📄 syn10.htm
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<title>MvTools Help : Synthesis ---> H-MIX</title>
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<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'>H-MIX<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>H-MIX is an <a href="syn09.htm"
title=" H-2 & H-INFINITY CONTROL help page ">H-INFINITY</a> synthesis with a
pole placement objective: it founds the controller K</span><span lang=EN-US
style='font-size:10.0pt'>(s)</span><span lang=EN-US> which minimizes the
maximum singular value over frequency (infinity-norm) of the transfer matrix <a
href="syn09.htm#Pzw" title=" H-2 & H-INFINITY CONTROL help page ">Pzw(s)</a></span><span
lang=EN-US style='font-size:10.0pt'>,</span><span lang=EN-US> between all the K</span><span
lang=EN-US style='font-size:10.0pt'>(s)</span><span lang=EN-US> that yields an
internally stable closed loop system and causes the closed loop poles to lie in
a certain region of the complex plane.</span></p>
<p style='text-align:justify'><span lang=EN-US>The first step in the H-MIX
control design is the choice of the region in which the closed loop poles have
to lie; at the opening of the following window,</span></p>
<p align=center style='text-align:center'><span lang=EN-US><img border=0
width=371 height=249 id="_x0000_i1027" src="Immagini\synhmix00.gif"></span></p>
<p style='margin:0cm;margin-bottom:.0001pt;text-align:justify'><span
lang=EN-US>the default region, made up of the intersection between an
half-plane and a conic-sector, is computed and displayed on the graphic: the
inner angle is always equal to 2 </span><span lang=EN-US style='font-size:10.0pt'>rad.</span><span
lang=EN-US>, while the maximum real part depends on the current model.</span></p>
<p style='margin:0cm;margin-bottom:.0001pt;text-align:justify'><span
lang=EN-US><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p>
<p style='margin:0cm;margin-bottom:.0001pt;text-align:justify'><span
lang=EN-US>Although it's suggested to maintain the default region, it's
possible to create a new one pressing the button <b>NEW</b>, which removes the
graphic, enables all the check-buttons in the frame and initializes a new
user-region equal to the entire complex plane; whenever the user selects a
check-button relative to a particular kind of sub-region and sets the
corresponding parameters, the user-region becomes equal to the intersection
between its previous value and the new sub-region; in order to explain the way
in which the user-region can be modified, consider the following example
relative to the selection of a conic sector sub-region:</span></p>
<p align=center style='text-align:center'><span lang=EN-US><img border=0
width=371 height=248 id="_x0000_i1028" src="Immagini\synhmix01.gif"></span></p>
<p style='margin:0cm;margin-bottom:.0001pt;text-align:justify'><span
lang=EN-US>The frame on the right is dedicated to the assignment of the
sub-region parameters (their meaning and, if necessary, their validity range are
expressly shown near to the corresponding edit-fields); the function associated
with the button <b>SET</b> checks their values and, if they are valid, plots
the relative sub-region, computes the new intersection with the pre-existing
user-region and updates it in memory; it's always possible to modify some
parameter of a sub-region but, obviously, the changes become actual only after
the pressing of the corresponding <b>SET</b> button.</span></p>
<p style='margin:0cm;margin-bottom:.0001pt;text-align:justify'><span
lang=EN-US>The <b>REMOVE</b> button eliminates the relative sub-region from the
user one, deletes the graphic and reinitializes the edit-fields, while the <b>CANCEL</b>
button allows to close the section of the considered sub-region.</span></p>
<p style='margin:0cm;margin-bottom:.0001pt;text-align:justify'><span
lang=EN-US>The button <b>DEFAULT</b> reloads the default region and visualizes
the window in its initial appearance.</span></p>
<p style='text-align:justify'><span lang=EN-US>The subsequent steps in H-MIX synthesis,
concerning the choice of the matrices which have to be minimized, the
assignment of their upper limit and the controller computation, are exactly the
same ones which have been explained in the <a href="syn09.htm#step"
title=" H-2 & H-INFINITY CONTROL help page ">H-INFINITY</a> help page; the
button <b>COMPUTE H-MIX</b> in the last window starts the controller
computation and only if the controller has been found the two buttons "<a
href="eva01.htm" title=" EVALUATION SECTION help page ">EVALUATION</a>"
and "<a href="sim01.htm" title=" SIMULATION SECTION help page ">SIMULATION</a>"
are activated.</span></p>
<p style='text-align:justify'><span lang=EN-US>Note:<i> </i></span><i><span
lang=EN-US style='font-size:10.0pt'>the function <b>hinfmix</b> uses the
general LMI-based approach, which is rather numerically intensive, and so the
computation may take a long time; in any case it's possible to visualize all
the steps of the computation on the Matlab window.<o:p></o:p></span></i></p>
<p align=center style='text-align:center'><span lang=EN-US><img border=0
width=536 height=4 id="_x0000_i1029" src="Immagini\riga.gif"></span></p>
<p align=center style='text-align:center'><span lang=EN-US><img border=0
width=536 height=4 id="_x0000_i1030" src="Immagini\riga.gif"></span></p>
<p align=center style='text-align:center'><span lang=EN-US><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p>
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