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<td valign=baseline bgcolor="#ffe4b0"><b>AutotunerPID Toolkit</b></td>
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<h1>pid_isatd</h1>
<h2><a name="_name"></a>PURPOSE <a href="#_top"><img alt="^" border="0" src="up.png"></a></h2>
<div class="box"><strong>Discrete time ISA-PID (implemented 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_isatd(t,x,u,flag,Ts,umin,umax,As,hystLevel) </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_ISATD Discrete time ISA-PID (implemented as an S-function)
The PID closely resemble the structure of a real industrial PID and has
the following features:
- filter on the derivative action
- set-point weight (but not the weight of the derivative action which
is fixed to 0)
- antiwindup on lower and higher saturation limits of the actuator
- bumpless auto-manual switch
It also implements the logic to perform the identification experiment:
- step response identification (with user-defined step amplitude)
- relay identification (with user-defined relay amplitude and
hysteresis level)
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)">
</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,stato] = mdlInitializeSizes(Ts)</a></li><li><a href="#_sub2" class="code">function [sys,stato] = mdlOutputs(t,x,u,stato,Ts,umin,umax,As,hystLevel)</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_isatd(t,x,u,flag,Ts,umin,umax,As,hystLevel)</a>
0002 <span class="comment">%PID_ISATD Discrete time ISA-PID (implemented as an S-function)</span>
0003 <span class="comment">%</span>
0004 <span class="comment">% The PID closely resemble the structure of a real industrial PID and has</span>
0005 <span class="comment">% the following features:</span>
0006 <span class="comment">% - filter on the derivative action</span>
0007 <span class="comment">% - set-point weight (but not the weight of the derivative action which</span>
0008 <span class="comment">% is fixed to 0)</span>
0009 <span class="comment">% - antiwindup on lower and higher saturation limits of the actuator</span>
0010 <span class="comment">% - bumpless auto-manual switch</span>
0011 <span class="comment">%</span>
0012 <span class="comment">% It also implements the logic to perform the identification experiment:</span>
0013 <span class="comment">% - step response identification (with user-defined step amplitude)</span>
0014 <span class="comment">% - relay identification (with user-defined relay amplitude and</span>
0015 <span class="comment">% hysteresis level)</span>
0016 <span class="comment">%</span>
0017 <span class="comment">% Author: William Spinelli (wspinell@elet.polimi.it)</span>
0018 <span class="comment">% Copyright 2004 W.Spinelli</span>
0019 <span class="comment">% $Revision: 1.0 $ $Date: 2004/02/27 12:00:00 $</span>
0020
0021 <span class="keyword">persistent</span> stato; <span class="comment">% internal state variable</span>
0022
0023 CVBlock = <span class="string">'ManValue'</span>;
0024 <span class="keyword">switch</span> flag,
0025 <span class="keyword">case</span> 0,
0026 [sys,x0,str,ts,stato] = <a href="#_sub1" class="code" title="subfunction [sys,x0,str,ts,stato] = mdlInitializeSizes(Ts)">mdlInitializeSizes</a>(Ts);
0027 <span class="keyword">case</span> 3,
0028 [sys,stato] = <a href="#_sub2" class="code" title="subfunction [sys,stato] = mdlOutputs(t,x,u,stato,Ts,umin,umax,As,hystLevel)">mdlOutputs</a>(t,x,u,stato,Ts,umin,umax,As,hystLevel);
0029 <span class="keyword">case</span> { 1, 2, 4, 9 }
0030 sys=[];
0031 <span class="keyword">otherwise</span>
0032 error([<span class="string">'Unhandled flag = '</span>, num2str(flag)]);
0033 <span class="keyword">end</span>
0034 <span class="comment">% end pid_isatd</span>
0035
0036
0037 <span class="comment">%=============================================================================</span>
0038 <span class="comment">% mdlInitializeSizes</span>
0039 <span class="comment">% Return the sizes, initial conditions, and sample times for the S-function.</span>
0040 <span class="comment">%=============================================================================</span>
0041 <a name="_sub1" href="#_subfunctions" class="code">function [sys,x0,str,ts,stato] = mdlInitializeSizes(Ts)</a>
0042 <span class="comment">% set up S-function</span>
0043 sizes = simsizes;
0044
0045 sizes.NumContStates = 0;
0046 sizes.NumDiscStates = 0;
0047 sizes.NumOutputs = 1;
0048 sizes.NumInputs = 4;
0049 sizes.DirFeedthrough = 1;
0050 sizes.NumSampleTimes = 1; <span class="comment">% at least one sample time is needed</span>
0051
0052 sys = simsizes(sizes);
0053
0054 x0 = [];
0055 str = [];
0056 ts = [Ts 0];
0057 stato = [0 0 0 0 0];
0058 <span class="comment">% end mdlInitializeSizes</span>
0059
0060 <span class="comment">%=============================================================================</span>
