Unformatted text preview: than aresthe damping
± j What 0.6 and
Which system(s) is/are likely having a pair of speciﬁcations? The
the undamped less than 9.2 s.
ratio ⇣ and settling time isnatural frequency !n ?
Solution: Based on the approximate formulas, we have 20. Consider the step1.responses of the following systems:
8
tr = (A) 0.6 !n !n 3, 1
1
(B)
.6
24+ 1
(s +s 2)
(s + 1)2 0.5 9
+
t=
9.2 (C) 1
(s + 1)2 + 1 Which system(s) ± j ! are the poles. For A, the poles are speciﬁcations? The risenaturalis less than 0.6 s and
wherep is/are likely to meet the following 2 ± j and p undamped time frequency is
the
p
the settling=
!n time2is less than For B, the poles are 1 ± 3j , and !n = 10. So the speciﬁcations are likely
+ ! 2 = 5. 9.2 s.
to be met for B . On the other hand, C has poles at
speciﬁcation. 1 ± j , and !n = p 2, violating the rise time 21. Find the 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
1
,
G( s )...
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 Winter '09
 IDAN
 Steady State, system S, following systems

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