final_f00

final_f00 - EE 850 FINAL EXAM 14 December 2000 Last Name 8...

Info iconThis preview shows pages 1–16. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 12
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 14
Background image of page 15

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 16
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: EE 850 FINAL EXAM 14 December 2000 Last Name: 8 9' gift] at); First Name: ID#: Section: DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO 1 Test Form B Instructions 1. You have 2 hours to complete this exam. 2. This is a. closed book exam. You are allowed one heet of 8.5” X 11” of paper for notes and a. calculator. 3. 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 4.2) Continued”. NO credit will be given to solution that does not meet this requirement. 4. DO NOT REMOVE ANY PAGES FROM THIS EXAM. Loose papers will not be accepted and a grade of ZERO will be assigned. 5. 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. (4 points) Consider the electronic circuit shown in Figure 1. By inspection, state whether the circuit implements a. lowpass filter, a. bandpass filter, a. notch filter, or a high pass filter. Justify your answer with one or two sentences. f(t) Figure 1: Filter circuit. T/Ole. 90w Fre 5‘12”? ya in 75 Zero EQCGLVJ‘Q 9% DC. the Con/MI'EOP CL appéahj a5 an open CI’TUI - T’p‘a- ar‘n the an, [ricer 1:; fro/orfronaz 75‘" a f the rw‘éco % {the IM/Qfleflfe, / K. aer C,_ 243‘ the grebuenfi /flCV€c¢JeS/ £359. er/éfiwxm/ C, ‘ 15:63 fleecreaJeJ and C119. far/7 (ficreaJaS. m I gualrfie‘lxvg, anagsls) the, Ir/éer arty/(é "flame/2‘55 o» fllgt gas; act/{en 2. (8 points) Once again consider the electronic circuit shown in Figure 2. If the operational amplifier is ideal, then the transfer function of the circuit can be expressed as _Y(8) _ 5232+b18+bo H“) _ F(a) — s +ao Determine the parameters (:9, be, 61, and b; in terms of the component values R1, R3, 0;, and 02. f(t) V+C$) = if”. => \f+($) = S RLCL {21 + file—«L J Fm sP-LCLH ()5 H15 m fiof m. 0P -6LM/0 C01") Ltdurwfifun {‘5 an "an -/}Ive)"b-O/ d.- mlall flew ll YCs) J— Vii—L53 SCI (1+ RI )Mm => fl=1+smq Cemhmm5_ tlm— ew" resvl'ifi atom} YCsE _ Wm .YCsl , “LC?— .(1+sR\c.) Fax ’ PCS) V4453 ” SKI-CL“ .. z c VA c -' .S RIRLGICL 4" 822.. 2- 2. 2.. ’____________,__.. .sRLCz, +1 3. (13 points) The first-order RC circuit in Figure 3 is driven by the input f(t) = 6u(—t) + 2u(t). 452 + fa) 0 m 0.21: ya) Figure 3: First-order RC circuit. 0 (2 points) Determine the output voltage y(0“ o [5 points) Calculate the zero-state response y“ (t) for t 2 0. o (5 points) Find the zero-input response y,,-(t) for t 2 O. o (1 point) Write an expression for the total response y(t) for t 2 0. 4t: 'l:=ov"J the. prGCIEVV‘ is an open crrcw'EJ (M‘Q So #055 = ?'Co"\ LR. :. 6n - In. 2-. 6 V. Using, ox.- .s owf‘CQ/ *5 Farmng ash: on, in. up. He) LIL : Fflt) In the. S— ego/71am mate, thJ: ate") .2: th- {w uuHT-L a.ch tub- C“?“’“ 9.17 1%: =0‘. To 4..»