{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

test1_sol_posted

# test1_sol_posted - EML4312 Fall 2007 Test1 Name...

This preview shows pages 1–3. Sign up to view the full content.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 3

test1_sol_posted - EML4312 Fall 2007 Test1 Name...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online