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9. What is the steady state 9. response (t(t) steady thesystem P ((s)yandwhen the system Pgiven bythe input u(t) are giv
responseis the when the system P s) (t) the input u(t) are (s) and the
What y )
state response
following?
following?
following? 2
P ( s) = 2 p ,
u(t) = 5 + 4 sin t.
P (s) = s p , 3 u(t) = 5 + (ssin t. 2p ,
P4)=
u(t) = 5 + 4 sin t.
+
s+ 3
s+ 3
p
Solution: Since the system is stable (pole of P (s) at p 3 has negative real part), the steady state exists
p
Solution: Since the system is stable (pole of P (s) at
Solution: Since the system 3 has negativeof P (part), the steady state exists
is stable sum real s at
3 has negative real
for the output. By linearity, the total response is given as the (poleof two;) one resulting from input part), the steady s
foru (t)output. By linearity, for the output. = 4 linearity, as the sum of two;is given as theinput of two; one resulting f
the = 5 and the other from input u (t) By singiven the total response one resulting from input
the total respo...
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 Winter '09
 IDAN
 Steady State

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