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<td valign=baseline bgcolor="#ffe4b0"><b>AutotunerPID Toolkit</b></td>
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<h1>pid_structure</h1>
<h2><a name="_name"></a>PURPOSE <a href="#_top"><img alt="^" border="0" src="up.png"></a></h2>
<div class="box"><strong>Structure selection for a ISA-PID regulator.</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 regStruct = pid_structure(model,reqStruct) </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">PID_STRUCTURE Structure selection for a ISA PID regulator.
REGSTRUCT = PID_STRUCTURE(MODEL,REQSTRUCT) returns the ``best''
structure for the regulator, assuming that the controlled plant can be
described with a FOPDT model.
MODEL is a structure with the description of the process model with the
fields {m L T} (parameters of a FOPDT model M(s) = m*exp(-sL)/(1+s*T)).
The structure may be computed through the function setting the flag
REQSTRUCT to 'AUTO', or may be constrained to a particular one by
setting the flag REQSTRUCT to 'PI' or 'PID' respectively.
The structure selection is performed only if a FOPDT model of the
process is given, otherwise the PID structure is selected. If the
control problem is intrinsically difficult the PID structure is
selected, and a warning message is prompted.
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="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></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 regStruct = pid_structure(model,reqStruct)</a>
0002 <span class="comment">%PID_STRUCTURE Structure selection for a ISA-PID regulator.</span>
0003 <span class="comment">%</span>
0004 <span class="comment">% REGSTRUCT = PID_STRUCTURE(MODEL,REQSTRUCT) returns the ``best''</span>
0005 <span class="comment">% structure for the regulator, assuming that the controlled plant can be</span>
0006 <span class="comment">% described with a FOPDT model.</span>
0007 <span class="comment">% MODEL is a structure with the description of the process model with the</span>
0008 <span class="comment">% fields {m L T} (parameters of a FOPDT model M(s) = m*exp(-sL)/(1+s*T)).</span>
0009 <span class="comment">% The structure may be computed through the function setting the flag</span>
0010 <span class="comment">% REQSTRUCT to 'AUTO', or may be constrained to a particular one by</span>
0011 <span class="comment">% setting the flag REQSTRUCT to 'PI' or 'PID' respectively.</span>
0012 <span class="comment">%</span>
0013 <span class="comment">% The structure selection is performed only if a FOPDT model of the</span>
0014 <span class="comment">% process is given, otherwise the PID structure is selected. If the</span>
0015 <span class="comment">% control problem is intrinsically difficult the PID structure is</span>
0016 <span class="comment">% selected, and a warning message is prompted.</span>
0017 <span class="comment">%</span>
0018 <span class="comment">% Author: William Spinelli (wspinell@elet.polimi.it)</span>
0019 <span class="comment">% Copyright 2004 W.Spinelli</span>
0020 <span class="comment">% $Revision: 1.0 $ $Date: 2004/02/27 12:00:00 $</span>
0021
0022 <span class="keyword">if</span> nargin < 2
0023 reqStruct = <span class="string">'AUTO'</span>;
0024 <span class="keyword">end</span>
0025
0026 <span class="keyword">switch</span> reqStruct
0027 <span class="keyword">case</span> <span class="string">'PI'</span>
0028 <span class="comment">% override selection</span>
0029 regStruct = <span class="string">'PI'</span>;
0030
0031 <span class="keyword">case</span> <span class="string">'PID'</span>
0032 <span class="comment">% override selection</span>
0033 regStruct = <span class="string">'PID'</span>;
0034
0035 <span class="keyword">case</span> <span class="string">'AUTO'</span>
0036 <span class="keyword">if</span> isfield(model,<span class="string">'m'</span>)
0037 <span class="comment">% selection performed only if a FOPDT model is provided</span>
0038 m = model.m; L = model.L; T = model.T;
0039
0040 <span class="comment">% compute the ultimate frequency</span>
0041 wmin = (-pi/2)/L; <span class="comment">% lower bound</span>
0042 wmax = (-pi)/L; <span class="comment">% upper bound</span>
0043 w = real(logspace(log10(wmin),log10(wmax),1024));
0044 phaseM = angle(m*exp(-j*L*w)./(1+j*w*T));
0045 wu = w(find(phaseM==min(phaseM)));
0046
0047 k1 = 1/abs(m*exp(-j*L*wu)/(1+j*wu*T));
0048 th1 = L/T;
0049
0050 <span class="keyword">if</span> th1>1 & k1<1.5
0051 regStruct = <span class="string">'PI'</span>;
0052 msgbox(<span class="string">'Bad results expected'</span>,<span class="string">'AutotunerPID'</span>,<span class="string">'warn'</span>);
0053 <span class="keyword">elseif</span> (th1>0.6 & th1<1) & (k1>1.5 & k1<2.25)
0054 regStruct = <span class="string">'PI'</span>;
0055 <span class="keyword">elseif</span> th1<0.6 & k1>2.25
0056 regStruct = <span class="string">'PID'</span>;
0057 <span class="keyword">else</span>
0058 regStruct = <span class="string">'PID'</span>;
0059 msgbox(<span class="string">'Bad results expected'</span>,<span class="string">'AutotunerPID'</span>,<span class="string">'warn'</span>);
0060 <span class="keyword">end</span>
0061 <span class="keyword">else</span>
0062 regStruct = <span class="string">'PID'</span>;
0063 <span class="keyword">end</span>
0064
0065 <span class="keyword">otherwise</span>
0066 msgbox(<span class="string">'Unknown structure'</span>,<span class="string">'AutotunerPID'</span>,<span class="string">'warn'</span>);
0067 regStruct = <span class="string">'PID'</span>;
0068 <span class="keyword">end</span></pre></div>
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