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test1_sol_posted - EML4312 Fall 2007 Test1 Name...

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Unformatted text preview: EML4312: Fall 2007 Test1 Name Instructions. This is a closed-book, closed notes exam. 1. (20 points) Mathematics Determine the Step Response (i.e., y(t)) for the following transfer function H(s) = Y (s) = = = = 2. (40 points) Engineering Science (20 points) Determine Y (s). 5 s(s + 1)(s + 10) 5/10 -5/9 5/90 + + s (s + 1) (s + 10) 1 5 1 - + 2s 9 (s + 1) 18 (s + 10) 1 1 5 u(t) - e-t + e-10t 2 9 18 Y 5 = 2 . R s + 11s + 10 R + + + - A + B + K Y C U + D Block Diagram 1 R + + + - A B 1+K Y C U + Y = D 1 + CD D A 1 + AB(1 + K) A R 1 + AB(1 + K) U+ (20 points) Determine Y (s)/R(s). a R 1 b c 1 Y 1 d -e Signal Flow Graph 1 P1 L1 = bc = cd P2 = a L2 = -de = 1 - (cd - de) 1 = 1 + de 2 = 1 - (cd - de) H= bc (1 + de) + a (1 - (cd - de)) 1 - (cd - de) 2 3. (15 points) Mathematics (10 points) Determine y(t), given the following expression for y(s) y(s) = 1 + 1 1 s+1 + + 2 s s + 1 s + 2s + 5 1 1 s+1 . = 1+ + + s s + 1 (s + 1)2 + 22 y(t) = + u + e-t + (cos 2t) e-t . (5 points) What value does r(t) converge to as time goes to infinity? r(s) = lim sr(s) = s+1 s (32s3 + 47s2 + 5) s+1 1 = 3 + 47s2 + 5) (32s 5 s0 4. (25 points) Mathematics For an Impulse Input, determine the output y(t) for the following transfer function H(s) = s2 + 3 (s + 1)2 = Y (s) s2 + 3 = R(s) (s + 1)2 2 s +3 2 - 2s =1+ 2 + 2s + 1 s (s + 1)2 2 - 2s -2 4 = + (s + 1)2 (s + 1) (s + 1)2 y(t) = (t) - 2e-t + 4te-t 3 ...
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test1_sol_posted - EML4312 Fall 2007 Test1 Name...

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