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<html><head><title>Process Identification :: Introduction to PID Autotuning (AutotunerPID Toolkit)</title>
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<p><font size=+2 color="#990000"><b>Process Identification</b></font><br>
<p>The first step in the autotuning process is the identification of a suitable description of the
plant. In the following, the two most common methods used to retrieve a process description are introduced.
The first one, called <em>Areas Method</em>, provides a model based process description and it is based on
an open-loop step experiment. The second one, called <em>Relay Method</em>, provides a characteristic
based model description and it is based on a closed-loop relay experiment.</p>
<p><a href="autopid_in3.html#t1">Areas Method</a></p>
<p><a href="autopid_in3.html#t2">Relay Method</a></p>
<a name="areas_method"></a><!-- H2 --><a name="t1"></a>
<p><font size=+1 color="#990000"><b>Areas Method</b></font><br>
<p>The areas method belong to the so called <em>model based process description</em> since
it identifies a model of the plant through a simple experiment performed on
the plant. In the great majority of process loops, the process model seen by
the regulator can be described by an asymptotically stable, strictly proper
transfer function, which can be reasonably modeled
with a <em>First
Order Plus Dead Time </em>(<em>FOPDT</em>) <em>model</em></p>
<img src="images/fopdtModel.gif">
<p>Given the step response record <font face="Courier New, Courier, mono">y<sub>s</sub>(t)</font>,
one must first compute the <em>gain</em> <font face="Courier New, Courier, mono">mu</font> by dividing the response total
swing by the input step amplitude <font face="Courier New, Courier, mono">A<sub>s</sub></font>, and the <em>unit step response</em>
<font face="Courier New, Courier, mono">y<sub>us</sub>(t)=y<sub>s</sub>(t)/A<sub>s</sub></font>.</p>
<p>Then, denoting by <font face="Courier New, Courier, mono">t<sub>end</sub></font> the final experiment time, i.e. assuming that from
<font face="Courier New, Courier, mono">t<sub>end</sub></font> on <font face="Courier New, Courier, mono">y<sub>us</sub>(t) = mu</font>,
it is necessary to compute in sequence the three quantities</p>
<img src="images/areasFormula.gif">
<p>where the areas <font face="Courier New, Courier, mono">A<sub>0</sub></font> and <font face="Courier New, Courier, mono">A<sub>1</sub></font>,
which motivate the method's name, are depicted below.</p>
<table width="100%" border="0">
<tr><td align="center"><img src="images/stepFig.png"></td></tr>
</table>
<p>Finally, the other two parameters of the model are obtained as</p>
<img src="images/areasFormula1.gif">
<p>and setting <font face="Courier New, Courier, mono">L=0</font> if the computed value be negative (which can happen
if the real delay is small).</p>
<p>The method of areas is very powerful, remarkably noise-insensitive (since it uses integration) and quite accurate.
Moreover, it has the ability of estimating the delay without obliging the user to define thresholds for deciding when
the process response has started moving.</p>
<p>However, there are cases where a control step causes the controlled variable
to asymptotically assume a ramp-like behavior: this case is commonly referred
to as "runaway", "integrating" or "non self-regulating"
processes and can be described by models with a pole in the origin of the s-plane.
This case is not considered in the present version of the application.</p>
<br>
<a name="relay_method"></a><!-- H2 --><a name="t2"></a>
<p><font size=+1 color="#990000"><b>Relay Method</b></font><br>
<p>The relay identification method belong to the so called <em>characteristic based process description</em> since it
identifies a set of distinctive feature of the model rather than a (simple) model of it.</p>
<p>The main idea in the relay identification is that almost any stable process subject to relay feedback enters a limit
cycle, from which some characteristics in the time or (especially) in the frequency domain are straightforward to obtain.</p>
<table width="100%" border="0">
<tr><td align="center"><img src="images/relaySchema.png"></td></tr>
</table>
<p>If a process with Nyquist curve <font face="Courier New, Courier, mono">P(jw)</font> is subject to relay feedback
with <em>amplitude</em> <font face="Courier New, Courier, mono">D</font> (i.e. whose output is <font face="Courier New, Courier, mono">±D</font>)
and <em>hysteresis</em> <font face="Courier New, Courier, mono">E</font> (i.e. whose switching points are at <font face="Courier New, Courier, mono">±E</font>),
a permanent oscillation of the process output occurs.</p>
<p>This oscillation has the frequency <font face="Courier New, Courier, mono">w<sub>ox</sub></font> where <font face="Courier New, Courier, mono">P(jw)</font>
intersects the critical point locus of the relay, which is a straight line parallel to the real negative axis,
located in the third quadrant of the complex plane and depending on the hysteresis entity.</p>
<table width="100%" border="0">
<tr><td align="center"><img src="images/relayFig.png"></td></tr>
</table>
<p>This allows to identify one point of the process Nyquist curve <font face="Courier New, Courier, mono">P(jw)</font>
(the point indicated above with the circle). Its magnitude is related to the <em>amplitude</em> <font face="Courier New, Courier, mono">A</font>
of the controlled variable oscillation by <font face="Courier New, Courier, mono">|G(jw<sub>ox</sub>)| = pA/4D</font>
and its phase can be easily deduced knowing that its real part is <font face="Courier New, Courier, mono">-pE/4D</font>. Moreover the period of the oscillation can be simply computed. </p>
<br>
<p><table bgcolor="#ffe4b0" border=0 width="100%" cellpadding=0 cellspacing=0><tr valign=top><td align=left width=20><a href="autopid_in2.html"><img src="b_prev.gif" alt="Previous page" border=0 align=bottom></a> </td><td align=left> The ISA PID Regulator</td><td> </td><td align=right>Synthesis Methods </td><td align=right width=20><a href="autopid_in4.html"><img src="b_next.gif" alt="Next page" border=0 align=bottom></a></td></tr></table>
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