Mercurial > hg > ltpda
view m-toolbox/html_help/help/ug/sdomainfit.html @ 33:5e7477b94d94 database-connection-manager
Add known repositories list to LTPDAPreferences
| author | Daniele Nicolodi <nicolodi@science.unitn.it> |
|---|---|
| date | Mon, 05 Dec 2011 16:20:06 +0100 |
| parents | f0afece42f48 |
| children |
line wrap: on
line source
<!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>