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Import.
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 23 Nov 2011 19:22:13 +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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Daniele Nicolodi <nicolodi@science.unitn.it>
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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;17255200">
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Daniele Nicolodi <nicolodi@science.unitn.it>
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10 </HEAD>
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11 <BODY LANG="de-DE" DIR="LTR">
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Daniele Nicolodi <nicolodi@science.unitn.it>
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12 <P>A collection of ssm arrays can be assembled into one ssm using the
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Daniele Nicolodi <nicolodi@science.unitn.it>
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13 assemble function.</P>
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Daniele Nicolodi <nicolodi@science.unitn.it>
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14 <H2>Managing inputs/outputs when assembling</H2>
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Daniele Nicolodi <nicolodi@science.unitn.it>
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15 <P>The order of the systems does not modify the output of .
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Daniele Nicolodi <nicolodi@science.unitn.it>
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16 The function assemble work by matching inputs and outputs of the same
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Daniele Nicolodi <nicolodi@science.unitn.it>
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17 name. Of course, they must have the same dimensionality, same
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Daniele Nicolodi <nicolodi@science.unitn.it>
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18 time-step. However, the check for units is not implemented yet.</P>
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Daniele Nicolodi <nicolodi@science.unitn.it>
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19 <P>In terms of time-step it is important to assemble all continuously
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Daniele Nicolodi <nicolodi@science.unitn.it>
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20 linked models together when the system is continuous, and discretize
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Daniele Nicolodi <nicolodi@science.unitn.it>
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21 it later on. Time discrete models (typically digital systems, and the
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Daniele Nicolodi <nicolodi@science.unitn.it>
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22 dynamical branch from the actuator input to the sensor output) should
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Daniele Nicolodi <nicolodi@science.unitn.it>
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23 be assembled together when they are time-discrete. The discretization
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Daniele Nicolodi <nicolodi@science.unitn.it>
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24 includes a zero hold which models correctly the A/D filter behavior.</P>
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Daniele Nicolodi <nicolodi@science.unitn.it>
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25 <P>Moreover, a system can be assembled in multiple steps. In this
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26 case there is a risk of &ldquo;closing a loop&rdquo; multiple times.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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27 To avoid this, the method &ldquo;assemble&rdquo; suppresses the
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Daniele Nicolodi <nicolodi@science.unitn.it>
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28 inputs once they are assembled. May the user need the input for a
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Daniele Nicolodi <nicolodi@science.unitn.it>
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29 simulation later on, he must duplicate it using the function
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Daniele Nicolodi <nicolodi@science.unitn.it>
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30 &ldquo;inputDuplicate&rdquo;. Built-in models should also have
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Daniele Nicolodi <nicolodi@science.unitn.it>
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31 built-in duplicated inputs to insert signals.</P>
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Daniele Nicolodi <nicolodi@science.unitn.it>
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32 <H2>Example using an existing built-in models</H2>
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33 <DIV CLASS="fragment"><PRE STYLE="margin-bottom: 0.5cm">&gt;&gt; <FONT COLOR="#000000"><FONT FACE="Courier New, monospace">sys = ssm(plist(</FONT></FONT><FONT COLOR="#a020f0"><FONT FACE="Courier New, monospace"><FONT SIZE=2>'built-in'</FONT></FONT></FONT><FONT COLOR="#000000"><FONT FACE="Courier New, monospace"><FONT SIZE=2>, </FONT></FONT></FONT><FONT COLOR="#a020f0"><FONT FACE="Courier New, monospace">'standard_system_params'</FONT></FONT><FONT COLOR="#000000"><FONT FACE="Courier New, monospace">, </FONT></FONT><FONT COLOR="#a020f0"><FONT FACE="Courier New, monospace">'setnames'</FONT></FONT><FONT COLOR="#000000"><FONT FACE="Courier New, monospace">, {</FONT></FONT><FONT COLOR="#a020f0"><FONT FACE="Courier New, monospace"><FONT SIZE=2>'W'</FONT></FONT></FONT><FONT COLOR="#000000"><FONT FACE="Courier New, monospace"><FONT SIZE=2>}, </FONT></FONT></FONT><FONT COLOR="#a020f0"><FONT FACE="Courier New, monospace"><FONT SIZE=2>'setvalues'</FONT></FONT></FONT><FONT COLOR="#000000"><FONT FACE="Courier New, monospace"><FONT SIZE=2>, 0.2*i ));</FONT></FONT></FONT></PRE></DIV><P>
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34 Trying sys.isStable with the first and the third system shows a
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Daniele Nicolodi <nicolodi@science.unitn.it>
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35 different result, the negative stiffness making the latter unstable.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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36 The system can be made time discrete using the function
