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<html><head><title>The ISA-PID Regulator :: Introduction to PID Autotuning (AutotunerPID Toolkit)</title>
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<td valign=baseline bgcolor="#ffe4b0"><b>AutotunerPID Toolkit</b></td>
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<p><font size=+2 color="#990000"><b>The ISA-PID Regulator</b></font><br>
<p>Several PID structure are available in literature: the regulator used in this
application is the so called "ISA PID", that is widely accepted
in the industrial domain. The ISA PID control law is expressed as</p>
<img src="images/pidFormula.gif">
<p>where <font face="Courier New, Courier, mono">Y<sup>0</sup>(s)</font>, <font face="Courier New, Courier, mono">Y<sub>m</sub>(s)</font>
and <font face="Courier New, Courier, mono">U(s)</font> are, respectively, the Laplace transforms of
the <em>set-point</em> (<em>SP</em>), the (measurement of the) controlled variable or <em>process value</em> (<em>PV</em>),
and the control signal or <em>control variable</em> (<em>CV</em>), <font face="Courier New, Courier, mono">K</font>
is the PID gain, <font face="Courier New, Courier, mono">Ti</font> the integral time, and
<font face="Courier New, Courier, mono">Td</font> the derivative time. The ISA PID encompasses the set-point
weights
<font face="Courier New, Courier, mono">b</font> and <font face="Courier New, Courier, mono">c</font> in
the proportional and derivative actions.</p>
<p>Traditionally, <font face="Courier New, Courier, mono">b</font> is thought to have the role to limit
the control step that may arise as a consequence of an error step, while <font face="Courier New, Courier, mono">c</font>
has to limit the control spike that may arise as a consequence of an error step, also with a proper controller.
In the autotuning context, <font face="Courier New, Courier, mono">b</font> and <font face="Courier New, Courier, mono">c</font>
can have a more extensive and flexible role, however. The derivative part is made proper by adding a pole with time
constant proportional to <font face="Courier New, Courier, mono">Td</font> via parameter
<font face="Courier New, Courier, mono">N</font>.</p>
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<p><table bgcolor="#ffe4b0" border=0 width="100%" cellpadding=0 cellspacing=0><tr valign=top><td align=left width=20><a href="autopid_int.html"><img src="b_prev.gif" alt="Previous page" border=0 align=bottom></a> </td><td align=left> Introduction to PID Autotuning</td><td> </td><td align=right>Process Identification </td><td align=right width=20><a href="autopid_in3.html"><img src="b_next.gif" alt="Next page" border=0 align=bottom></a></td></tr></table>
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