PracticeProblemsMidterm_solu

# N 10 so the specications are likely p where j the

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Unformatted text preview: p undamped natural frequency is the the 2 + !2 = !n = 5. For B, the poles are 1 ± 3j , and !n = 10. So the speciﬁcations are likely p where ± j ! the poles. For A, the poles are 2 j ± j , undamped 2, violating the the the to be met forpB2 . Onarep other hand, C has poles at ± 1 and pand !n = natural frequency is rise time 2= !n = +! 5. For B, the poles are 1 ± 3j , and !n = 10. So the speciﬁcations are likely p speciﬁcation. to be met for B . On the other hand, C has poles at 1 ± j , and !n = 2, violating the rise time 21. Find thespeciﬁcation. 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 , s D (s ) = 1 G( s ) = k s , . 1 s+ G (s ) = 2 . s+2 w r y D(s) − G(s) u v Solution: The transfer function is Solution: The transfer function is H ( s) = DG k DG 1 + DG = s2k+ 2s + k H (s) = =2 1 + DG s + 2s + k 22. For the system in the previous problem, ﬁnd the range of control gain k for which the followi...
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