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Daniele Nicolodi <nicolodi@science.unitn.it>
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37 &ldquo;modifTimeStep&rdquo;.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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38 The input is then duplicated to be used for a controller feedback.</P>
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Daniele Nicolodi <nicolodi@science.unitn.it>
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39 <DIV CLASS="fragment"><PRE>&gt;&gt; sys = ssm(plist(<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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Daniele Nicolodi <nicolodi@science.unitn.it>
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40 &gt;&gt; sys.modifTimeStep(0.01);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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41 &gt;&gt; sys.duplicateInput(<FONT COLOR="#a020f0">'U'</FONT>,<FONT COLOR="#a020f0">'Negative Bias'</FONT>)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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42 ------ ssm/1 -------
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Daniele Nicolodi <nicolodi@science.unitn.it>
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43 amats: { [2x2] } [1x1]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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44 mmats: { [2x2] } [1x1]
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45 bmats: { [2x1] [2x2] [2x1] } [1x3]
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46 cmats: { [1x2] } [1x1]
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47 dmats: { [] [1x2] [] } [1x3]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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48 timestep: 0.01
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Daniele Nicolodi <nicolodi@science.unitn.it>
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49 inputs: [1x3 ssmblock]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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50 1 : U | Fu [kg m s^(-2)]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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51 2 : N | Fn [kg m s^(-2)], On [m]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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52 3 : Negative Bias | Fu [kg m s^(-2)]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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53 states: [1x1 ssmblock]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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54 1 : standard test system | x [m], xdot [m s^(-1)]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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55 outputs: [1x1 ssmblock]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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56 1 : Y | y [m]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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57 params: (empty-plist) [1x1 plist]
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58 version: $Id: ssm_assemble_content.html,v 1.4 2009/08/28 15:11:53 adrien Exp $--&gt;$Id: ssm_assemble_content.html,v 1.4 2009/08/28 15:11:53 adrien Exp $
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Daniele Nicolodi <nicolodi@science.unitn.it>
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59 Ninputs: 3
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60 inputsizes: [1 2 1]
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61 Noutputs: 1
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Daniele Nicolodi <nicolodi@science.unitn.it>
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62 outputsizes: 1
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Daniele Nicolodi <nicolodi@science.unitn.it>
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63 Nstates: 1
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64 statesizes: 2
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Daniele Nicolodi <nicolodi@science.unitn.it>
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65 Nparams: 0
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66 isnumerical: true
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67 hist: ssm.hist [1x1 history]
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68 procinfo: (empty-plist) [1x1 plist]
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69 plotinfo: (empty-plist) [1x1 plist]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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70 name: standard_system_params
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Daniele Nicolodi <nicolodi@science.unitn.it>
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71 description: standard spring-mass-dashpot test system
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Daniele Nicolodi <nicolodi@science.unitn.it>
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72 mdlfile:
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73 UUID: 284b0ae3-947d-430a-802e-d9c3738ebb14
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74 --------------------
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Daniele Nicolodi <nicolodi@science.unitn.it>
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75 M: running isStable
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76 ans =
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Daniele Nicolodi <nicolodi@science.unitn.it>
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77 2.05114794494015
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78 warning, system named &quot;standard_system_params&quot; is not stable
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79 ans =
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Daniele Nicolodi <nicolodi@science.unitn.it>
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80 0</PRE></DIV><P>
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Daniele Nicolodi <nicolodi@science.unitn.it>
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81 Then a controller can be created to make the system stable.</P>
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82 <DIV CLASS="fragment"><PRE>&gt;&gt; <FONT COLOR="#000000"><FONT FACE="Courier New, monospace"><FONT SIZE=2>controller = ssm(plist( </FONT></FONT></FONT><FONT COLOR="#0000ff"><FONT FACE="Courier New, monospace"><FONT SIZE=2>...</FONT></FONT></FONT>
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Daniele Nicolodi <nicolodi@science.unitn.it>
