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author Daniele Nicolodi <nicolodi@science.unitn.it>
date Mon, 05 Dec 2011 16:20:06 +0100
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1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
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2 "http://www.w3.org/TR/1999/REC-html401-19991224/loose.dtd">
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3
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4 <html lang="en">
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5 <head>
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6 <meta name="generator" content=
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7 "HTML Tidy for Mac OS X (vers 1st December 2004), see www.w3.org">
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8 <meta http-equiv="Content-Type" content=
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9 "text/html; charset=us-ascii">
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10
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11 <title>Simulations (LTPDA Toolbox)</title>
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12 <link rel="stylesheet" href="docstyle.css" type="text/css">
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13 <meta name="generator" content="DocBook XSL Stylesheets V1.52.2">
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14 <meta name="description" content=
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15 "Presents an overview of the features, system requirements, and starting the toolbox.">
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16 </head>
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17
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18 <body>
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19 <a name="top_of_page" id="top_of_page"></a>
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20
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21 <p style="font-size:1px;">&nbsp;</p>
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22
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23 <table class="nav" summary="Navigation aid" border="0" width=
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24 "100%" cellpadding="0" cellspacing="0">
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25 <tr>
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26 <td valign="baseline"><b>LTPDA Toolbox</b></td><td><a href="../helptoc.html">contents</a></td>
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27
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28 <td valign="baseline" align="right"><a href=
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29 "ssm_assemble.html"><img src="b_prev.gif" border="0" align=
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30 "bottom" alt="Assembling systems"></a>&nbsp;&nbsp;&nbsp;<a href=
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31 "TransferFunction_model.html"><img src="b_next.gif" border="0" align=
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32 "bottom" alt="Transfer Function Modelling"></a></td>
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33 </tr>
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34 </table>
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35
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36 <h1 class="title"><a name="f3-12899" id="f3-12899"></a>Simulations</h1>
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37 <hr>
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38
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39 <p>
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40 <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
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41 <HTML>
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42 <HEAD>
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43 <META HTTP-EQUIV="CONTENT-TYPE" CONTENT="text/html; charset=windows-1252">
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44 <TITLE></TITLE>
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45 <META NAME="GENERATOR" CONTENT="OpenOffice.org 3.1 (Win32)">
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46 <META NAME="CREATED" CONTENT="0;0">
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47 <META NAME="CHANGEDBY" CONTENT="Adrien G">
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48 <META NAME="CHANGED" CONTENT="20090827;18204600">
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49 </HEAD>
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50 <BODY LANG="en-US" DIR="LTR">
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51 <P>The function simulate can use ssm object to produce simulations.
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52 </P>
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53 <H2>Simulation example.
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54 </H2>
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55 <P>The following closed loop system is built.
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56 </P>
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57 <DIV CLASS="fragment"><PRE><FONT SIZE=2>&gt;&gt; sys = ssm(plist(</FONT><FONT COLOR="#a020f0">'built-in'</FONT>, <FONT COLOR="#a020f0">'standard_system_params'</FONT>, <FONT COLOR="#a020f0">'setnames'</FONT>, {<FONT COLOR="#a020f0">'W'</FONT> <FONT COLOR="#a020f0">'C'</FONT>}, <FONT COLOR="#a020f0">'setvalues'</FONT>, [-0.2 -0.5]));
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58 &gt;&gt; sys.modifTimeStep(0.01);
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59 <FONT SIZE=2>&gt;&gt; sys.duplicateInput(</FONT><FONT COLOR="#a020f0">'U'</FONT>,<FONT COLOR="#a020f0">'Negative Bias'</FONT>);
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60 &gt;&gt; controller = ssm(plist( <FONT COLOR="#0000ff">...</FONT>
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61 <FONT COLOR="#a020f0">'amats'</FONT><FONT COLOR="#000000">,cell(0,0), </FONT><FONT COLOR="#a020f0">'bmats'</FONT><FONT COLOR="#000000">,cell(0,1), </FONT><FONT COLOR="#a020f0">'cmats'</FONT><FONT COLOR="#000000">,cell(1,0), </FONT><FONT COLOR="#a020f0">'dmats'</FONT><FONT COLOR="#000000">,{-1}, </FONT><FONT COLOR="#0000ff">...</FONT>
