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Update ao_model_retrieve_in_timespan
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Mon, 05 Dec 2011 16:20:06 +0100
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Daniele Nicolodi <nicolodi@science.unitn.it>
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1 <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
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2 <HTML>
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3 <HEAD>
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4 <META HTTP-EQUIV="CONTENT-TYPE" CONTENT="text/html; charset=windows-1252">
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5 <TITLE></TITLE>
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6 <META NAME="GENERATOR" CONTENT="OpenOffice.org 3.1 (Win32)">
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7 <META NAME="CREATED" CONTENT="0;0">
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8 <META NAME="CHANGEDBY" CONTENT="Adrien G">
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9 <META NAME="CHANGED" CONTENT="20090827;18204600">
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10 </HEAD>
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11 <BODY LANG="en-US" DIR="LTR">
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12 <P>The function simulate can use ssm object to produce simulations.
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13 </P>
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14 <H2>Simulation example.
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15 </H2>
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16 <P>The following closed loop system is built.
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17 </P>
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18 <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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19 &gt;&gt; sys.modifTimeStep(0.01);
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20 <FONT SIZE=2>&gt;&gt; sys.duplicateInput(</FONT><FONT COLOR="#a020f0">'U'</FONT>,<FONT COLOR="#a020f0">'Negative Bias'</FONT>);
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21 &gt;&gt; controller = ssm(plist( <FONT COLOR="#0000ff">...</FONT>
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22 <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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23 <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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24 <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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Daniele Nicolodi <nicolodi@science.unitn.it>
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25 ------ ssm/1 -------
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26 amats: { [2x2] } [1x1]
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27 mmats: { [2x2] } [1x1]
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28 bmats: { [2x2] [2x1] } [1x2]
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29 cmats: { [1x2]
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30 [1x2] } [2x1]
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31 dmats: { [1x2] []
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32 [1x2] [] } [2x2]
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33 timestep: 0.01
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34 inputs: [1x2 ssmblock]
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35 1 : N | Fn [kg m s^(-2)], On [m]
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36 2 : Negative Bias | Fu [kg m s^(-2)]
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37 states: [1x1 ssmblock]
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38 1 : standard test system | x [m], xdot [m s^(-1)]
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39 outputs: [1x2 ssmblock]
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40 1 : Y | y [m]
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41 2 : U | U &gt; 1 []
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42 params: (empty-plist) [1x1 plist]
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43 version: $Id: ssm_simulation_content.html,v 1.3 2009/08/28 14:20:07 adrien Exp $
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44 Ninputs: 2
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45 inputsizes: [2 1]
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46 Noutputs: 2
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47 outputsizes: [1 1]
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48 Nstates: 1
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49 statesizes: 2
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50 Nparams: 0
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51 isnumerical: true
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52 hist: ssm.hist [1x1 history]
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53 procinfo: (empty-plist) [1x1 plist]
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54 plotinfo: (empty-plist) [1x1 plist]
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55 name: assembled( standard_system_params + controller))
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56 description:
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57 mdlfile:
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58 UUID: 163d7103-063b-4a57-af7e-b08d22fe42c1
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59 --------------------</PRE></DIV><P>
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60 Then we wish to use the inputs of N for a correlated force noise and
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61 measurement noise, &ldquo;Negative Bias&rdquo; for a sinewave, and
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62 there will be an observation DC offset.</P>
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63 <P>We want as an output the controller output &ldquo;U&rdquo; and the
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64 sensor output &ldquo;y&rdquo;.</P>
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65 <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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66 <FONT COLOR="#000000">&gt;&gt; ao_out = sysCL.simulate( plist(</FONT><FONT COLOR="#0000ff">...</FONT>
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67 <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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68 <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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69 <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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70 <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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71 <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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72 &gt;&gt; iplot(ao_out([1, 2, 3]));</PRE></DIV><P>
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73 <IMG SRC="images/simulate.png" NAME="images1" ALIGN=LEFT WIDTH=567 HEIGHT=454 BORDER=0><BR CLEAR=LEFT>It
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74 turns out the system output (blue) is not much like the state (red),
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75 causing the control (green) to waste a lot of energy. The state is
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76 not experimentally available, but might be obtained through
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77 filtering. The kalman method is so far the only filtering method
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78 implemented in the toolbox.</P>
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79 <DIV CLASS="fragment"><PRE><FONT COLOR="#000000">&gt;&gt; ao_est = sysCL.kalman( plist(</FONT><FONT COLOR="#0000ff">...</FONT>
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80 <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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81 <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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82 <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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83 <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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84 <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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85 &gt;&gt; iplot(ao_out(2), ao_est(1), ao_out(1))</PRE></DIV><P>
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86 <IMG SRC="images/kalman.png" NAME="images2" ALIGN=LEFT WIDTH=567 HEIGHT=454 BORDER=0><BR CLEAR=LEFT>In
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87 this example the estimate (blue) of the state (green) is
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Daniele Nicolodi <nicolodi@science.unitn.it>
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88 satisfactory. It leads us to think that such a filter should be used
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89 to provide with the input of the controller.
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90 </P>
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91 <P>However, the DC offset correction by the kalman filter is one
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92 information that is not available under usual circumstances.
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93 </P>
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94 <P><BR><BR>
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95 </P>
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96 <P STYLE="margin-bottom: 0cm"><BR>
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97 </P>
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98 <P STYLE="margin-bottom: 0cm"><BR>
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99 </P>
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100 <P><BR><BR>
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101 </P>
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102 </BODY>
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103 </HTML>