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CVR_FRAN5717_08_SE_IFC — 2017/11/17 — 13:26 — page 1 — #1
Table of Laplace Transforms
Number F(s) f(t), t ≥ 0
11 δ(t)
2
1
s
1(t)
3
1
s
2
t
4
2!
s
3
t
2
5
3!
s
4
t
3
6
m!
s
m+1
t
m
7
1
(s + a)
e
−at
8
1
(s + a)
2
te
−at
9
1
(s + a)
3
1
2!
t
2
e
−at
10
1
(s + a)
m
1
(m − 1)!
t
m−1
e
−at
11
a
s(s + a)
1 − e
−at
12
a
s
2
(s + a)
1
a
(at − 1 + e
−at
)
13
b − a
(s + a)(s + b)
e
−at
− e
−bt
14
s
(s + a)
2
(1 − at)e
−at
15
a
2
s(s + a)
2
1 − e
−at
(1 + at)
16
(b − a)s
(s + a)(s + b)
be
−bt
− ae
−at
17
a
(s
2
+ a
2
)
sin at
18
s
(s
2
+ a
2
)
cos at
19
s + a
(s + a)
2
+ b
2
e
−at
cos bt
20
b
(s + a)
2
+ b
2
e
−at
sin bt
21
a
2
+ b
2
s
(s + a)
2
+ b
2
1 − e
−at
cos bt +
a
b
sin bt
CVR_FRAN5717_09_SE_IBC — 2017/11/17 — 16:07 — page 3 — #1
main_1 — 2019/2/5 — 17:55 — page 1 — #1
Chronological History of Feedback Control
Automotive stability augmentation systems
Farm tractor auto-steering via GPS
Drones
Driverless cars
GPS
Unmanned aircraft
High precision disk drive control
Computer-aided control design
Internal model control
Feedback control of automotive engines
Aircraft auto-landing
Apollo digital autopilot
Aircraft stability augmentation
LQG design
Inertial navigation
Maximum principle
Dynamic programming
Numerical optimization
Optimal filtering
Sampled data systems
Root locus
Nyquist stability
Frequency-response tools
Feedback amplifier
Autopilot
Stability analysis of governor
Routh stability
Fly-ball governor
Incubator
1600s 1700s 1800s 1910 1920 1930 1940 1950 1960 1970 1980 1990
2010 20202000
Microprocessor
main_1 — 2019/2/5 — 17:55 — page 2 — #2
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main_1 — 2019/2/5 — 17:55 — page 3 — #3
Feedback Control
of Dynamic Systems
Eighth Edition
Global Edition
Gene F. Franklin
Stanford University
J. David Powell
Stanford University
Abbas Emami-Naeini
SC Solutions, Inc.
330 Hudson Street, NY, NY 10013
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