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Σεπτ13

1. A system is presented with a transfer function including a parameter δ. The question asks for the maximum value of δ such that the original system from part A remains stable. 2. A system of equations is given modeling an unknown process where the parameter ρ is assumed to be 0, but is actually positive. 3. The questions ask (A) to place the system poles and (B) to show that the system's robustness increases with respect to changes in the parameter ρ, consistent with the real value being positive.

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Γιάννης Μανουσαρίδης
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89 views1 page

Σεπτ13

1. A system is presented with a transfer function including a parameter δ. The question asks for the maximum value of δ such that the original system from part A remains stable. 2. A system of equations is given modeling an unknown process where the parameter ρ is assumed to be 0, but is actually positive. 3. The questions ask (A) to place the system poles and (B) to show that the system's robustness increases with respect to changes in the parameter ρ, consistent with the real value being positive.

Uploaded by

Γιάννης Μανουσαρίδης
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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ΣAE ll

Σεrrr€μβριοq 2013

Θ€μα 1 Δ[vεται o0ατημα με ouv&ρτηoη μεταQoρ&q:

H p(") =;,
i;J. _

A) Nα o1εδιαoτεi oιiorημα ελ€γ1oυ κλειατo0 βρ61oυ με σUvdιρπισΙl


μεια$oρdq:

r Hr(r)=;,
.11r.r,
+:
κdι vα πραγματoπoιηΘεl με σχημα ελ6γ1oυ 2.DoF χρησιμoπoιιbvrαq πoλυιilvυμo g(s)
ελιi1ιαιηg διαoταoηg.

B) To ελεμ6βεvo o0ατημα υQ[αταται βλιiβη με απoτ6λεσμα vα τρoπoπoιηθεi


η oυvιiρτηoη μεταQoρα4 H ωg εξfg:
"(s)

fl.(,)= {*''*δ^, δ>0.


t'\ / s'+6s+8-

Πoιo ε[vαι τo ελα1ιαro αvω Qριiγμα τηξ παραμ€τρoυ δ ιbατε τo o0αιημα ελ6ψoυ κλειαιo0
βρ6xoυ πoυ o1εδιαστηκε αco εριi.lτημα A) vα παραμ€vει ευαrαΘ€q.

Θ€μα 2 Δlvεται o0αιημα:

*ι = _χι *3x.z
*z= Pxι_4x,+ιι.
!=χι
(6πoυ y η 6ξoδoq, u η εlooδog, x|)Χ2ot κατααταoειξ) για τo oπolo voμiζoυμε
(εoQαλμ€vα) πωq ρ = Ο, εvιb αηv πραγματικ6τητα ιo1ιiει ρ > 0 .

A) Nα τoπoΘετηΘoOv oι π6λoι τoυ oυorιjματoξ (πιξ Θ€oειq .6 και.7.


B) Δεi'ξτε πωζ τo oΟαιημα κλειαro0 βρ6xoυ τoυ ερωτιjματoq A) παρoυoιαζει αυξημ€vη
ευρωoτiα ωξ πρoξ μεταβoλ€q τηg παραμ€τρoυ ρ, oε o1€oη με τo πραγματικ6.

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