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62 <FONT COLOR="#a020f0">'timestep'</FONT><FONT COLOR="#000000">,0.01, </FONT><FONT COLOR="#a020f0">'name'</FONT><FONT COLOR="#000000">,</FONT><FONT COLOR="#a020f0">'controller'</FONT><FONT COLOR="#000000">, </FONT><FONT COLOR="#a020f0">'params'</FONT><FONT COLOR="#000000">,plist, </FONT><FONT COLOR="#0000ff">...</FONT>
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63 <FONT COLOR="#a020f0">'statenames'</FONT><FONT COLOR="#000000">,{}, </FONT><FONT COLOR="#a020f0">'inputnames'</FONT><FONT COLOR="#000000">,{</FONT><FONT COLOR="#a020f0">'Y'</FONT><FONT COLOR="#000000">}, </FONT><FONT COLOR="#a020f0">'outputnames'</FONT><FONT COLOR="#000000">,{</FONT><FONT COLOR="#a020f0">'U'</FONT><FONT COLOR="#000000">} ));</FONT>
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64 ------ ssm/1 -------
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65 amats: { [2x2] } [1x1]
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66 mmats: { [2x2] } [1x1]
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67 bmats: { [2x2] [2x1] } [1x2]
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68 cmats: { [1x2]
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69 [1x2] } [2x1]
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70 dmats: { [1x2] []
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71 [1x2] [] } [2x2]
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72 timestep: 0.01
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73 inputs: [1x2 ssmblock]
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74 1 : N | Fn [kg m s^(-2)], On [m]
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75 2 : Negative Bias | Fu [kg m s^(-2)]
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76 states: [1x1 ssmblock]
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77 1 : standard test system | x [m], xdot [m s^(-1)]
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78 outputs: [1x2 ssmblock]
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79 1 : Y | y [m]
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80 2 : U | U &gt; 1 []
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81 params: (empty-plist) [1x1 plist]
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82 version: $Id: ssm_simulation_content.html,v 1.3 2009/08/28 14:20:07 adrien Exp $
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83 Ninputs: 2
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84 inputsizes: [2 1]
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85 Noutputs: 2
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86 outputsizes: [1 1]
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87 Nstates: 1
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88 statesizes: 2
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89 Nparams: 0
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90 isnumerical: true
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91 hist: ssm.hist [1x1 history]
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92 procinfo: (empty-plist) [1x1 plist]
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93 plotinfo: (empty-plist) [1x1 plist]
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94 name: assembled( standard_system_params + controller))
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95 description:
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96 mdlfile:
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97 UUID: 163d7103-063b-4a57-af7e-b08d22fe42c1
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98 --------------------</PRE></DIV><P>
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99 Then we wish to use the inputs of N for a correlated force noise and
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100 measurement noise, &ldquo;Negative Bias&rdquo; for a sinewave, and
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101 there will be an observation DC offset.</P>
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102 <P>We want as an output the controller output &ldquo;U&rdquo; and the
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103 sensor output &ldquo;y&rdquo;.</P>
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104 <DIV CLASS="fragment"><PRE>&gt;&gt; ao1 = ao(plist(<FONT COLOR="#a020f0">'FCN'</FONT>,<FONT COLOR="#a020f0">'sin(0:0.01:100)'</FONT>));
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105 <FONT COLOR="#000000">&gt;&gt; ao_out = sysCL.simulate( plist(</FONT><FONT COLOR="#0000ff">...</FONT>
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106 <FONT COLOR="#a020f0"> 'NOISE VARIABLE NAMES'</FONT><FONT COLOR="#000000">, {</FONT><FONT COLOR="#a020f0">'Fn'</FONT><FONT COLOR="#000000"> </FONT><FONT COLOR="#a020f0">'On'</FONT><FONT COLOR="#000000">}, </FONT><FONT COLOR="#a020f0">'COVARIANCE'</FONT><FONT COLOR="#000000">, [1 0.1 ; 0.1 2] , </FONT><FONT COLOR="#0000ff">...</FONT>
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107 <FONT COLOR="#a020f0"> 'AOS VARIABLE NAMES'</FONT><FONT COLOR="#000000">, {</FONT><FONT COLOR="#a020f0">'Fu'</FONT><FONT COLOR="#000000">} ,</FONT><FONT COLOR="#a020f0">'AOS'</FONT><FONT COLOR="#000000">, ao1 ,</FONT><FONT COLOR="#0000ff">...</FONT>
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108 <FONT COLOR="#a020f0"> 'CONSTANT VARIABLE NAMES'</FONT><FONT COLOR="#000000">, {</FONT><FONT COLOR="#a020f0">'On'</FONT><FONT COLOR="#000000">}, </FONT><FONT COLOR="#a020f0">'CONSTANTS'</FONT><FONT COLOR="#000000">, 35, </FONT><FONT COLOR="#0000ff">...</FONT>
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109 <FONT COLOR="#a020f0"> 'RETURN STATES'</FONT><FONT COLOR="#000000">, {</FONT><FONT COLOR="#a020f0">'x'</FONT><FONT COLOR="#000000">}, </FONT><FONT COLOR="#a020f0">'RETURN OUTPUTS'</FONT><FONT COLOR="#000000">, {</FONT><FONT COLOR="#a020f0">'y'</FONT><FONT COLOR="#000000"> </FONT><FONT COLOR="#a020f0">'U &gt; 1'</FONT><FONT COLOR="#000000">}, </FONT><FONT COLOR="#0000ff">...</FONT>
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110 <FONT COLOR="#a020f0"> 'SSINI'</FONT><FONT COLOR="#000000"> , {[100;3]}, </FONT><FONT COLOR="#a020f0">'TINI'</FONT><FONT COLOR="#000000">, 0));</FONT>
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111 &gt;&gt; iplot(ao_out([1, 2, 3]));</PRE></DIV><P>
