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speciﬁcations are satisﬁed: The rise time is less than 2 s, and the settling time is less than 3 s.
Solutions: Using the approximate formula, 5 1.8
tr ⇠
2
=
!n ) 4.6
ts ⇠
3
= ) !n 0.9, 1.5. 22. For the system in the previous problem, ﬁnd the range of control gain k for which the following
speciﬁcations are satisﬁed: The rise time is less than 2 s, and the settling time is less than 3 s.
Solutions: Using the approximate formula,
1.8
tr ⇠
2
=
!n ) 4.6
ts ⇠
3
= ) !n 0.9,
1.5. Note that the system parameters are determined from the denominator of the transfer function:
2
Note that (s system parameters are determined
s2 + 2s + k = the+ )2 + ! 2 = s2 + 2⇣!n s + !n .from the denominator of the transfer function:
2
s2 + 2s + k = (s + )2 + ! 2 = s2 + 2⇣!n s + !n . We then see that We then see 2
that = 1, k = !n .
= 1, 2
k = !n . The rise time speciﬁcation is met by choosing
The rise time speciﬁcation is met by choosing 2
k = !n > 0.92 = 0.81, 2
k = !n > 0.92 = 0.81, but the setting time s...
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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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