Unformatted text preview: s! 0 s! 0 1
= lim H (s) = H (0).
s s! 0 These are A, E
16. Which system(s) exhibit(s) undershoot in the step response?
Solution: Undershoot is a typical behavior of nonminimum phase systems which have a zero in the
RHP. This is E
17. Find the natural frequency ! , undamped natural frequency !n , and damping ratio ⇣ for the following
transfer function:
P (s) = s+1
.
s2 + 4s + 20 2
Solution: Comparing the coefﬁcients of the denominator with those of s2 + 2⇣!n s + !n , we have 2⇣!n = 4, 2
!n = 20. Solving these equations,
p
!n = 2 5, p
⇣ = 1/ 5, != p
1 ⇣ 2 !n = 4
4 18. Which system has the step response converging to a steady state value at the fastest rate?
(A) 1
s+5 2
s+1 (B) (C) 4
(s + 3)2 + 92 (D) s 1
100 Solution: System D is unstable and its step response does not converge. Systems A and B have
time constants 0.2 and 1, respectively, so A has faster convergence. The rate of convergence for C is
determined by the real part of the poles, = 3. The step response of C is oscilla...
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 Winter '09
 IDAN

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