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83 <FONT COLOR="#000000"> </FONT><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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84 <FONT COLOR="#000000"> </FONT><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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85 <FONT COLOR="#000000"> </FONT><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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86 &gt;&gt; sysCL = assemble(sys, controller);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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87 &gt;&gt; sysCL.isStable
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Daniele Nicolodi <nicolodi@science.unitn.it>
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88
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89 ------ ssm/1 -------
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90 amats: { [2x2] } [1x1]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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91 mmats: { [2x2] } [1x1]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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92 bmats: { [2x2] [2x1] } [1x2]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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93 cmats: { [1x2]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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94 [1x2] } [2x1]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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95 dmats: { [1x2] []
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Daniele Nicolodi <nicolodi@science.unitn.it>
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96 [1x2] [] } [2x2]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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97 timestep: 0.01
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Daniele Nicolodi <nicolodi@science.unitn.it>
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98 inputs: [1x2 ssmblock]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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99 1 : N | Fn [kg m s^(-2)], On [m]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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100 2 : Negative Bias | Fu [kg m s^(-2)]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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101 states: [1x1 ssmblock]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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102 1 : standard test system | x [m], xdot [m s^(-1)]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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103 outputs: [1x2 ssmblock]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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104 1 : Y | y [m]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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105 2 : U | U &gt; 1 []
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Daniele Nicolodi <nicolodi@science.unitn.it>
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106 params: (empty-plist) [1x1 plist]
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107 version: $Id: ssm_assemble_content.html,v 1.4 2009/08/28 15:11:53 adrien Exp $
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Daniele Nicolodi <nicolodi@science.unitn.it>
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108 Ninputs: 2
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Daniele Nicolodi <nicolodi@science.unitn.it>
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109 inputsizes: [2 1]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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110 Noutputs: 2
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Daniele Nicolodi <nicolodi@science.unitn.it>
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111 outputsizes: [1 1]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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112 Nstates: 1
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113 statesizes: 2
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Daniele Nicolodi <nicolodi@science.unitn.it>
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114 Nparams: 0
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Daniele Nicolodi <nicolodi@science.unitn.it>
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115 isnumerical: true
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Daniele Nicolodi <nicolodi@science.unitn.it>
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116 hist: ssm.hist [1x1 history]
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117 procinfo: (empty-plist) [1x1 plist]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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118 plotinfo: (empty-plist) [1x1 plist]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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119 name: assembled( standard_system_params + controller))
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Daniele Nicolodi <nicolodi@science.unitn.it>
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120 description:
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Daniele Nicolodi <nicolodi@science.unitn.it>
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121 mdlfile:
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122 UUID: c6f7397e-add7-4f4c-8eb0-fd0a4841e3cf
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123 --------------------
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Daniele Nicolodi <nicolodi@science.unitn.it>
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124 M: running isStable
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Daniele Nicolodi <nicolodi@science.unitn.it>
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125 System named &quot;assembled( standard_system_params + controller))&quot; is stable
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Daniele Nicolodi <nicolodi@science.unitn.it>
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126 ans =
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127 1</PRE></DIV><P>
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128 We can then use the system to produce a simulation.</P>
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129 <P><BR><BR>
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130 </P>
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131 </BODY>
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132 </HTML>