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Automatic Control System.pdf


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Laplace Transform Table
Laplace Transform F(s)

Time Function f(t)

1

Unit-impulse function 8{t)

1
s

Unit-step function Us{i)

1

Unit-ramp function t

f(n = positive integer)

1

„-«'

e

i' + Q!

1

fa—at

te

(s + a)2
n\
(s + a)" + 1
1
(s + a)(s + p)
s
(s + a)(s + p)

t"e~°"(n = positive integer)

1
(r-M
{S-cSC

1
fi-o

1
s(s + a)

5(5 + a ) 2

i ( l - e~at or

1
s2 (s + a)
1
2

s (s + a)
s
(s + a)2

pe-P-ae-*)^®
a

1

2

r~Pl\{n=Lt
){a J 0
*

C

+ e-m)

L{ca-\
or
1
a2

a
(1

ate'0")

\

ct/

-at)e-°"

CO,,

2

s + col
s
s +co2
2

sin co„t
IWWfll