PracticeProblemsMidterm_solu

# 4 we have n 5 the damping 1 1 ratio is given by sin

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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.

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