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<td valign=baseline bgcolor="#ffe4b0"><b>AutotunerPID Toolkit</b></td>
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<h1>pid_autotuner</h1>
<h2><a name="_name"></a>PURPOSE <a href="#_top"><img alt="^" border="0" src="up.png"></a></h2>
<div class="box"><strong>Supervisor of a PID autotuner (implmented as a Matlab S-function).</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 [sys,x0,str,ts] = pid_autotuner(t,x,u,flag,Ts,As) </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_SUPERV Supervisor of a PID autotuner (implmented as an S-function)
The supervisor, rules out the autotuning process mainly performing the
identification of a process model and the synthesis of the new
parameters with various methods.
Moreover it is possible to constrain the structure of the regulator to
be a PI or a PID, or the structure can be automatically selected by the
supervisor.
In particular, the autotuner has the following feature:
- identification of process description:
* a FOPDT model through the areas method
* one point of the frequency response through the method of the
relay
- sythesis of the PID parameters using
* KT method
* IMC method
* First and second ZN method
- it's still a work in progress!! ;-)
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_structure.html" class="code" title="function regStruct = pid_structure(model,reqStruct)">pid_structure</a> PID_STRUCTURE Structure selection for a ISA PID regulator.</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)">
</ul>
<!-- crossreference -->
<h2><a name="_subfunctions"></a>SUBFUNCTIONS <a href="#_top"><img alt="^" border="0" src="up.png"></a></h2>
<ul style="list-style-image:url(matlabicon.gif)">
<li><a href="#_sub1" class="code">function [sys,x0,str,ts] = mdlInitializeSizes(Ts)</a></li><li><a href="#_sub2" class="code">function [sys] = mdlOutputs(t,x,u,Ts,As)</a></li></ul>
<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 [sys,x0,str,ts] = pid_autotuner(t,x,u,flag,Ts,As)</a>
0002 <span class="comment">%PID_SUPERV Supervisor of a PID autotuner (implmented as an S-function)</span>
0003 <span class="comment">%</span>
0004 <span class="comment">% The supervisor, rules out the autotuning process mainly performing the</span>
0005 <span class="comment">% identification of a process model and the synthesis of the new</span>
0006 <span class="comment">% parameters with various methods.</span>
0007 <span class="comment">% Moreover it is possible to constrain the structure of the regulator to</span>
0008 <span class="comment">% be a PI or a PID, or the structure can be automatically selected by the</span>
0009 <span class="comment">% supervisor.</span>
0010 <span class="comment">% In particular, the autotuner has the following feature:</span>
0011 <span class="comment">% - identification of process description:</span>
0012 <span class="comment">% * a FOPDT model through the areas method</span>
0013 <span class="comment">% * one point of the frequency response through the method of the</span>
0014 <span class="comment">% relay</span>
0015 <span class="comment">% - sythesis of the PID parameters using</span>
0016 <span class="comment">% * KT method</span>
0017 <span class="comment">% * IMC method</span>
0018 <span class="comment">% * First and second ZN method</span>
0019 <span class="comment">% - it's still a work in progress!! ;-)</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">switch</span> flag,
0026 <span class="comment">% Initialization</span>
0027 <span class="keyword">case</span> 0,
0028 [sys,x0,str,ts] = <a href="#_sub1" class="code" title="subfunction [sys,x0,str,ts] = mdlInitializeSizes(Ts)">mdlInitializeSizes</a>(Ts);
0029 <span class="comment">% Outputs</span>
0030 <span class="keyword">case</span> 3,
0031 [sys] = <a href="#_sub2" class="code" title="subfunction [sys] = mdlOutputs(t,x,u,Ts,As)">mdlOutputs</a>(t,x,u,Ts,As);
0032 <span class="comment">% Unused flags</span>
0033 <span class="keyword">case</span> { 1, 2, 4, 9 }
0034 sys = [];
0035 <span class="keyword">otherwise</span>
0036 error([<span class="string">'Unhandled flag = '</span>,num2str(flag)]);
0037 <span class="keyword">end</span>
0038 <span class="comment">% end pid_superv</span>
0039
0040
0041 <span class="comment">%=============================================================================</span>
0042 <span class="comment">% mdlInitializeSizes</span>
0043 <span class="comment">% Return the sizes, initial conditions, and sample times for the S-function.</span>
0044 <span class="comment">%=============================================================================</span>
0045 <a name="_sub1" href="#_subfunctions" class="code">function [sys,x0,str,ts] = mdlInitializeSizes(Ts)</a>
0046 <span class="keyword">global</span> Y_AUTOTUNING <span class="comment">% store the step (or relay) response used for tuning</span>
0047
0048 Y_AUTOTUNING = []; <span class="comment">% initialized to an empty vector</span>
0049
0050 <span class="comment">% set up S-function</span>
0051 sizes = simsizes;
0052
0053 sizes.NumContStates = 0;
0054 sizes.NumDiscStates = 0;
0055 sizes.NumOutputs = 2;
0056 sizes.NumInputs = 1;
0057 sizes.DirFeedthrough = 1;
0058 sizes.NumSampleTimes = 1; <span class="comment">% at least one sample time is needed</span>
0059
0060 sys = simsizes(sizes);
0061
0062 x0 = [];
0063 str = [];
0064 ts = [Ts 0];
0065 <span class="comment">% end mdlInitializeSizes</span>
0066
0067
0068 <span class="comment">%=============================================================================</span>
