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<td valign=baseline bgcolor="#ffe4b0"><b>AutotunerPID Toolkit</b></td>
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<h1>bodePIDcompare</h1>
<h2><a name="_name"></a>PURPOSE <a href="#_top"><img alt="^" border="0" src="up.png"></a></h2>
<div class="box"><strong>Comparison of Bode Diagrams with different autotuning method.</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 bodePIDcompare(num,den,tau) </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">BODEPIDCOMPARE Comparison of Bode Diagrams with different autotuning
methods
The function is typically called through the GUI in AutotunerPID.mdl
and provides a graphical comparison of four different autotuning
methods (STEP/ZN(OL), STEP/KT, STEP/IMC, RELAY/ZN(CL)) in frequency
domain.
By default the parameter Ms is set to 2 in KT methods, while the
parameter lambda is set 1/5 of the settling time of the plant.
BODEPIDCOMPARE(NUM,DEN,TAU) performs the comparative analysis directly
considering the plant described by the transfer function
NUM(s)
P(s) = -------- * exp(-TAU*s)
DEN(s)
See also STEPPID
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)">
<li><a href="idareas.html" class="code" title="function model = idareas(y,As,Ts)">idareas</a> IDAREAS Identification of a FOPDT model using the method of the</li><li><a href="pid_tuning.html" class="code" title="function [K,Ti,Td,N,b] = pid_tuning(model,method,param,regStruct,As)">pid_tuning</a> PID_TUNING Tune the parameters of a ISA-PID regulator with some</li></ul>
This function is called by:
<ul style="list-style-image:url(matlabicon.gif)">
<li><a href="envgui.html" class="code" title="function [sys,x0,str,ts] = envgui(t,x,u,flag,NoiseBlock,LoadDistBlock)">envgui</a> ENVGUI S-function for making a simple PID GUI</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 bodePIDcompare(num,den,tau)</a>
0002 <span class="comment">%BODEPIDCOMPARE Comparison of Bode Diagrams with different autotuning</span>
0003 <span class="comment">% methods</span>
0004 <span class="comment">%</span>
0005 <span class="comment">% The function is typically called through the GUI in AutotunerPID.mdl</span>
0006 <span class="comment">% and provides a graphical comparison of four different autotuning</span>
0007 <span class="comment">% methods (STEP/ZN(OL), STEP/KT, STEP/IMC, RELAY/ZN(CL)) in frequency</span>
0008 <span class="comment">% domain.</span>
0009 <span class="comment">% By default the parameter Ms is set to 2 in KT methods, while the</span>
0010 <span class="comment">% parameter lambda is set 1/5 of the settling time of the plant.</span>
0011 <span class="comment">%</span>
0012 <span class="comment">%</span>
0013 <span class="comment">% BODEPIDCOMPARE(NUM,DEN,TAU) performs the comparative analysis directly</span>
0014 <span class="comment">% considering the plant described by the transfer function</span>
0015 <span class="comment">% NUM(s)</span>
0016 <span class="comment">% P(s) = -------- * exp(-TAU*s)</span>
0017 <span class="comment">% DEN(s)</span>
0018 <span class="comment">%</span>
0019 <span class="comment">% See also STEPPID</span>
0020 <span class="comment">%</span>
0021 <span class="comment">% Author: William Spinelli (wspinell@elet.polimi.it)</span>
0022 <span class="comment">% Copyright 2004 W.Spinelli</span>
0023 <span class="comment">% $Revision: 1.0 $ $Date: 2004/02/27 12:00:00 $</span>
0024
0025 <span class="keyword">global</span> PIDPARAMETERS
0026
0027 <span class="comment">% Bode diagram of the real plant model</span>
0028 P = tf(num,den,<span class="string">'IODelay'</span>,tau);
0029 [m,f,w] = bode(P);
0030 w = logspace(log10(w(1)),log10(w(end)),512);
0031 s = j*w;
0032
0033 <span class="comment">% compute step response</span>
0034 [y,t] = step(P);
0035 Ts = min(real(abs(pole(P))))/50;
0036 [y,t] = step(P,0:Ts:t(end));
0037 Tf = t(end);
0038
0039 <span class="comment">% identify a FOPDT model</span>
0040 modelFOPDT = <a href="idareas.html" class="code" title="function model = idareas(y,As,Ts)">idareas</a>(y,1,Ts);
0041
0042 <span class="comment">% identify the point of the frequency response with omega_n = -pi</span>
0043 [Gm,Pm,Wcg,Wcp] = margin(P);
0044 modelPI.A = 2/Gm;
0045 modelPI.T = 2*pi/Wcg;
0046
0047 <span class="comment">% evaluate the frequency response of the plant</span>
0048 P = squeeze(freqresp(P,w)).';
0049
0050 <span class="comment">% Create new figure</span>
0051 Lfig = figure(<span class="keyword">...</span>
0052 <span class="string">'Name'</span>, <span class="string">'Bode diagram - Open loop function'</span>,<span class="keyword">...</span>
0053 <span class="string">'NumberTitle'</span>, <span class="string">'off'</span>,<span class="keyword">...</span>
0054 <span class="string">'MenuBar'</span>, <span class="string">'figure'</span>);
0055 Ffig = figure(<span class="keyword">...</span>
0056 <span class="string">'Name'</span>, <span class="string">'Bode diagram - Complementary sensitivity'</span>,<span class="keyword">...</span>
0057 <span class="string">'NumberTitle'</span>, <span class="string">'off'</span>,<span class="keyword">...</span>
0058 <span class="string">'MenuBar'</span>, <span class="string">'figure'</span>);
0059 Sfig = figure(<span class="keyword">...</span>
0060 <span class="string">'Name'</span>, <span class="string">'Bode diagram - Sensitivity'</span>,<span class="keyword">...</span>
0061 <span class="string">'NumberTitle'</span>, <span class="string">'off'</span>,<span class="keyword">...</span>
0062 <span class="string">'MenuBar'</span>, <span class="string">'figure'</span>);
0063
0064 <span class="comment">% Bode diagrams with different autotuner</span>
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