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<title>MvTools Help : Synthesis ---> LQ - SERVO</title>
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<p align=center style='text-align:center'><span lang=EN-US><img width=371
height=51 id="_x0000_i1233" 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_i1234" 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'>LQ-SERVO<o:p></o:p></span></u></b></p>
<p style='margin-bottom:0cm;margin-bottom:.0001pt;text-align:justify'><span
lang=EN-US>The LQ-SERVO (Linear Quadratic SERVOmechanism) belongs to the group
of control laws that solve the general tracking problem of a reference signal
using the LQR (Linear Quadratic Regulator) approach.</span></p>
<p style='margin-top:0cm;text-align:justify'><span lang=EN-US>If we consider
the following plant with the matrices C = I and D = 0</span></p>
<p align=center style='text-align:center'><span lang=EN-US>X<b><sup>'</sup></b>
= A X + B U</span></p>
<p align=center style='text-align:center'><span lang=EN-US style='color:red'>Y</span><span
lang=EN-US> = C</span><span lang=EN-US style='font-size:7.5pt'> </span><span
lang=EN-US>X + DU = </span><span lang=EN-US style='color:red'>X</span></p>
<p style='text-align:justify'><span lang=EN-US>the purpose of LQ-SERVO is to
find a closed loop control law that lets some of the states X track a not null
reference command vector; owing to disturbances or to a static gain different
from zero, it is possible to obtain a not null static error and then it is
necessary that all the channels concerned in the tracking have an integral
behavior (their type must be equal to 1).</span></p>
<p style='text-align:justify'><span lang=EN-US>The first step in the LQ-SERVO
synthesis is the choice of the state variables that have to be assigned and the
addition of the desired integrators to the channels relative to the selected
states. In the following scheme, the state vector X has been partitioned in the
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