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# Less than aresthe damping j what 06 and which systems

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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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