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| 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/sdomainfit.html Wed Nov 23 19:22:13 2011 +0100 @@ -0,0 +1,268 @@ +<!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>S-Domain Fit (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= + "zdomainfit.html"><img src="b_prev.gif" border="0" align= + "bottom" alt="Z-Domain Fit"></a> <a href= + "gui.html"><img src="b_next.gif" border="0" align= + "bottom" alt="Graphical User Interfaces in LTPDA"></a></td> + </tr> + </table> + + <h1 class="title"><a name="f3-12899" id="f3-12899"></a>S-Domain Fit</h1> + <hr> + + <p> + +<!-- ================================================== --> +<!-- BEGIN CONTENT FILE --> +<!-- ================================================== --> +<!-- ===== link box: Begin ===== --> +<p> + <table border="1" width="80%"> + <tr> + <td> + <table border="0" cellpadding="5" class="categorylist" width="100%"> + <colgroup> + <col width="37%"/> + <col width="63%"/> + </colgroup> + <tbody> + <tr valign="top"> + <td> + <a href="#description">Description</a> + </td> + <td>S-domain system identification in LTPDA.</td> + </tr> + <tr valign="top"> + <td> + <a href="#algorithm">Algorithm</a> + </td> + <td>Fit Algorithm.</td> + </tr> + <tr valign="top"> + <td> + <a href="#examples">Examples</a> + </td> + <td>Usage example of s-domain system identification tool.</td> + </tr> + <tr valign="top"> + <td> + <a href="#references">References</a> + </td> + <td>Bibliographic references.</td> + </tr> + </tbody> + </table> + </td> + </tr> + </table> +</p> +<!-- ===== link box: End ====== --> + +<h2><a name="description">S-domain system identification in LTPDA</a></h2> +<p> + System identification in s-domain is performed with the function + <a href="matlab:doc('ao/sDomainFit')">sDomainFit</a>. + It is based on a modeified version of the vector fitting algorithm. + Details on the core agorithm can be found in [1 - 2]. +</p> + + + +<h2><a name="algorithm">Fit Algorithm</a></h2> + +<p> + The function performs a fitting loop to automatically identify model + order and parameters in s-domain. Output is a s-domain model expanded + in partial fractions: +</p> +<div class="fragment"><pre> + r1 rN + f(s) = ------- + ... + ------- + d + s - p1 s - pN +</pre></div> +<p> + Since the function can fit more than one input analysis object at a time + with a common set of poles, output + <a href="parfrac.html">parfrac</a> are embedded in a + <a href="class_desc_matrix.html">matrix</a> (note that this characteristic + will be probably changed becausse of the introduction of the + <a href="class_desc_collection.html">collection</a> class). +</p> +<p> + Identification loop stops when the stop condition is reached. + Stop criterion is based on three different approachs: + <ol> + <li> Mean Squared Error and variation <br> + Check if the normalized mean squared error is lower than the value specified in + <tt>FITTOL</tt> and if the relative variation of the mean squared error is lower + than the value specified in <tt>MSEVARTOL</tt>. + E.g. <tt>FITTOL = 1e-3</tt>, <tt>MSEVARTOL = 1e-2</tt> search for a fit with + normalized meam square error lower than <tt>1e-3</tt> and <tt>MSE</tt> relative + variation lower than <tt>1e-2</tt>. + </li> + <li> Log residuals difference and root mean squared error + <ul> + <li> Log Residuals difference </br> + Check if the minimum of the logarithmic difference between data and + residuals is larger than a specified value. ie. if the conditioning + value is <tt>2</tt>, the function ensures that the difference between data and + residuals is at lest two order of magnitude lower than data itsleves. + <li> Root Mean Squared Error </br> + Check that the variation of the root mean squared error is lower than + <tt>10^(-1*value)</tt>. + </ul> + </li> + <li> Residuals spectral flatness and root mean squared error + <ul> + <li> Residuals Spectral Flatness </br> + In case of a fit on noisy data, the residuals from a good fit are + expected to be as much as possible similar to a white noise. This + property can be used to test the accuracy of a fit procedure. In + particular it can be tested that the spectral flatness coefficient of + the residuals is larger than a certain qiantity sf such that <tt>0 < sf < 1</tt>. + <li> Root Mean Squared Error </br> + Check that the variation of the root mean squared error is lower than + <tt>10^(-1*value)</tt>. + </ul> + </li> + </ol> + +</p> +<p> + The function can also perform a single loop without taking care of + the stop conditions. This happens when <span class="string">'AutoSearch'</span> parameter is + set to <span class="string">'off'</span>. +</p> + + +<h2><a name="examples">Usage example of s-domain system identification tool</a></h2> +<p> + In this example we fit a given frequency response to get a partial fraction model. + For the meaning of any parameter please refer to + <a href="matlab:doc('ao')">ao</a> and + <a href="matlab:doc('ao/sDomainFit')">sDomainFit</a> + documentation pages. +</p> + +<div class="fragment"><pre> + pl = plist(... + <span class="string">'fsfcn'</span>, <span class="string">'(1e-3./(f).^2 + 1e3./(0.001+f) + 1e5.*f.^2).*1e-10'</span>,... + <span class="string">'f1'</span>, 1e-6,... + <span class="string">'f2'</span>, 5,... + <span class="string">'nf'</span>, 100); + + a = ao(pl); + a.setName; + + <span class="comment">% Fit parameter list</span> + pl_fit = plist(... + <span class="string">'AutoSearch'</span>,<span class="string">'on'</span>,... + <span class="string">'StartPolesOpt'</span>,<span class="string">'clog'</span>,... + <span class="string">'maxiter'</span>,50,... + <span class="string">'minorder'</span>,7,... + <span class="string">'maxorder'</span>,15,... + <span class="string">'weightparam'</span>,<span class="string">'abs'</span>,... + <span class="string">'CONDTYPE'</span>,<span class="string">'MSE'</span>,... + <span class="string">'FITTOL'</span>,1e-3,... + <span class="string">'MSEVARTOL'</span>,1e-2,... + <span class="string">'Plot'</span>,<span class="string">'on'</span>,... + <span class="string">'ForceStability'</span>,<span class="string">'off'</span>); + + <span class="comment">% Do fit</span> + mod = sDomainFit(a, pl_fit); +</pre></div> + +<p> + <tt>mod</tt> is a <tt>matrix</tt> object containing a <tt>parfrac</tt> object. +</p> + +<div class="fragment"><pre> + >> mod + ---- matrix 1 ---- + name: fit(a) + size: 1x1 + 01: parfrac | parfrac(fit(a)) + description: + UUID: 2dc1ac28-4199-42d2-9b1a-b420252b3f8c + ------------------ +</pre></div> + +<div class="fragment"><pre> + >> mod.objs + ---- parfrac 1 ---- + model: fit(a) + res: [1.69531090137847e-006;-1.69531095674486e-006;1.39082537801437e-007;-1.39094453401266e-007;3.9451875151135e-007;-3.94524993613367e-007;4.53671387948961e-007;-4.53664974359603e-007;1124.81020427899;0.000140057852149302-i*0.201412268649905;0.000140057852149302+i*0.201412268649905] + poles: [-1.18514026248382e-006;1.18514354570495e-006;-0.00457311582050939;0.0045734088943545;-0.0316764149343339;0.0316791653277322;-0.276256442292693;0.27627799022013;330754.550617933;-0.0199840558095427+i*118.439896186467;-0.0199840558095427-i*118.439896186467] + dir: 0 + pmul: [1;1;1;1;1;1;1;1;1;1;1] + iunits: [] + ounits: [] + description: + UUID: 2afc4c82-7c2a-4fe3-8910-d8590884d58c + ------------------- +</pre></div> + + +<h2><a name="references">References</a></h2> +<p> + <ol> + <li> B. Gustavsen and A. Semlyen, "Rational approximation of frequency + domain responses by Vector Fitting", IEEE Trans. Power Delivery + vol. 14, no. 3, pp. 1052-1061, July 1999. + <li> B. Gustavsen, "Improving the Pole Relocating Properties of Vector + Fitting", IEEE Trans. Power Delivery vol. 21, no. 3, pp. + 1587-1592, July 2006. + </ol> +</p> + </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="zdomainfit.html"><img src= + "b_prev.gif" border="0" align="bottom" alt= + "Z-Domain Fit"></a> </td> + + <td align="left">Z-Domain Fit</td> + + <td> </td> + + <td align="right">Graphical User Interfaces in LTPDA</td> + + <td align="right" width="20"><a href= + "gui.html"><img src="b_next.gif" border="0" align= + "bottom" alt="Graphical User Interfaces in LTPDA"></a></td> + </tr> + </table><br> + + <p class="copy">©LTP Team</p> +</body> +</html>