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<td valign=baseline bgcolor="#ffe4b0"><b>AutotunerPID Toolkit</b></td>
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<h1>idareas</h1>
<h2><a name="_name"></a>PURPOSE <a href="#_top"><img alt="^" border="0" src="up.png"></a></h2>
<div class="box"><strong>Identification of a FOPDT model using the method of the areas.</strong></div>
<h2><a name="_synopsis"></a>SYNOPSIS <a href="#_top"><img alt="^" border="0" src="up.png"></a></h2>
<div class="box"><strong>function model = idareas(y,As,Ts) </strong></div>
<h2><a name="_description"></a>DESCRIPTION <a href="#_top"><img alt="^" border="0" src="up.png"></a></h2>
<div class="fragment"><pre class="comment">IDAREAS Identification of a FOPDT model using the method of the
areas.
MODEL = IDAREAS(Y,As,Ts) returns a structure describing the identified
FOPDT (First Order Plus Dead Time) model in the form
M(s) = m*exp(-s*L) / (1+s*T)
The structure has the following fields MODEL.m, MODEL.L and MODEL.T
with obvious meaning.
The function requires the recorded step response Y, the amplitude of
the step used for identification As and the sample time Ts.
Author: William Spinelli (wspinell@elet.polimi.it)
Copyright 2004 W.Spinelli
$Revision: 1.0 $ $Date: 2004/02/27 12:00:00 $</pre></div>
<!-- crossreference -->
<h2><a name="_cross"></a>CROSS-REFERENCE INFORMATION <a href="#_top"><img alt="^" border="0" src="up.png"></a></h2>
This function calls:
<ul style="list-style-image:url(matlabicon.gif)">
</ul>
This function is called by:
<ul style="list-style-image:url(matlabicon.gif)">
<li><a href="bodePIDcompare.html" class="code" title="function bodePIDcompare(num,den,tau)">bodePIDcompare</a> BODEPIDCOMPARE Comparison of Bode Diagrams with different autotuning</li><li><a href="pid_autotuner.html" class="code" title="function [sys,x0,str,ts] = pid_autotuner(t,x,u,flag,Ts,As)">pid_autotuner</a> PID_SUPERV Supervisor of a PID autotuner (implmented as an S-function)</li><li><a href="stepPIDcompare.html" class="code" title="function stepPIDcompare(num,den,tau)">stepPIDcompare</a> STEPPIDCOMPARE Comparison of step response on setpoint and load</li></ul>
<!-- crossreference -->
<h2><a name="_source"></a>SOURCE CODE <a href="#_top"><img alt="^" border="0" src="up.png"></a></h2>
<div class="fragment"><pre>0001 <a name="_sub0" href="#_subfunctions" class="code">function model = idareas(y,As,Ts)</a>
0002 <span class="comment">%IDAREAS Identification of a FOPDT model using the method of the</span>
0003 <span class="comment">% areas.</span>
0004 <span class="comment">%</span>
0005 <span class="comment">% MODEL = IDAREAS(Y,As,Ts) returns a structure describing the identified</span>
0006 <span class="comment">% FOPDT (First Order Plus Dead Time) model in the form</span>
0007 <span class="comment">% M(s) = m*exp(-s*L) / (1+s*T)</span>
0008 <span class="comment">% The structure has the following fields MODEL.m, MODEL.L and MODEL.T</span>
0009 <span class="comment">% with obvious meaning.</span>
0010 <span class="comment">% The function requires the recorded step response Y, the amplitude of</span>
0011 <span class="comment">% the step used for identification As and the sample time Ts.</span>
0012 <span class="comment">%</span>
0013 <span class="comment">% Author: William Spinelli (wspinell@elet.polimi.it)</span>
0014 <span class="comment">% Copyright 2004 W.Spinelli</span>
0015 <span class="comment">% $Revision: 1.0 $ $Date: 2004/02/27 12:00:00 $</span>
0016
0017 <span class="comment">% compute auxiliary parameters</span>
0018 m = (y(end)-y(1))/As; <span class="comment">% process gain</span>
0019
0020 <span class="comment">% if m<0 reverse the step response</span>
0021 <span class="keyword">if</span> m<0
0022 y = -y;
0023 <span class="keyword">end</span>
0024
0025 <span class="comment">% change this setting one can try to robustify the identification process</span>
0026 <span class="comment">% with noisy step response</span>
0027 y1 = y(1);
0028 yN = y(end);
0029
0030 <span class="comment">% reverse undershoot and overshoot</span>
0031 y(y<y1) = y1;
0032 y(y>yN) = y(y>yN) - 2*(y(y>yN)-yN);
0033
0034 A0 = sum(yN-y)*Ts; <span class="comment">% upper area</span>
0035 it0 = fix(A0/abs(m)/Ts); <span class="comment">% compute the index of the vector</span>
0036 <span class="comment">% (not the value of t0)</span>
0037 A1 = sum(y(1:it0)-y1)*Ts; <span class="comment">% lower area</span>
0038
0039 <span class="comment">% compute model parameters</span>
0040 T = exp(1)*A1/abs(m);
0041 L = max((A0-exp(1)*A1)/abs(m),0);
0042
0043 model.L = L;
0044 model.T = T;
0045 model.m = m;</pre></div>
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