Control_exma1_sol - 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

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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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This note was uploaded on 01/14/2012 for the course EEL 3657 taught by Professor Staff during the Spring '08 term at University of Central Florida.

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Control_exma1_sol - 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

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