0061 <span class="comment">% mdlOutputs</span>
0062 <span class="comment">% Return the block outputs.</span>
0063 <span class="comment">%=============================================================================</span>
0064 <a name="_sub2" href="#_subfunctions" class="code">function [sys,stato] = mdlOutputs(t,x,u,stato,Ts,umin,umax,As,hystLevel)</a>
0065 <span class="keyword">global</span> CVVALUE <span class="comment">% control variable (used for M/A commutation)</span>
0066 <span class="keyword">global</span> IDENTIFICATION_METHOD
0067 <span class="keyword">global</span> TUNING_METHOD
0068 <span class="keyword">global</span> PIDPARAMETERS
0069
0070 <span class="comment">% measured signals</span>
0071 sp = u(1); <span class="comment">% setpoint value</span>
0072 pv = u(2); <span class="comment">% process value</span>
0073
0074 <span class="comment">% control signals</span>
0075 auto = u(3); <span class="comment">% auto/man switch (MANUAL=0; AUTO=1)</span>
0076 autotune = u(4); <span class="comment">% true when autotuning</span>
0077
0078 <span class="comment">% PID parameters (c=0)</span>
0079 K = PIDPARAMETERS(1);
0080 Ti = PIDPARAMETERS(2);
0081 Td = PIDPARAMETERS(3);
0082 N = PIDPARAMETERS(4);
0083 b = PIDPARAMETERS(5);
0084
0085 <span class="comment">% translation of the vector stato (for simplicity)</span>
0086 <span class="comment">% state variable</span>
0087 ui = stato(1); <span class="comment">% integral action</span>
0088 ud = stato(2); <span class="comment">% derivative action (filter)</span>
0089
0090 <span class="comment">% auxiliary variable</span>
0091 pvold = stato(3); <span class="comment">% old process value</span>
0092 cvold = stato(4); <span class="comment">% old control variable</span>
0093 atold = stato(5); <span class="comment">% old autotune state (to ensure bumpless switch)</span>
0094
0095 <span class="comment">% PID algorithm</span>
0096 <span class="comment">% compute the constants (made each time since PID parameters may change)</span>
0097 <span class="keyword">if</span> Ti
0098 a1 = K*Ts/Ti;
0099 <span class="keyword">else</span>
0100 <span class="comment">% when Ti = 0 turn off the integral action</span>
0101 a1 = 0;
0102 <span class="keyword">end</span>
0103 b1 = Td/(Td + N*Ts);
0104 b2 = K*Td*N/(Td + N*Ts);
0105
0106 <span class="comment">% compute control actions</span>
0107 up = K*(b*sp - pv);
0108
0109 ud = b1*ud - b2*(pv-pvold);
0110
0111 <span class="keyword">if</span> ~autotune & atold
0112 <span class="comment">% ensure bumpless switch after a change in the regulator parameters</span>
0113 ui = cvold - up - ud;
0114 <span class="keyword">end</span>
0115
0116 <span class="keyword">if</span> autotune
0117 <span class="keyword">if</span> strcmp(IDENTIFICATION_METHOD,<span class="string">'STEP'</span>)
0118 <span class="comment">% increment the value of the control variable</span>
0119 cv = CVVALUE+As;
0120 <span class="keyword">elseif</span> strcmp(IDENTIFICATION_METHOD,<span class="string">'RELAY'</span>)
0121 <span class="keyword">if</span> ~atold
0122 cv = CVVALUE+As;
0123 <span class="keyword">else</span>
0124 <span class="keyword">if</span> pv >= sp+hystLevel
0125 cv = CVVALUE-As;
0126 <span class="keyword">elseif</span> pv <= sp-hystLevel
0127 cv = CVVALUE+As;
0128 <span class="keyword">else</span>
0129 cv = cvold;
0130 <span class="keyword">end</span>
0131 <span class="keyword">end</span>
0132 <span class="keyword">end</span>
0133 <span class="keyword">else</span>
0134 <span class="keyword">if</span> ~auto
0135 <span class="comment">% manual mode</span>
0136 cv = CVVALUE;
0137 <span class="keyword">else</span>
0138 <span class="comment">% automatic regulation</span>
0139 cv = up + ui + ud;
0140 <span class="keyword">end</span>
0141
0142 <span class="keyword">if</span> cv > umax
0143 <span class="comment">% saturation on maximum value (note that the state of the integrator is</span>
0144 <span class="comment">% not updated)</span>
0145 cv = umax;
0146 <span class="keyword">elseif</span> cv < umin
0147 <span class="comment">% saturation on minimum value</span>
0148 cv = umin;
0149 <span class="keyword">else</span>
0150 <span class="comment">% update the state of the integrator</span>
0151 <span class="keyword">if</span> auto
0152 ui = ui + a1*(sp-pv);
0153 <span class="keyword">else</span>
0154 ui = cv - up - ud;
0155 <span class="keyword">end</span>
0156 <span class="keyword">end</span>
0157 <span class="comment">% update control variable value</span>
0158 CVVALUE = cv;
0159 <span class="keyword">end</span>
0160
0161 <span class="comment">% update internal state vector</span>
0162 stato = [ui ud pv cv autotune];
0163 <span class="comment">% generate control variable</span>
0164 sys = cv;
0165 <span class="comment">% end mdlOutputs</span></pre></div>
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