0069 <span class="comment">% mdlOutputs</span>
0070 <span class="comment">% Return the block outputs.</span>
0071 <span class="comment">%=============================================================================</span>
0072 <a name="_sub2" href="#_subfunctions" class="code">function [sys] = mdlOutputs(t,x,u,Ts,As)</a>
0073 <span class="comment">% sys(1) : auto/manual switch</span>
0074 <span class="comment">% sys(2) : autotuning (0 : autotuning in progress; 1 : normal operation)</span>
0075
0076 <span class="comment">% u(1) : new sample of the step response</span>
0077
0078 <span class="keyword">global</span> PIDPARAMETERS
0079 <span class="keyword">global</span> IDENTIFICATION_METHOD
0080 <span class="keyword">global</span> TUNING_STRUCTURE
0081 <span class="keyword">global</span> TUNING_METHOD
0082 <span class="keyword">global</span> TUNING_PARAM
0083 <span class="keyword">global</span> AUTOTUNE
0084 <span class="keyword">global</span> AUTOMAN
0085
0086 <span class="keyword">global</span> Y_AUTOTUNING
0087
0088 step_steadyThr = 0.05; <span class="comment">% threshold on derivative to consider the</span>
0089 <span class="comment">% step response to a stedy state</span>
0090 relay_steadyThr = 0.05; <span class="comment">% threshold on peaks percentual difference to</span>
0091 <span class="comment">% consider the relay response to steady state</span>
0092
0093 <span class="keyword">if</span> AUTOTUNE
0094 <span class="comment">% store the new sample of the step response</span>
0095 Y_AUTOTUNING = [Y_AUTOTUNING; u(1)];
0096 y = Y_AUTOTUNING;
0097
0098 <span class="keyword">if</span> strcmp(IDENTIFICATION_METHOD,<span class="string">'STEP'</span>)
0099 <span class="comment">% check if the step response has reached a steady state (i. e. check if</span>
0100 <span class="comment">% the last 10% of the step response is ``flat'' enough)</span>
0101 N = fix(length(y)/10); <span class="comment">% last 10% of the step response</span>
0102 <span class="keyword">if</span> N > 15
0103 <span class="comment">% the step response must be made at least by 150 samples</span>
0104 deltay = abs(y(end)-y(1));
0105 yw = y(end-N:end);
0106 <span class="comment">% mean value of the derivative in the window lower than a fraction</span>
0107 <span class="comment">% of the maximum value of the derivative</span>
0108 idok = (max(yw)-min(yw)) < step_steadyThr*(max(y)-min(y));
0109 <span class="keyword">else</span>
0110 idok = 0;
0111 <span class="keyword">end</span>
0112 <span class="keyword">if</span> idok
0113 model = <a href="idareas.html" class="code" title="function model = idareas(y,As,Ts)">idareas</a>(y,1,Ts);
0114 <span class="keyword">end</span>
0115 <span class="keyword">elseif</span> strcmp(IDENTIFICATION_METHOD,<span class="string">'RELAY'</span>)
0116 <span class="comment">% IDENTIFICATION WITH THE RELAY METHOD</span>
0117 dy = diff(y);
0118 ind = find(dy(1:end-1)>0 & dy(2:end)<0);
0119
0120 <span class="comment">% at least 4 oscillations but no more than 10 oscillations</span>
0121 <span class="keyword">if</span> length(ind)>=4 & length(ind)<10
0122 ym = mean(y);
0123 <span class="comment">% mean value of the difference between the last three peaks is</span>
0124 <span class="comment">% less than a fraction of the overall range of the response</span>
0125 idok = mean(abs(diff(y(ind(end-2:end))))) < relay_steadyThr*(max(y)-min(y));
0126 <span class="comment">% the last ``period'' must cross the zero</span>
0127 idok = idok & any(abs(y(ind(end-1):ind(end))-ym) < relay_steadyThr/2*abs(max(y)-ym));
0128 <span class="keyword">elseif</span> length(ind)>=10
0129 <span class="comment">% force the stop of the relay identification</span>
0130 idok = 1;
0131 <span class="keyword">else</span>
0132 idok = 0;
0133 <span class="keyword">end</span>
0134
0135 <span class="keyword">if</span> idok
0136 model.A = max(y)-min(y);
0137 model.T = Ts*(ind(end)-ind(end-1));
0138 <span class="keyword">end</span>
0139 <span class="keyword">end</span>
0140
0141 <span class="comment">% autotuning required</span>
0142 <span class="keyword">if</span> idok
0143 <span class="comment">% selection of the regulator structure</span>
0144 regStruct = <a href="pid_structure.html" class="code" title="function regStruct = pid_structure(model,reqStruct)">pid_structure</a>(model,TUNING_STRUCTURE);
0145
0146 <span class="comment">% synthesis of the PID parameters</span>
0147 <span class="keyword">try</span>
0148 [K,Ti,Td,N,b] = <a href="pid_tuning.html" class="code" title="function [K,Ti,Td,N,b] = pid_tuning(model,method,param,regStruct,As)">pid_tuning</a>(model,TUNING_METHOD,TUNING_PARAM,regStruct,As);
0149 <span class="comment">% update PID parameters</span>
0150 PIDPARAMETERS = [K Ti Td N b];
0151 <span class="keyword">catch</span>
0152 <span class="comment">% no change in the parameters</span>
0153 <span class="keyword">end</span>
0154
0155 AUTOTUNE = 0;
0156 <span class="keyword">end</span>
0157 <span class="comment">% put the PID in manual mode during autotuning and propagate the</span>
0158 <span class="comment">% ``autotuning running'' signal</span>
0159 sys = [AUTOMAN 1];
0160 <span class="keyword">else</span>
0161 <span class="comment">% empty the step response vector</span>
0162 Y_AUTOTUNING = [];
0163 <span class="comment">% put the PID in auto mode during autotuning and propagate the</span>
0164 <span class="comment">% ``autotuning not running'' signal</span>
0165 sys = [AUTOMAN 0];
0166 <span class="keyword">end</span>
0167 <span class="comment">% end mdlOutputs</span></pre></div>
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