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7. Let a system with input u and output y be represented by transfer function P (s). Suppose
P (s) = 2
,
s+3 u ( t) = 1 + e t . What is y (t)?
Solution:
U (s) = 1
1
+
,
s s+1 Y (s) = P (s)U (s) = 2
s+3 ✓ 1
1
+
s s+1 ◆ = c1
c2
c3
+
+
,
s
s+1 s+3 where
c1 = sY (s)s=0 = 2
,
3 c2 = (s + 1)Y (s)s= 1 = 1, Taking the inverse Laplace transform of Y (s), we have
y ( t) = 1
(2 + 3e
3 t 5e 3t ) 2 c3 = (s + 3)Y (s)s= 3 = 5
.
3 8. Sketch y (ty (in in the previousSketch y (t) in the previous problem.
8. Sketch ) t) the previous problem.
8. problem.
Solution:
Solution:
Solution:
LetLet the three terms in t) t) be denoted byterms and(C), be denoted by A, B , and C ,
the three terms in y (y ( be Let the threeAABBandy t,
denoted by , , , , in C
A+B
where A is the ﬁrst term andwhere A islast. ﬁrst term and C is the last. Then each
C is the last. Then each
where A is the ﬁrst term and C is the theThen each
y(t)
1
term can sketched as shown on the sketched as
term can be be sketched as showncan...
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This note was uploaded on 01/27/2014 for the course MAE 171A taught by Professor Idan during the Winter '09 term at UCLA.
 Winter '09
 IDAN

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