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Unformatted text preview: Exam #3
EEL 3657 ‘ Wam  SS Problem 1. (35 points) The bode plot for a unity feedback s stem is shown below: Please show all work for partial credit. (100 points total) kl: J J 2 7:“: vnnv?~v~?ﬁnLEv‘n flJ—~VviwvJ—L 4~4»A4 A~_4£ .
a:
A
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... a _ .
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c: . . .
L a a . . . . b). Find the phase crossover frequency. a). Find the gain crossover frequency.
c). Find the gain margin. e). What is the system type? SOL/dim d). Find the phase margin. 0t)» ‘ Problem 2. (65 points) For the system shown in the ﬁgure, where 0(5) = __K____ Q+DQ+®w+® a). Plot the Nyquist diagram for K=1 and ﬁnd the negative r al axis crossing; (30 points) b). Is the system stable for K=1? (15 points) b). Use Nyquist criterion to ﬁnd the range of gain, K, for the closedloop system to be
static. (20 points) g” (M’Hm ‘ a) . The frequency response is 1/48 at an angle of zer degrees at a) = 0. Each pole
‘ ' rotates 90° in going from a) = 0 to a) = 00. Thus, the resultant rotates —2700 while its magnitude goes to zero. The result is shown belo . 1 1
'Sbt'tut' 'w't G =__———'— —_——and
“SI mg] “1° (S) (s+2)(s+4)(s+6) s3+12s2+44S+48 (48—12(02)—j(44 — (03) .TheN ist
w°+56w4+784w +2304 yqu simplifying, we obtain G(ja)) = ..__._... diagram crosses the real axis when the imaginary pa of G( j co) is zero. Thus, the Nyquist diagram crosses the real axis at (02 = 44, o a) = W = 6.63 rad/s. At
1 Ragga; 700(0) = —m. i). 2mm: 0 .«> gym we C), K:::ZJ:{_8: :qgoV 7; ‘r $va #4485, ...
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 Spring '08
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