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112 <IMG SRC="images/simulate.png" NAME="images1" ALIGN=LEFT WIDTH=567 HEIGHT=454 BORDER=0><BR CLEAR=LEFT>It
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113 turns out the system output (blue) is not much like the state (red),
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114 causing the control (green) to waste a lot of energy. The state is
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115 not experimentally available, but might be obtained through
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116 filtering. The kalman method is so far the only filtering method
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117 implemented in the toolbox.</P>
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118 <DIV CLASS="fragment"><PRE><FONT COLOR="#000000">&gt;&gt; ao_est = sysCL.kalman( plist(</FONT><FONT COLOR="#0000ff">...</FONT>
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119 <FONT COLOR="#a020f0"> 'NOISE VARIABLE NAMES'</FONT><FONT COLOR="#000000">, {</FONT><FONT COLOR="#a020f0">'Fn'</FONT><FONT COLOR="#000000"> </FONT><FONT COLOR="#a020f0">'On'</FONT><FONT COLOR="#000000">}, </FONT><FONT COLOR="#a020f0">'COVARIANCE'</FONT><FONT COLOR="#000000">, [1 0.1 ; 0.1 2] , </FONT><FONT COLOR="#0000ff">...</FONT>
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120 <FONT COLOR="#a020f0"> 'AOS VARIABLE NAMES'</FONT><FONT COLOR="#000000">, {</FONT><FONT COLOR="#a020f0">'Fu'</FONT><FONT COLOR="#000000">} ,</FONT><FONT COLOR="#a020f0">'AOS'</FONT><FONT COLOR="#000000">, ao1 ,</FONT><FONT COLOR="#0000ff">...</FONT>
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121 <FONT COLOR="#a020f0"> 'CONSTANT VARIABLE NAMES'</FONT><FONT COLOR="#000000">, {</FONT><FONT COLOR="#a020f0">'On'</FONT><FONT COLOR="#000000">}, </FONT><FONT COLOR="#a020f0">'CONSTANTS'</FONT><FONT COLOR="#000000">, 35, </FONT><FONT COLOR="#0000ff">...</FONT>
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122 <FONT COLOR="#a020f0"> 'OUTPUT VARIABLE NAMES'</FONT><FONT COLOR="#000000">, {</FONT><FONT COLOR="#a020f0">'y'</FONT><FONT COLOR="#000000">}, </FONT><FONT COLOR="#a020f0">'OUTPUTS'</FONT><FONT COLOR="#000000"> , ao_out(2), </FONT><FONT COLOR="#0000ff">...</FONT>
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123 <FONT COLOR="#a020f0"> 'RETURN STATES'</FONT><FONT COLOR="#000000">, 1, </FONT><FONT COLOR="#a020f0">'RETURN OUTPUTS'</FONT><FONT COLOR="#000000">, 1 ));</FONT>
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124 &gt;&gt; iplot(ao_out(2), ao_est(1), ao_out(1))</PRE></DIV><P>
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125 <IMG SRC="images/kalman.png" NAME="images2" ALIGN=LEFT WIDTH=567 HEIGHT=454 BORDER=0><BR CLEAR=LEFT>In
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126 this example the estimate (blue) of the state (green) is
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127 satisfactory. It leads us to think that such a filter should be used
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128 to provide with the input of the controller.
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129 </P>
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130 <P>However, the DC offset correction by the kalman filter is one
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131 information that is not available under usual circumstances.
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132 </P>
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133 <P><BR><BR>
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134 </P>
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135 <P STYLE="margin-bottom: 0cm"><BR>
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136 </P>
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137 <P STYLE="margin-bottom: 0cm"><BR>
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138 </P>
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139 <P><BR><BR>
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140 </P>
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141 </BODY>
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142 </HTML>
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143 </p>
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144
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145 <br>
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146 <br>
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147 <table class="nav" summary="Navigation aid" border="0" width=
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148 "100%" cellpadding="0" cellspacing="0">
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149 <tr valign="top">
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150 <td align="left" width="20"><a href="ssm_assemble.html"><img src=
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151 "b_prev.gif" border="0" align="bottom" alt=
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152 "Assembling systems"></a>&nbsp;</td>
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153
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154 <td align="left">Assembling systems</td>
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155
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156 <td>&nbsp;</td>
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157
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158 <td align="right">Transfer Function Modelling</td>
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159
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160 <td align="right" width="20"><a href=
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161 "TransferFunction_model.html"><img src="b_next.gif" border="0" align=
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162 "bottom" alt="Transfer Function Modelling"></a></td>
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163 </tr>
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164 </table><br>
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165
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166 <p class="copy">&copy;LTP Team</p>
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167 </body>
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168 </html>