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con_exam1_sol

# con_exam1_sol - mac Exam#1i EEL 3657(Summexl 2003 yam 9 Wm...

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Unformatted text preview: mac. Exam #1i EEL 3657 (Summexl 2003 yam - 9 Wm ‘ ss Please show all work for partial credit. (100 points total) Problem 1. (25 points) Find the transfer function, G(s)=C s)/R(s), corresponding to the differential equation 3 2 2 d—3E+3£70+7£+5c=d—2’:+4 +3r dt dt. dt dt CORR V“ 1 7 , , Taking the Laplace transform of the differential equation ssuming zero initial conditions yields: s3C(s) + 3SZC(S) + 7sC(s) + 5C(s) = szR(s) + 4sR(s) + 3R( ) Collecting terms, (s3 + 332 + 7s + 5)C(s) = (s2 + 4s + 3)R(s) Thus, C(s) = s2 +4s+3 R(s) s3 +3s2 +7s+5 Problem 2. (25 points) Find the equivalent transfer functio , T(s)=C(s)/R(s), for the system shown below: : (3(3) __ \$1- ‘ 3 3(5) 13(5) , Si 5+! . 2. ‘_L A Combine the parallel blocks in the forward path. Then, r sh 1 pickoff point. — to the leﬁ past the s 13(5) + . sz+-:: - l C(S) Problem 3. (50 points) For a unity feedback system shown ‘elow, R(s) + .2 5(5) 5') K (s2 — 2s + 2) (s +1)(s + 2) 1). break-away/break-in points; 2). jw axis crossings; 3). K value at the jw axis crossings; 4). angle of arrival at the zeros; 5). the value ofK at the point s = —O.75 i j1.199. 6). The range of K within which the closed-loop syst m is stable. where G(s) = , sketch the root locus and ﬁn: .00 j- -1.50 3.00 l). o‘(s>Lu>:w)J;<g) <zs~2> (SZ‘USJQ) : (25+ 2:) (Egg—{1) 2? 551_ to: Q : S :i'LH \$an SI-H-LH {s hO'l’ q. “6% m+ INC“), WM taut—ma {Wk {9, , NH . [éwlmk] +(Z+2I<i[ +j f “WZCHHﬁl—rlt) to ...
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con_exam1_sol - mac Exam#1i EEL 3657(Summexl 2003 yam 9 Wm...

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