final_f02 - EE 350 ‘ EXAM IV 16 December 2002 Last Name...

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Unformatted text preview: EE 350 ‘ EXAM IV 16 December 2002 Last Name: 5‘; le-L’loas ' First Name: ID number (Last 4 digits): Section: I DO: NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO “- Test Form B Instructions 1. esoso You have two hours to complete this exam. This is a closed-book exam. You are allowed one 8.5” by 11” note sheet. Calculators are not allowed. . 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 2.1) Continued.” No credit will be given to a solution that does 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. . 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) 1. (10 points) Find the transfer function of the circuit shown in Figure 1 assuming that the operational amplifier is ideal, and express your answer in standard form m 111-1 .0- H(5) = Y(8) bins + b -13 + + b13+ b0- F(8) _ 8" +an—1sn‘1+---+a1s+ao 2. (15 points) In the circuit shown in Figure 2 the switch has been opened a long time before it is closed at time t = 0. Find an expression for the current Y(s) and express your answer in standard form bm8m+b -13m_1+"'+b18+bo s"+an—1s"'1+---+ars+ao ' Y(s) = 2e 532 9 9%“ W Ebugvadefl'l- mph“; er" Ikeucnm Cleax‘ Lwho kl 0’15 '- 12. .J— ch> = ’5— + 2‘ ‘ 5+2, “5”) ________________ ,_____— 25 +10 sun) + V5 “3 L = [234-794 + 25 (5,; + 253(25 +10) ,, W bar-20$ Problem 2: (25 points) 1. (10 points) Find the closed-loop transfer function Y(s)/F(s) of the feedback control system shown in Figure 3. 2. (15 points) The closed-loop system in Figure 4 contains a proportional controller with gain K > 0 and a plant with transfer function Figure 4: Feedback control system with plant Gp(s), proportional gain K > 0, input F(s), output Y(s). (a) (7 points) What is the DC gain of the closed-loop transfer function Y(s)/F(s) in terms of the proportional gain K ? (b) (8 points) What is the 3 dB bandwidth of the closed-loop transfer function in terms of the proportional gain K ? YCS) :2 m ': piiiiflf : #12” FCD 14'me ”rig.” 5+ Karla Problem 3: (25 points) 1. (8 points) Find the unilateral Laplace transform of the causal signal f(t) = e4t u(t —— 1) by direct integration and specify the region of convergence. co m F<§> = Yea-.3 éy‘i’c = J 8.6-”)qu l 2. (10 points) The unilateral Laplace transform of a causal signal f(t) is 382 + 10.9 + 13 F(8)= ——————————(s+2)(82+28+5). Find the signal f (t) using the method of partial fractions. If f(t) involves a sinusoidal function of time, express your answer in terms of sin(wt) and/ or cos(wt), rather than sin(wt + 0) and/ or cos(wt + 6). ObSQNa ‘U‘i the aijfw 7c 75‘2”" «an: Coflfl/ex (agvaaféz. (bots: 9‘ 41 [,5- : .41— Z 9 + 85 4-C- PMCQ [I ”‘17 5+2. 7-+ 5+5" 1 €¥Pan9~ PCS) “A’ 5 ‘ me’U‘MQ the, HewVISuQC “ Cw-Qr’vp I 1’2. —- 20 4 I3 7 :2: r q r, +5 5‘ (£31.! 9'1 351—1405 413 A: (“76 (5%(51'+25+53J:-Z Fmfl- C bél as“? #2! any“ S¢£E9L 520: C. 331+ 105 +l3 ._ l + 85 + " 5+2. $1+u+y 5:0 (5+L3CS7-+ZJ+S) 5:0 7 L l3 :_L_4,_§'_. >1) 13:574—2ch l lo 2‘ 5 3d; Szl to -va9— E: 3+IO+I3 3. (7 points) At a recent meeting in David Salvia’s office a student noticed two boxes stacked vertically on a sofa. After taking a seat next to the boxes, the student noticed‘ that both boxes had a return address of Frederick’s of Hollywood, with the upper box also bearing the label Deluze Elvis Impersonator Costume. To determine whether or not the boxes were empty, the student gently tapped the upper box. In response, the boxes swayed back and forth for a short period of time. While waiting for David to finish a phone conversation, the student noticed that it took 1/3 second for the boxes to sway back and forth once. She also noticed that the amplitude of the motion decreased by a factor e‘1 in 4 seconds. If the boxes are modeled as a LTI second-order mechanical system, where are the poles of the system located ? 9 r6! ( Problem 4: (25 points) 1. (16 points) Given a. system with the transfer function representation 10008 5 + 10' H(s) : create a straight-line approximations of the Bode magnitude and phase response of the system using the graphs provided on the the next two pages. Clearly label 311! relevant features of the graphs. S H lo 5/!0 4' @D @ Hde) = w//o+l © 10 Magnitude construction plot. Magnitude plot. Magnitude [dB] 10‘ 107* 10*3 1o ‘! 1o 0 Frequency [rad/sec] Figure 5: Graphs for constructing the Bode magnitude response. 145 or, Check) the “€11 ‘Fmgenng got/77 f5 loco 1.. A 00 2‘- /— 6 H( > #10 #0 —- looo ’9 6000 11 Phase [Degrees] Phase [Degrees] 10") Phase construction plot. Phase plot. 10 ° 10 ’ 107- 103 Frequency [rad/sec] Figure 6: Graphs for constructing the Bode phase response. 12 10‘1 (s) are shown of the system. Find the sinusoidal steady-state response y(t) 13 Phase (deg); Magnitude (dB) Bode Plots of G p(s) Frequency (rad/sec) Figure 7: Bode magnitude and phase response of the plant transfer function 01(3). 14 ...
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