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Unformatted text preview: EE 3657 Makeup Test (Optional) - April 18, 2011 1. Find the inverse Laplace transform of F (s) “[3415: Cllrfi '
Hf) s 2. Find all ﬁxed points for the-f0
those points: (30) 5—3 a
z , 10
3+1 ( ) Fig? : 56%“0a/f—0
J17 ﬂowing dynamical system and linearize the system about a': = —m+m3+y(1+y) 3. For a second order underdamped system whose characteristic equation is given by
J32 + B3 + K = 0, the gain K has been ﬁxed, all other parameters can be varied. How
can you increase damping ratio without affecting settling time. (25) @ 7:13 Zia/47M» WWMW
ggﬂmn / 12-71 jzi: WW/ “’2‘ 2m 2467 7% 7MMWA¢Ammaae. 4. A closed—loop system has a feedforward transfer function that consists of a proportional 1
controller K in series with the plant G (s) = j. The feedback transfer function is given
1 by H (S) : 1 + s
the closed~loop. (15) _ a CA 33+ ﬂf f/ (WM54WW&WWWXM@W . Find a range of K (if it exists) for which this system is stable in 5. When are poles closest to the imaginary axis not dominant? (10) 6. Unity feedback systems of Type 71 exhibit a zero steady—stateerror to a ramp input.
What value(s) of n will make the preceding statement true? (10) my; M ...
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