PracticeProblemsMidterm_solu

# Which systems exhibits undershoot in the step

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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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