Copyright by Chul-Goo Kang
Control Engineering
Laplace Transform 3/4
학습목표
1. 미분, 적분함수의 Laplace 변환 구하기 2. Convolution의 Laplace 변환 구하기 3. 최종값정리의 이해
Copyright by Chul-Goo Kang
Laplace Transform 3/4
() 0 (0) (0)Similarly,
) 0 ( 0
) 0 ( ) 0 ( ) ( ) 0 ( ) (
) 0 ( ) ( ) ( ) (
Then ).
( Let
) 0 ( ) 0 ( ) ( ) (
parts by n integratio by
, ) 0 ( ) (
) )(
( )
( )
( ) (
Laplace변a 미분의
, ) 0 ( ) ( ) ( (6)
2 3 2
2
0 0 0
f f s ) f(
s F(s) s t f
f ) sf(
F(s) s
f f s sF s f t f s
g t g s t g t f
t f g(t)
f sf s F s t f
f s sF
dt e s t f e
t f dt e t f t f
f s sF t dt f
d
-st -st
-st
( )
( ), 적분의 Laplace변환
(7) 0 s
s d F
t f
참고. t = 0에서 impulse가 있으면
() () ,
() () 구별
0 0
f t e dt f t f t e dt t
f st st
+ -
L
/ ) ( )}
( {
0 ) 0 ( ), 0 ( )}
( { ) ( )}
( {
) ( ) ( Then . ) ( ) ( Let
0
s s F t h
h h t h s s F t h
t f t h d
f t
h t
Copyright by Chul-Goo Kang
Laplace Transform 3/4
(8) 최종값정리(final value theorem)).
( lim ) ( lim then,
exits, ) ( lim and ble, transforma -
Laplace are ) ( , ) ( If
0sF s t
f
t f t
f t f
s t
t
? Why . 0 ) ( 1 lim )
(
) 진동 ( lim ) cos(
) ( : Ex
? ) ( lim 때 )일 1 ( ) 1 ( : Ex
2 0
s s sF
s s F
t f t t f
t s f
s s F
s t
t
able.
transform -
Laplace are ) ( and ) ( where
) ( ) ( )
( ) (
) ( ) ( )
( ) ( n convolutio
) 9 (
2 1
2 1 0 1 2
0 1 2 0 1 2
t f t f
s F s F d f t f
d t f f d f t f
t
t t
e d s ts
t
0
3 2
1
- ( )
3 1 1
: Ex
1 ( )
) ( )
( ), (
) 10
( 2
2 2
s ds F f(t) d
t
s ds F t d f t s dsF t f(t) d
n n
n n
Copyright by Chul-Goo Kang
