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Unformatted text preview: EB  350 Last Name Exam 4 29 April 2002 0L) First Name Student # Section :5pr DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO Test Form A
Instructions You have 115 minutes hours to complete the exam. Calculators are not allowed. This exam is closed book. You may use one 8.5" x 11" note sheet. Solve each part of the problem in the space following the question. If you need more space,
continue your solution on the reverse side labeling the page with the question number, for
example, "Problem 1.2 Continued". NO credit will be given to solutions that do not meet
this requirement. DO NOT REMOVE ANY PAGES FROM THIS EXAM. Loose papers will not be accepted
and a grade of ZERO will be assigned. If you introduce a voltage or current in the analysis of a circuit, you must clearly label the
new variable in the circuit diagram and indicate the voltage polarity or current direction. If
you fail to clearly deﬁne the voltages and currents used in your analysis, you will receive
ZERO credit. The quality of your analysis and evaluation is as important as your answers. Your reasoning
must be precise and clear; your complete English sentences should convey what you are
doing. To receive credit, you must show your work. Problem 1 (25 points) To receive credit for this problem, you must use Laplace transform
methods to perform your analysis.
Y (s) F (5)
answer in standard form. Assume that Rl = 2 Q and R2 =1 (2. 1.1 (10 points) Compute the transfer function of the circuit shown below and place your mg;
#1
Q R\+$¢

+
PCS) _1_ ﬂ
St.
I
PCS) Scﬂ‘+‘ 9
l ___. PCS)
FCs) 5mm! 3 ___,_——/“ YCS) = __,___—————————"""‘ 2.
J1...— .,_ .3 .,. gL R. + scﬂﬁz+ K7, +5LcR, 4SL.
z. SethH
’chR,
“r M " " rz +R2.
ﬂ ‘ ‘ {12. J..— \ a 5" w? + SCCR.KL+L) “W15 87‘1 5C1“? an * 72.7:
\ Sumatran 62%;) W) 1.2 (8 points) Compute the zero input response, YZIR (s) , of the circuit shown below. Assume
thatR=4 o, vc(0')=4Vandthat y(0')=3 A. Set $CQ :0 “my” "Whig Im'blul Conﬂt'klon generaM 'Qr‘
‘Lhe Capacrbor‘ amQ. incauo 4". 1.3 (7 points) Determine y(t) , given t __ 2
Y(S)— s(s2 +3s+2)'
= 2' : ﬁ—u L + C 2..
9,: =. I
5:0 / z " '2
3 .S I; . . "
B C )scs MS”? 5:4
3 ' S
C . SCSﬂ}(sw 5:.L. 1 .
YCS) i ‘z'("’i_'> + 5+7. Problem 2 (25 points)
2.1 (15 points) Consider the system represented by the block diagram shown below. Find the
X
(S) , assuming that K = 2 andG(s) =—:—l.
s closed — loop transfer function, H (s) = F (S) 2.2 (10 points) A system has the closed — loop transfer function
Y (s) 9 F(s) = s2 +Ks+9'
Assume that the input to the system is f (t) = u (t). For what value of control gain K will the response of the closed — loop system be under damped with 4' = 0.1. Yts) _ ‘I 7 w: Problem 3 (25 points)
3.1 (16 points) A system has the transfer function H(s)=_s(£ilﬂ_
(s+10)(s+105)' Sketch the magnitude and phase Bode plots of the system using the semilog graph paper
provided in the following two pages. In order to receive credit: 0 In both the magnitude and phase plots, indicate construction'lines for each term using
dashed lines. 0 Indicate the slope for each straight  line segment and corner frequencies for the ﬁnal
magnitude and phase plot. 10‘{ f” (dW/"ﬂ *0 W Ht?» 3 lo  l05 gw/Iorl) WWI/05“”) 2. Elf—1 F’ﬂ : ' aLw/Io‘l (fur/10V +l)
/_____________,__. (£15112 W 3.2 (9 points) Find the steady? state response to the input f (t) = 5 +17sin(104t) of the system
whose transfer function is depicted in the following Bode plot. {lea : 5 4 I7 (osCIO‘Ll: ‘76) am) = 5 We) + :7 nglIO“)C05(to%7o°+ wow) From W \ngﬂule == éoJB Q “(#0) 34.1000
mute) = 0° .... H( tom 3
IHCWO‘HAE' “OMS ’9 1 / “10° 23 Motw“) : 10 33 03....qu Frequency (Mince) 11 Problem 4 (25 points)
4.1 (10 points) A system has the impulse response h (t) = (3e’ — 2e‘2’ )u (t) . Determine the transfer function, H (s) , of the system and place it; in standard form, and sketch the pole —— zero
map of H 2.—l:
hot} ,7. 3e”: “(a " 2‘3 “(45) 12 4.2 (5 points) Determine if the system with the impulse response h (t) = (3e’ — 2e'2’ )u (t) , as
given in part 1, is bounded input — bounded output stable. BQCMSQ the. eastern ball. a. PO/Qa ajé 53"") I": ‘45 unS’iSQMQJ amQ, theer is n01":
EHSO sﬁc‘o‘e. A’kvnw‘EIVRJ‘J) a
co °° ‘zt
[MiniE = [55—22. we : °°
.09 0
Lemma 3"}: z 9’
taco 13 4.3 (10 points) A system is modeled by the relationship dZS’)+2d—yd(;g+6y(t)=4f(’)' Determine Y (s) in terms 0f the input, F (s) , and the system’s initial conditions y(0’) and
y'(o) . .32 YC$3  53(6) *5! (0‘) + zis {(5) 9/033 + 67153 = LIFCS) {52“ 23 1' 63m) : Sawo‘) +305) 4» '4ch) 14 ...
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 Fall '07
 SCHIANO,JEFFREYLDAS,ARNAB

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