PracticeProblemsMidterm_solu

# These are a d e 13 which systems isare neutrally

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Unformatted text preview: olution: Stable systems are those with all poles in the LHP. These are A, D, E 13. Which system(s) is/are neutrally stable? Solution: A system is said to be neutrally stable if its poles are in the LHP or on the imaginary axis, at least one of them is on the imaginary axis, and the pole(s) on the imaginary axis is/are not repeated. This is C 14. For which system(s) does the step response converge to zero? Solution: The system should be stable. The step response: Y (s) = H (s) 1 . By ﬁnal value theorem, s 0 = y (1) = lim sY (s) = lim sH (s) s! 0 This is D . s! 0 1 = lim H (s) = H (0). s s! 0 Final value theorem: If all poles of sF (s) are in LHP, then f (1) = lims!0 sF (s). 15. Suppose transfer functions in Problem 11 are from the reference r(t) to the error e(t) = r(t) y (t), where y (t) is the output. Which system(s) is/are Type 0 for tracking? Solution: A system is Type 0 for tracking iff it is stable and e(1) = constant 6= 0. By ﬁnal value theorem, e(1) = lim sE (s) = lim sH (s)...
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