📄 syn08.htm
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<title>MvTools Help : Synthesis ---> PID</title>
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<div class=Section1>
<p align=center style='text-align:center'><span lang=EN-US><img width=371
height=51 id="_x0000_i1025" src="Immagini\logosyn.jpg"></span></p>
<p align=center style='text-align:center'><span lang=EN-US><a
href="HelpDeskmvt.htm" title=" MVTOOLS HELP DESK "><b><i>MvTools Help Desk</i></b></a></span></p>
<p align=center style='text-align:center'><span lang=EN-US><img border=0
width=536 height=5 id="_x0000_i1026" src="Immagini\riga.gif"></span></p>
<p align=center style='text-align:center'><b><u><span lang=EN-US
style='font-size:13.5pt;color:red'>PID<o:p></o:p></span></u></b></p>
<p align=center style='text-align:center'><span lang=EN-US>(Output Feedback)</span></p>
<p style='text-align:justify'><span lang=EN-US>The PID
(Proportional-Integrative-Derivative) synthesis allows designing an output
feedback controller K</span><span lang=EN-US style='font-size:7.5pt'>of</span><span
lang=EN-US style='font-size:10.0pt'>(s)</span><span lang=EN-US> in accordance
with the desired step responses of the channels on the principal diagonal of
the plant transfer matrix</span></p>
<p align=center style='text-align:center'><span lang=EN-US>G</span><span
lang=EN-US style='font-size:10.0pt'>(s)</span><span lang=EN-US> = C inv( </span><span
lang=EN-US style='font-size:10.0pt'>s</span><span lang=EN-US>I -A ) B +D</span></p>
<p style='text-align:justify'><span lang=EN-US>If <i>m</i> and <i>r</i> are
respectively the number of plant inputs and outputs, the matrix G has size(G) =
[<i>r</i>, <i>m</i>] and the number of channels on its principal diagonal is n</span><span
lang=EN-US style='font-size:7.5pt'>chp</span><span lang=EN-US> = min{<i>r</i>, <i>m</i>};
after designing a SISO standard regulator R</span><span lang=EN-US
style='font-size:7.5pt'>i</span><span lang=EN-US style='font-size:10.0pt'>(s)</span><span
lang=EN-US> for each one of these n</span><span lang=EN-US style='font-size:
7.5pt'>chp</span><span lang=EN-US> SISO subsystems, the controller K</span><span
lang=EN-US style='font-size:7.5pt'>of</span><span lang=EN-US style='font-size:
10.0pt'>(s)</span><span lang=EN-US> is built in such a way that the closed loop
behavior of every subsystem depends only on the corresponding standard
regulator; therefore, depending on the minimum dimension of the plant, the
structure of K</span><span lang=EN-US style='font-size:7.5pt'>of</span><span
lang=EN-US> can be:</span></p>
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