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Import.
| author | Daniele Nicolodi <nicolodi@science.unitn.it> |
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| date | Wed, 23 Nov 2011 19:22:13 +0100 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/m-toolbox/html_help/help/ug/ltpda_training_topic_4_3.html Wed Nov 23 19:22:13 2011 +0100 @@ -0,0 +1,261 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/1999/REC-html401-19991224/loose.dtd"> + +<html lang="en"> +<head> + <meta name="generator" content= + "HTML Tidy for Mac OS X (vers 1st December 2004), see www.w3.org"> + <meta http-equiv="Content-Type" content= + "text/html; charset=us-ascii"> + + <title>Modelling a system (LTPDA Toolbox)</title> + <link rel="stylesheet" href="docstyle.css" type="text/css"> + <meta name="generator" content="DocBook XSL Stylesheets V1.52.2"> + <meta name="description" content= + "Presents an overview of the features, system requirements, and starting the toolbox."> + </head> + +<body> + <a name="top_of_page" id="top_of_page"></a> + + <p style="font-size:1px;"> </p> + + <table class="nav" summary="Navigation aid" border="0" width= + "100%" cellpadding="0" cellspacing="0"> + <tr> + <td valign="baseline"><b>LTPDA Toolbox</b></td><td><a href="../helptoc.html">contents</a></td> + + <td valign="baseline" align="right"><a href= + "ltpda_training_topic_4_2.html"><img src="b_prev.gif" border="0" align= + "bottom" alt="Transforming models between representations"></a> <a href= + "ltpda_training_topic_4_4.html"><img src="b_next.gif" border="0" align= + "bottom" alt="How to filter data"></a></td> + </tr> + </table> + + <h1 class="title"><a name="f3-12899" id="f3-12899"></a>Modelling a system</h1> + <hr> + + <p> + <p> + To show some of the possibilities of the toolbox to model digital system we + introduce the usual notation for a closed loop model +</p> +<div align="center"> + <img src="images/ltpda_training_1/topic4/ClosedLoop.png" alt="Closed Loop" border="3"> +</div> +<p> + In our example we will assume that we know the <tt>pzmodel</tt> of the filter, + <tt>H</tt>, and the open loop gain (OLG). These are related with the closed + loop gain (CLG) by the following equation +</p> +<br> +<div align="center"> + <img src="images/ltpda_training_1/topic4/ClosedLoop_eq.png" border="3"> +</div> +<br> +<p> + We want to determine H and CLG. We would also like to find a digital filter + for H, but we will deal with this in the following section. +</p> +<h2>Loading the starting models</h2> +<p> + Imagine that we have somehow managed to find the following model for OLG +</p> +<table cellspacing="0" class="body" cellpadding="2" border="0" width="50%"> + <colgroup> + <col width="15%"/> + <col width="35%"/> + </colgroup> + <thead> + <tr valign="top"> + <th class="categorylist">Key</th> + <th class="categorylist">Value</th> + </tr> + </thead> + <tbody> + <!-- Key 'filename' --> + <tr valign="top"> + <td bgcolor="#f3f4f5"> + <p><tt>GAIN</tt></p> + </td> + <td bgcolor="#f3f4f5"> + 4e6 + </td> + </tr> + <!-- Key 'filename' --> + <tr valign="top"> + <td bgcolor="#f3f4f5"> + <p><tt>POLES</tt></p> + </td> + <td bgcolor="#f3f4f5"> + 1e-6 + </td> + </tr> + </tbody> +</table> +<p> + then we can create a <tt>pzmodel</tt> with these parameters as follows +</p> +<div class="fragment"><pre> + OLG = pzmodel(4e6,1e-6,[],<span class="string">'OLG'</span>) + ---- pzmodel 1 ---- + name: OLG + gain: 4000000 + delay: 0 + iunits: [] + ounits: [] + description: + UUID: 3d8bce32-a9a9-4e72-ab4d-183da69a9b5d + pole 001: (f=1e-06 Hz,Q=NaN) + ------------------- +</pre></div> +<p> + To introduce the second model, the one describing <tt>H</tt>, we will show another feature + of the <tt>pzmodel</tt> constructor. We will read it from a LISO file, + since this contructor accepts this files as inputs. We can then type +</p> +<div class="fragment"><pre> + H = pzmodel(<span class="string">'topic4/LISOfile.fil'</span>) + ---- pzmodel 1 ---- + name: none + gain: 1000000000 + delay: 0 + iunits: [] + ounits: [] + description: + UUID: e683b32f-4653-474e-b457-939d33aeb63c + pole 001: (f=1e-06 Hz,Q=NaN) + pole 002: (f=1e-06 Hz,Q=NaN) + zero 001: (f=0.001 Hz,Q=NaN) +------------------- +</pre></div> +<pp> + and we see how the constructor recognizes and translates the poles and zeros in the file. + The model gets the name from the file but we can easily change it to have + the name of our model +</pp> +<div class="fragment"><pre> + H.setName; +</pre></div> +<pp> + According to our previous definition we can get the <tt>plant</tt> by dividing the + OLG by H. We can do so directly when dealing with <tt>pzmodel</tt> objects + since multiplication and division are allowed for these objects, then +</pp> +<div class="fragment"><pre> + G = OLG/H + ---- pzmodel 1 ---- + name: (OLG./H) + gain: 0.004 + delay: 0 + iunits: [] + ounits: [] + description: + UUID: fcd166f7-d726-4d39-ad2e-0f3b7141415b + pole 001: (f=1e-06 Hz,Q=NaN) + pole 002: (f=0.001 Hz,Q=NaN) + zero 001: (f=1e-06 Hz,Q=NaN) + zero 002: (f=1e-06 Hz,Q=NaN) + ------------------- +</pre></div> +<pp> + which we need to simplify to get rid of cancelling poles and zeros. We also + set the model name here. +</pp> +<div class="fragment"><pre> + G.setName; + G.simplify + ---- pzmodel 1 ---- + name: simplify(G) + gain: 0.004 + delay: 0 + iunits: [] + ounits: [] + description: + UUID: c1883713-b860-4942-a127-e42ea565460f + pole 001: (f=0.001 Hz,Q=NaN) + zero 001: (f=1e-06 Hz,Q=NaN) + ------------------- +</pre></div> +<pp> + The CLG requires more than a simple multiplication or division between models + and we will not be able to derive a <tt>pzmodel</tt> for it. However, we can + evaluate the response of this object as follows +</pp> +<div class="fragment"><pre> + pl = plist(<span class="string">'f1'</span>,1e-3,<span class="string">'f2'</span>,5,<span class="string">'nf'</span>,100); + CLG = 1/(1-resp(OLG,pl)); + CLG.setName(); + CLG.iplot(); +</pre></div> +<pp> + which gives us an AO that we can plot +</pp> +<div align="center"> + <img src="images/ltpda_training_1/topic4/ClosedLoop_resp.png" alt="Closed Loop response" width="800px" border="1"> +</div> +<h2>Fine, but my (real) system has a delay...</h2> +<p> + You can now repeat the same procedure but loading a <tt>H</tt> model with a delay + from the LISO file 'LISOFileDelay.fil' +</p> +<div class="fragment"><pre> + >> HDel = pzmodel(<span class="string">'topic4/LISOfileDelay.fil'</span>) + ---- pzmodel 1 ---- + name: none + gain: 1000000000 + delay: 0.125 + iunits: [] + ounits: [] + description: + UUID: 6dfbddc5-b186-4405-8f6e-02a2822a22c5 + pole 001: (f=1e-06 Hz,Q=NaN) + pole 002: (f=1e-06 Hz,Q=NaN) + zero 001: (f=0.001 Hz,Q=NaN) + ------------------- + HDel.setName(); + pl = plist(<span class="string">'f1'</span>,1e-3,<span class="string">'f2'</span>,5,<span class="string">'nf'</span>,100); + resp([H, HDel],pl) +</pre></div> +<p> + you will see how the delay is correctly handled, meaning that it is added when + we multiply two models and substracted if the models are divided. +</p> +<div align="center"> + <img src="images/ltpda_training_1/topic4/ClosedLoop_H_delay.png" alt="Response with delay" width="800px" border="1"> + <img src="images/ltpda_training_1/topic4/ClosedLoop_G_delay.png" alt="Response with delay" width="800px" border="1"> +</div> + + + + + + + + </p> + + <br> + <br> + <table class="nav" summary="Navigation aid" border="0" width= + "100%" cellpadding="0" cellspacing="0"> + <tr valign="top"> + <td align="left" width="20"><a href="ltpda_training_topic_4_2.html"><img src= + "b_prev.gif" border="0" align="bottom" alt= + "Transforming models between representations"></a> </td> + + <td align="left">Transforming models between representations</td> + + <td> </td> + + <td align="right">How to filter data</td> + + <td align="right" width="20"><a href= + "ltpda_training_topic_4_4.html"><img src="b_next.gif" border="0" align= + "bottom" alt="How to filter data"></a></td> + </tr> + </table><br> + + <p class="copy">©LTP Team</p> +</body> +</html>