=lft(J,r,Q)</VERB>. The controller which corresponds to <VERB>Q=0</VERB> is
 
84
    <VERB>K=J(1:nu,1:ny)</VERB> (this <VERB>K</VERB> is returned by <VERB>K=obscont(P,Kc,Kf)</VERB>).
 
85
    <VERB>r</VERB> is <VERB>size(P)</VERB> i.e the vector [number of outputs, number of inputs];</P>
 
86
  </DESCRIPTION>
 
87
  <EXAMPLE>
 
88
<![CDATA[
 
89
ny=2;nu=3;nx=4;P=ssrand(ny,nu,nx);[A,B,C,D]=abcd(P);
 
90
Kc=-ppol(A,B,[-1,-1,-1,-1]);  //Controller gain
 
91
Kf=-ppol(A',C',[-2,-2,-2,-2]);Kf=Kf';    //Observer gain
 
92
cl=P/.(-obscont(P,Kc,Kf));spec(cl('A'))   //closed loop system
 
93
[J,r]=obscont(P,Kc,Kf);
 
94
Q=ssrand(nu,ny,3);Q('A')=Q('A')-(maxi(real(spec(Q('A'))))+0.5)*eye(Q('A')) 
 
95
//Q is a stable parameter
 
96
K=lft(J,r,Q);
 
97
spec(h_cl(P,K))  // closed-loop A matrix (should be stable);
 
98
 ]]>
 
99
  </EXAMPLE>
 
100
  <SEE_ALSO>
 
101
    <SEE_ALSO_ITEM>
 
102
      <LINK>ppol</LINK>
 
103
    </SEE_ALSO_ITEM>
 
104
    <SEE_ALSO_ITEM>
 
105
      <LINK>lqg</LINK>
 
106
    </SEE_ALSO_ITEM>
 
107
    <SEE_ALSO_ITEM>
 
108
      <LINK>lqr</LINK>
 
109
    </SEE_ALSO_ITEM>
 
110
    <SEE_ALSO_ITEM>
 
111
      <LINK>lqe</LINK>
 
112
    </SEE_ALSO_ITEM>
 
113
    <SEE_ALSO_ITEM>
 
114
      <LINK>h_inf</LINK>
 
115
    </SEE_ALSO_ITEM>
 
116
    <SEE_ALSO_ITEM>
 
117
      <LINK>lft</LINK>
 
118
    </SEE_ALSO_ITEM>
 
119
    <SEE_ALSO_ITEM>
 
120
      <LINK>syslin</LINK>
 
121
    </SEE_ALSO_ITEM>
 
122
    <SEE_ALSO_ITEM>
 
123
      <LINK>feedback</LINK>
 
124
    </SEE_ALSO_ITEM>
 
125
    <SEE_ALSO_ITEM>
 
126
      <LINK>observer</LINK>
 
127
    </SEE_ALSO_ITEM>
 
128
  </SEE_ALSO>
 
129
  <AUTHOR>F.D. ; ;   </AUTHOR>
 
130
</MAN>