‘0. the, aim—5% reafionsa] .Se’é 51(o-):_o_ p. + F6} é“ Y (3) 515' Fm ' F“) C— : z _ *5 RJ, g2 SCR H 05.3 JFC-D: 2.0gth (1:20)) Rg‘y-RU 619.2,?— we. OLE“?! 2. .: 25 z: YZS($)'= 1:. .g.+ 3%;1 35:385.:0 Z- ' .. 26-“) :-2. B " sum )3»: Problem 2: (25 points) 1. (8 points) The closed-loop system system shown in Figure 4 has an output Y(s), a command input 12(5), and a disturbance input 13(3). Using superposition, the Laplace transform of the output can be expressed as m) = Ems) 1200+ Ems) ms), where Hw(s) is the transfer function from R(s) to Y(s) when 13(3) = 0, and Hinds) is the transfer function from D(s) to Y(s) when R(s) = 0. Find 0 (4 points) H,..(s), and o (4 points) Hyde). To receive credit, you must place your answer in the form bmem + b _1sm‘1 + - . 4);: + b0 H = (a) s"+an_1s"“+---a1s+ao controller ¢_ ®—> sensor gain Y(s) 2. (8 points) For a. different closed-loop system, the transfer function from the command input R(s) to the output error E(s) is given by E(s) = s 12(8) si+2s——3 Suppose that r(t) = u(t), determine £31086} } .. EC—‘fl __ _____’§_________ L :. 5(5) ‘— 73) RC5) — 52425—3 ‘5‘ (Si-3%?!) Becavm’. .SE LS3 has a. pole, (+0 )1) the, fig fir-40¢} the. ‘Clflu.’ Valve, Chauigm :5 (:94.— “qzilgggfe. we neeca 4:0 "Cumfla BUS) Mncg, then funk—2.. the ,anf «U f. “560: H __ 5+3 = __'11__. A 3 C5+3)C$'13 3: .3 5(5) == —“ + "f‘ 5+3 5! S" 1 Jq 3 = (smcsm i5“ _L_ J_. E0) = —lqgl;3 + '1 5-: 3. (9 points) A closed-loop system with two independent control gains K1 and K3 has the closed-loop transfer function Y(s) _ 25 R(s) _ 5‘ + (K1 + 1):: + K2 Choose the gains K1 and K2 so that the following performance specifications are met. a The closed-loop transfer function has a. DC gain of one, and o in response to a. unit-step input 1-(t) = u(t), the closed-loop response y(t) is underdamped with a damping ratio of 0.7. The the gain (#9 YIN/p.05 is fiewen 17 flu'é 3 m K; '> 5:0 the, 5C, gain ‘5 049.. TAQ. tranaén‘b PESfoflJ—D— ahurmcEQWS'btcs owe, £éQrm1;a£ y the, Poles Croats # the OL’EKFMEQIG'eI‘c. Eém'élufl )2 5" + (K,+ 05 + "2. «"- D L________1 L_.__1 LPWfl WnL wn :Kl'r—ZS" :1; wngg Z.- fwn = [Q] + | :9 2: Z Fwn —! ($10.7) W0 : = 209.?) (S '1 Problem 3: (25 points) 1. (10 points) A LTI system has the transfer function 40.9 H =—. (a) sz+5s+4 Construct the Bode magnitude and phase plots using the semilog graphs provided in Figure 5 (a duplicate copy appears in Figure 6). \In order to receive credit: 0 In both your magnitude and phase plots, indicate each term separately using dashed lines. I Indicate the slope of the straight—line segments and corner frequencies of the final magnitude and phase plots. 0 Do not show the 3 dB corrections in the magnitude plot. Eecwse fin pales al.79- both .2. the lace wigs t1CD} '05 c, ‘n Ll H 53 : —-——-—-—--‘ _ tun». the. K0 n C (S-t‘DCS'r‘n (51'1365/‘1 ‘4) (s): flang- So weCcm Smt :Mgls-iw w = __‘°_£2’.__—_ “a” WuMMH) 10 Figure 5: Semilog paper for Bode magnitude and phase plots. 11 Figure 6: Semilog paper for Bode magnitude and phase plots. 