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Unformatted text preview: he pole +
p
2 + ! 2 . With numerical values
j ! , that is, !n =
= 3 and ! = 4, we have !n = 5 . The damping
1
1
ratio is given by sin where 1s the angle between the imaginary axis and the line connecting the
i
(A)
(B)
(C)
origin and2the 1
pole
+(j !+ 1)2 + 9the ﬁgure,s + see2that1
. Drawing
we 1) + sin = /!n = 3/5. Hence, ⇣ = 0.6 .
(s + 2) +
s
( 20. Consider the step responses of the following systems: Which system(s) is/are likely to meet the following speciﬁcations? The rise time is less than 0.6 s and
the settling time is less than 9.2 s. 1
1
1
(A)
(B)
(C)
s + 2)2 approximate formulas, we+ 1)2 + 1
(s + 1)2 + 9
(s have
Solution: Based (on the + 1
Which system(s) is/are likely to meet the following speciﬁcations? The rise time is less than 0.6 s and
1.8
the
less
tr ⇠ settling0time is ) than n .2 s.3, .6
!9
=
!n
Solution: Based on the approximate formulas, we have 4.6 ⇠ 1.8
6
=2
ts ⇠ tr 9.n 0.) )
=
! !n .5 3,
0 4.6 ⇠ )
0
s=
wherep ± tj ! arep 9.2poles. For A,.5the poles are 2 ± j and...
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This note was uploaded on 01/27/2014 for the course MAE 171A taught by Professor Idan during the Winter '09 term at UCLA.
 Winter '09
 IDAN

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