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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)?
U (s) = 1
s s+1 Y (s) = P (s)U (s) = 2
s+3 ✓ 1
s s+1 ◆ = c1
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
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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