Unformatted text preview: p undamped natural frequency is
the
the
2 + !2 =
!n =
5. For B, the poles are 1 ± 3j , and !n = 10. So the speciﬁcations are likely
p
where
± j ! the poles. For A, the poles are 2 j ± j , undamped 2, violating the
the
the
to be met forpB2 . Onarep other hand, C has poles at ± 1 and pand !n = natural frequency is rise time
2=
!n =
+!
5. For B, the poles are 1 ± 3j , and !n = 10. So the speciﬁcations are likely
p
speciﬁcation.
to be met for B . On the other hand, C has poles at 1 ± j , and !n = 2, violating the rise time 21. Find thespeciﬁcation.
transfer function from r to y for the system shown below, where
21. Find the transfer function from r to y for the system shown below, where D (s) = k , s
D (s ) = 1 G( s ) =
k
s , .
1
s+
G (s ) = 2 .
s+2
w
r y
D(s)
− G(s) u v Solution: The transfer function is Solution: The transfer function is
H ( s) = DG k DG 1 + DG = s2k+ 2s + k
H (s) =
=2
1 + DG
s + 2s + k 22. For the system in the previous problem, ﬁnd the range of control gain k for which the followi...
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 Winter '09
 IDAN
 Steady State

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