exam4_sol - ECE 301 Exam 4 Daniel Aguiar July 29, 2011 This...

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Unformatted text preview: ECE 301 Exam 4 Daniel Aguiar July 29, 2011 This exam will be 60 minutes. It is closed notes, closed book and there are NO CALCULATORS to be used on the exam. There are THREE problems. Name: Ea {ufz‘dws Problem 1 (30 points) Fun Motivating Story You are the chief engineer on the USS Crazy Horse, which has been sent on an emergency mission to mediate a dispute between the Romulans and the Klingons. In order to ensure that the talks are free from conflict, they are being held on a neutral Federation planet. You have been tasked with creating a sensor net around the planet to detect any cloaked vessels, thereby preventing either side from attacking the other side’s delegation. Fortunately, you have special subspace sensors that can be placed on a rectangular grid and have a known frequency response. Unfortunately, you have a finite number of these sensors and must therefore space them as far apart as possible. However, as you might imagine, detecting cloaked ships is not easy and you must deploy these sensors in a way that does not cause aliasing. Problem Satement You have sensors that have frequency response X ( j ,LL, ju), where X ( jn, jv) = 0 for MI > W1 or |I/| > W2, and you are placing your sensors on a rectangular grid represented by p(u, 11). You are actually able to measure y(u, 11). Find the maximum spacing (maximum values of Au and A) before aliasing occurs in y(u, 12). Show all work to receive full credit. P(u,v) = hi: [2: 6(a—kva—1AU) wa) = :r(u,v)p(u,v) w, v) : MM 2M (W142 v’ °3 .4 ~ .11! v=i£ 7:1 amt-E; 4% A rt“): '25“: :fl""fia“/ PM / A“”“"=““‘“ V3914 Av 2127 .——x 604/) = A? EJJYV" Problem 2 (35 points total) Fun Motivating Story After several questionable business decisions, you have discovered that you have a bounty on your head and the Trandoshan bounty hunter Bossk is hot on your trail. In need of rapid transport off of Tatooine, you have made your way to the Mos Eis— ley Cantina in an attempt to book passage on a smuggler ship. After doing your best bargaining, you still cannot afford the price of safe transport on the Millenium Falcon. However, after hearing that you are an accomplished engineer, Han Solo agrees to re— duce the cost to something you can afford if you can fix the cruise control on his hyper drive. Problem Statement Given that the ship responds as P(5) and the cruise control is modeled as K(s), and that they are connected as shown in the block diagram below, answer the following questions. 1 w A CI: V H 32—35 W) Part a (5 points): Find and plot the poles and zeroes of P(s). Part b (5 points): Find the transfer function, H (s), for the entire system in the block diagram. 4 Part c (5 points): Find the range of values of a for which H (s) is stable. Part d (5 points): Find and plot the poles and zeros of H (s) for a : 5. Part e (5 points): State if 19(3) is or is not stable and if H(5) for a = 5 is or is not stable and Why. Part f (10 points): — 1 Given the Region of Convergence Re{s} > —2 and a : 5, find Mt). ) A a " JO, 3/ Po/d; @ )‘3d 3 3 £3 Yb) : k/s)P/r/(X(,)- 279/ W { / 2L 4%) p/u/ : k{J//)/1/X/r) IQ ’ HA) — WW ; é9397 - W40“) L WNW) W ' [MM/[1} mg; 31.3) Mm Hula-32+” (,3 Pale: @) J: JG”) I \l(4~3)1‘ Wall/M 2a #5, +4 My 7’?) [a in M, /e/‘%'Cc/1[~p/Nne’ 4420, a>3 J: Em @ :=-/ P/(s @ 5: ~11 JV-zo 2. , 41357 ~ w: ~ 1" l {.02 6: (‘5 rfwéfl Y/‘nta A4; fld/a l‘fl yéjllf-4d/{-/a/qfle HA) 13 mm {Ame If: fl/c; W ;,l 74‘ /e/¢-4a/{,//dw ,5: 6); 3737‘!) N Eff ’ 5": >_/ H 511‘2: f’J— ~ — {[SH) Alf} :{e'éCds(l-t)fi,([{) ‘ '0‘6 $73 ‘ o< Sm¢< e (43(466/ e——-b 1L 1 MZJS>4 Problem 3 (35 points total) Fun Motivating Story Jack Ryan, a friend of yours, comes to you for help on the control software on a newly defected Russian submarine. In the process of getting the submarine to the US, the hardware for the nuclear reactor’s control rods has been damaged. The CIA has man— aged to procure a control unit, but Jack Ryan worries that it may be part of a Russian attempt to cause the submarine to explode in US waters. It is also not possible to ex— amine the internal workings of the control unit without damaging it. Engineers have so far been able to determine the impulse response, but Jack would like you to determine the transfer function and if the system is stable and therefore safe to use. Problem Statement Part a (20 points): Given Mn], find the Z—transform, H (2), including the region of convergence. Part b (15 points): Draw the pole—zero plot and, based only on H (2), state if the system is stable or not and why. a: H(%)= f [EH/‘ng CZ {~;’/"fn-</—w]2’" Arr—04 '4 N :4 Al“ :2 d/k n~7tl< Ld a J gill if: JE i k. I [fig/d Nomi/(Z (’3) ¥ 5 (327) ‘ /+3"‘27 A :d ; 2‘7 m. 25:? /%/>?/3’ W72): //,,{2/ + [WM a flaw I :: g — laci/2/95" new - “5;?” fl 5 W2} :3 m“: flaw J/ +4 W!” “’6 "W’Jc +43 W7 0""[e' ...
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This note was uploaded on 02/14/2012 for the course ECE 301 taught by Professor V."ragu"balakrishnan during the Fall '06 term at Purdue University-West Lafayette.

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exam4_sol - ECE 301 Exam 4 Daniel Aguiar July 29, 2011 This...

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