# exam3-so - Exam#3 EEL 3657(Spring 2003 Name Ljfm SS Please...

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Unformatted text preview: Exam #3 EEL 3657 (Spring 2003) Name % Ljfm SS# Please show all work for partial credit. (100 points total) b+\$®+\$ s(s + 2)(s + 4) . l). Derive an analytical expression (as a function of ﬁequenc ) for magnitude of G( j 0)) . (15 points) 2). Derive an analytical expression (as a function of frequenc ) for phase of G( j w) . (15 points) Problem 1. (30 points) Given G(s) = 5 3: + .w _ —2w(w2+1 —i(w4+25w2+120) mG’Jm‘i 1; 6(5) =52; £33) :60 )_ “snow-4+6” _ (2w[w2+13])2+(w4+25w2+120)2 w =+a ‘ w4+2502+120] MM - ws+20w3+64w .ﬂ ) m 2w[w2+ 13] ‘iGHSwl : UWBi‘ HWY“ wit - Aiwﬁzi’ M UWI‘UWH‘UWH WWI-Hr ‘A/wl—Hé Problem 2. (70 points) For a unity feedback system shown b low, R(s) + . Em Co 0.4 G(s) K s(s +1)2 ’ 1). Sketch the Nyquist plot for K=1, and use Nyquist crite on to claim stability for the closed-loop system at K=1. (50 points) 2). For what range of K is the closed-loop system stable? (10 points) 3). What is the gain margin and phase crossover frequency? 10 points) where G(s) = . Im[G(s)] MW 5 “lakes V“ e W “52’ JL I Arc at 00 from w E 0 * all I D . a) = 00, E sA V “ Re[G(S)] N _ I ' -—m‘+‘, (“P-w) q GUN) “ Swgw-H)?’ wé—l—qu +w‘— ’ 2 “Nu XW) 1.2+ Kamio r; wzil. SDXLW)IW:1' :1 “0-5. NW Cm‘ﬁmfon; A/r—o, P>o ; 2=N+P:0. dosed-WP Lysi-v» \KS fin/ML kt! - ...
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exam3-so - Exam#3 EEL 3657(Spring 2003 Name Ljfm SS Please...

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