Laplace Transforms and Transfer Functions
Bạn đang xem bản rút gọn của tài liệu. Xem và tải ngay bản đầy đủ của tài liệu tại đây (336.01 KB, 4 trang )
Laplace
transform
solution in
time domain
solution in s domain
inverse
Laplace
transform
problem in
time domain
transform
solution in
original way
of thinking
solution in transform
way of thinking
inverse
transform
problem in
original way
of thinking
linear
differential
equation
time domain
solution
Laplace
transformed eq.
(algebra eq.)
Laplace
solution
Laplace transform
Inverse Laplace transform
easy
time domain
difficult
frequency domain (Laplace domain)
transform
solution in
original way
of thinking
solution in transform
way of thinking
inverse
transform
problem in
original way
of thinking
System OutputInput
()
()
Input flowrate
Output flowrate
R
C
()
()
()
inlet air signal
=
=
flexible diaphragm
flow
direction
spring with capacitance,
C
m
stem and diaphragm plate
are the moving mass,
m
seal with resistance,
R
m
applied force
Fluid temperature,
T
a
(actual temperature)
The liquid in the bulb
expands as in its
temperature increases,
forcing more liquid up
the small tube. The
height of liquid is a
measure of the liquid in
the bulb
Bulb temperature,
T
m
(measured temperature)
()
()
()
Input flowrate
Output flowrate
(
0
)
()
Positive displa-
cement pump
T
m
T
a
inlet air signal
=
=
flow
direction
applied force
System
OutputInput
()
()
()
()
()
0.5
0
i
(
t
),
mA
1.0 1.5 2.5 3.52.0 3.0 4.0
2
4
6
8
10
12
14
time
,
s
Input current
i
(
t
)
0.5
0
x
(
t
),
mm
1.0 1.5 2.5 3.52.0 3.0 4.0
2
4
6
8
10
12
14
time
,
s
final value of
x
(
t
)=8
mm
control valve position
x
(
t
)
= 8+8.04
(10+174.3
0
)
inlet air signal
0
period=
1
output,
input,
Frequency (rad/sec)
Magnitude (dB)
10
20
30
40
50
60
0 10
-4
10
-3
10
-2
10
-1
Frequency (rad/sec)
-90
-80
-70
-50
-30
-20
-10
0
-40
-60
Phase (deg)
0 10
-4
10
-3
10
-2
10
-1
gain
phase angle
Inverse Laplace transform
algebra
time domain
operational calculus
frequency domain (Laplace domain)
() + () =
()
=
=
0 < 0
0
()
+ () =
()
=
1
=
( + 1)