12 2. (15 points) Consider a second-order LTI system Whose frequency response magnitude and phase plots are given in Figure 7. Magnitude (dB) Phase (deg) 1 1o" 10 Frequency (radlsec) Figure 7: Bode Plot for problem 3 part 2. 10 O (3 points) Find the DC gain and high frequency gain of the system. Express your answer in terms of a ratio between the system output and inputs magnitudes, and not dB. "The. OY‘ DC- awin ‘15 2009.9: The. high 'Fv‘eguenca, gain in use Of‘ 0. IO. 0 (4 points) Determine the damping ratio of the system. Is the system under-damped, overdamped or critically damped? Fr am the s \Le'hclfi Al‘XJJL) So if? = to or- P = 10 the 566mb." 75 unaQQRanmpefl . 13 20 90510 g? 5.0: =7 2.0. AnJL &,C‘d-ufie, l) o (3 points) Determine the system transfer function 11(5). 2. K w HCS3 = .___#———-“——————-; 52— 1_ szOS 'f'wfl _ “9- The. DC anon KT-IO, ‘F=-c9.§') DUILO. Wn“5'£57e:_1 $0 e (5 points) Compute the sinusoidal steady-state response y(t) due to the input flt) : 0.3 + 0.1 cos(5 t — 45°). (t) 2"- 0-3 H 03 '9' HC 5')! COSCS4: _L.’SO+}L‘Hf 5—)) 3 (0‘ f a" PM tine, r5092. pm;- H’Liuw : ‘0 [Mann : $0428 or [00 fingJ) *r—-70° Hag, So #023 = 3 + {0 (213.5(5‘E —I3S°) 14 Problem 4: (25 points) In many cases a. mathematical model of a dynamic system can be obtained using fundamental equations, such as Newton’s Law or KVL and KCL. In certain situations, where the theoretical model is complicated or the physics of the process is poorly understood, it is convenient to obtain a model using experimental data. In this problem you will obtain the transfer function based on the system’s transient response. Consider a LTI system with input f(t) and output y(t). The zero-state response of this system to the unit step input fit) = u(t) is given by y(t) = 2u(t) — e"(1 -— 4t)u(t). 1. (8 points) Find the transfer function 3(a) = Y(s)/F(s) of the system. Place your answer in the form bms’” + bm_1s'""1 + - - -bls+ be H = (8) s“+an_1s“‘1+---a1a+ao 30:3 = 2M9 - {tuna-A + life“? sects z _ I + H Y“) :1 “'5‘; (5+0 ($4.01- : 2.65 +1)?" " 59"") + his 3 sL—e- 75 +2. -'—-—.__—r-I—I——'_'"_'—"——'—_—-__—‘ —_____,_,__,__—_-—__ SCS+I)7— sC$+I)" flu-D soot-D 4——> Pm =45— (QQ’L\nl-Llufl) Hggdzj’éil: fl 30* 15 2. (3 points) Is the system BIBO stable ? Justify your answer. HAS) ha; two Pole; of S'=‘-“I' anL .50 {Lth sds'bam F5 BIBO statute. (than, are, no. ales in the, We 4mm piqnet L 3. (3 points) What is the DC gain of the system ? =0 DC. 80m = M98 7—7— 4. (3 points) What is the high frequency gain of the system ? iii 'pr'a _, nc Tn -__—_, :1- ”d e a 3“ M“LN, ’ 5. (8 points) Using the transfer function 3(a), derive a linear differential equation that relates the output y(t) to the input fit). Y0) _ .37- + '75 + 2 F“) .sL-r— 2.5 +1 gm + 2.209 yam =- fica-r véca+fiéfi> 16 ...
View Full Document

Page1 / 16

final_f00 - EE 850 FINAL EXAM 14 December 2000 Last Name 8...

This preview shows document pages 1 - 16. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online