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control_exma1_sol

# control_exma1_sol - Exam#1 EEL 3657(Fall 2003 Name goMg SS...

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Unformatted text preview: Exam #1 EEL 3657 (Fall 2003) Name goMg SS#' Please show all work for partial credit. (100 points total) Problem 1. (25 points) Given the following differential quation, solve for y(t) if all initial conditions are zero. Use the Laplace transform. d 232m dy(t) ’-+12———+32 t =32u t dtz dt y() ) u(t) is the unit step function. ; L YCS) :; -—--—- '2 Sa’lﬂn-th) , in k2. S s++ k s '1', i (s +\$,)(_L+8) §’>o kl; 1/ a, 5 S (H 9) Cr Problem 2. (25 points) Find the equivalent transfer function, T(s)=C(s)/R(s), for the system shown below: 1 Problem 3. (50 points) For a unity feedback system shown elow, R .E C ' (s) + (s) () 1((s2 — 2s + 2) s(s +1)(s + 2) 1. break-away/break-in points; 2. jw axis crossings and the K value at the jw ax s crossings; 3. angle of deparmre/arrival; 4. The range of K for which the closed-loop sys m is stable. where G(s) = , sketch the root locus and ﬁnd w ' (+3 //Cli / _ ‘- 0 £5 / (I > a ' Qt ll "‘ w #:— i J l. S“: 2.9-9. ‘ mg) g Ls-rl)Lm) Lu) (A‘Ls) Eu) .1 Ms) W) S4,LF\$3.—2\$m+n\$’i‘(f50 Ti) 5: ’0‘311?’ 1‘77”; ’4- 1 CE : + S 231' K Su-ﬂﬂhl) O s(&+‘)(\$1°")‘+ K (\$7715 +1) % 35 + (5+0 6+ twin); Wm - 1N \$=3w , «M3 'w'léﬂc) +jwc2 2k) +2I<=o f—Vi—Q‘rk) +3.14% K 77 ~w3+wC2‘1k)=0 fwzvioéq w 0‘90: 1‘ A J (WWW M- iJ o-é‘]L K: 0.77 ’ 7L + —-~" r l 2"), ¢y‘¢L‘¢;: : I 9b°—— ' 2h I 7h"? ¢, 552/ +78 ...
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