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<title>MvTools Help : Synthesis ---> EIG \ ASSIGN</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'>EIG \ ASSIGN<o:p></o:p></span></u></b></p>
<p style='text-align:justify'><span lang=EN-US>The EIG\ASSIGN (EIGenstructure
ASSIGNment) is a control method that shapes the transient response of a linear
time invariant system altering directly its eigenvalues and eigenvectors
through the use of feedback <a href="biblo.htm#b5" title=" REFERENCES ">[5]</a>.
Without explaining carefully the theory of this kind of regulator it's
important to remember that, if A is the system dynamic matrix and </span><span
lang=EN-US style='font-size:10.0pt;font-family:Symbol'>l</span><span
lang=EN-US style='font-size:8.0pt;mso-bidi-font-size:10.0pt'>i </span><span
lang=EN-US>\ </span><span lang=EN-US style='font-size:10.0pt;font-family:Symbol'>u</span><span
lang=EN-US style='font-size:8.0pt;mso-bidi-font-size:10.0pt'>i</span><span
lang=EN-US> (with i = 1,2,...,#states)</span><span lang=EN-US style='font-size:
10.0pt'>, </span><span lang=EN-US>is a generic pair eigenvalue\eigenvector so
that</span></p>
<p align=center style='text-align:center'><span lang=EN-US style='color:red'>A </span><span
lang=EN-US style='font-family:Symbol;color:red'>u</span><span lang=EN-US
style='font-size:8.0pt;mso-bidi-font-size:10.0pt;color:red'>i</span><span
lang=EN-US style='color:red'> = </span><span lang=EN-US style='font-family:
Symbol;color:red'>l</span><span lang=EN-US style='font-size:8.0pt;mso-bidi-font-size:
10.0pt;color:red'>i</span><span lang=EN-US style='color:red'> </span><span
lang=EN-US style='font-family:Symbol;color:red'>u</span><span lang=EN-US
style='font-size:8.0pt;mso-bidi-font-size:10.0pt;color:red'>i</span><span
lang=EN-US style='mso-bidi-font-size:10.0pt;color:red'> </span><span
lang=EN-US>,</span><span lang=EN-US style='font-family:Symbol;color:red'><o:p></o:p></span></p>
<p style='text-align:justify'><span lang=EN-US>then the self-conjugate set of
scalars {</span><span lang=EN-US style='font-size:10.0pt;font-family:Symbol'>l</span><span
lang=EN-US style='font-size:8.0pt;mso-bidi-font-size:10.0pt'>i</span><span
lang=EN-US>} (eigenvalues) influences the decay\growth rate of the system free
transient responses, while the self-conjugate set of vectors {</span><span
lang=EN-US style='font-size:10.0pt;font-family:Symbol'>u</span><span
lang=EN-US style='font-size:8.0pt;mso-bidi-font-size:10.0pt'>i</span><span
lang=EN-US>} (eigenvectors) influences their shape.</span></p>
<p style='margin:0cm;margin-bottom:.0001pt;text-align:justify'><span
lang=EN-US>Then, given a self-conjugate set of <i>Desired</i> eigenvalues {</span><span
lang=EN-US style='font-size:10.0pt;font-family:Symbol'>l</span><span
lang=EN-US style='font-size:8.0pt;mso-bidi-font-size:10.0pt'>j</span><span
lang=EN-US>}</span><span lang=EN-US style='font-size:8.0pt;mso-bidi-font-size:
12.0pt'>D</span><span lang=EN-US> and a corresponding self-conjugate set of <i>Desired</i>
eigenvectors {</span><span lang=EN-US style='font-size:10.0pt;font-family:Symbol'>u</span><span
lang=EN-US style='font-size:8.0pt;mso-bidi-font-size:10.0pt'>j</span><span
lang=EN-US>}</span><span lang=EN-US style='font-size:8.0pt;mso-bidi-font-size:
12.0pt'>D</span><span lang=EN-US>, the Eig\Assign technique allows to compute the
feedback matrix K such that the resulting <i>Closed Loop</i> system has </span><span
lang=EN-US style='color:red'>{</span><span lang=EN-US style='font-size:10.0pt;
font-family:Symbol;color:red'>l</span><span lang=EN-US style='font-size:8.0pt;
mso-bidi-font-size:10.0pt;color:red'>i</span><span lang=EN-US style='color:
red'>}</span><span lang=EN-US style='font-size:8.0pt;mso-bidi-font-size:12.0pt;
color:red'>CL</span><span lang=EN-US style='color:red'> </span><span
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