PPT - Pulse Transfer Function - Electrical Engineering (EE) PDF Download

 Page 1


Pulse Transfer Function
Page 2


Pulse Transfer Function
Analysis of Discrete-Time Systems
1. The sampling process
2. z-transform
3. Properties of z-transforms
4. Analysis of open-loop and closed-loop discrete
time systems
5. Design of discrete-time controllers
Page 3


Pulse Transfer Function
Analysis of Discrete-Time Systems
1. The sampling process
2. z-transform
3. Properties of z-transforms
4. Analysis of open-loop and closed-loop discrete
time systems
5. Design of discrete-time controllers
n Continuous signal and its discrete-time representation with different sampling rates
3
t (sec)
y
*
6
9 12
3
t (sec)
1
y
7 9 11 5 3
t (sec)
1
y
*
6
9 12
y y
*
Continuous
signal
Disontinuous
signal
Dt
t = nT t
y
*
Dt
t = nT t
y
*
t = nT t
y
*
( ) nT area Impulse Ñ º
n From the response of a real sampler to the response of an ideal impulse sample
(a)
(b)
(c)
(a) (b)
(c)
T = 1 sec
T = 3 sec
Page 4


Pulse Transfer Function
Analysis of Discrete-Time Systems
1. The sampling process
2. z-transform
3. Properties of z-transforms
4. Analysis of open-loop and closed-loop discrete
time systems
5. Design of discrete-time controllers
n Continuous signal and its discrete-time representation with different sampling rates
3
t (sec)
y
*
6
9 12
3
t (sec)
1
y
7 9 11 5 3
t (sec)
1
y
*
6
9 12
y y
*
Continuous
signal
Disontinuous
signal
Dt
t = nT t
y
*
Dt
t = nT t
y
*
t = nT t
y
*
( ) nT area Impulse Ñ º
n From the response of a real sampler to the response of an ideal impulse sample
(a)
(b)
(c)
(a) (b)
(c)
T = 1 sec
T = 3 sec
The Sampling Process
1. At sampling times, strength of impulse is equal to value of input signal.
2. Between sampling times, it is zero.
( )
å
¥
=
=
+ + + + =
0 n
*
nT) - (t y(nT)
... nT) - (t y(nT) .... T) - (t y(T) (t) y(0) t y
d
d d d
Impulse
Sampler
y (t) y
*
nT)] - (t [ y(nT) (s) y
0 n
*
d L
å
¥
=
=
nTs -
0 n
*
e y(nT) (s) y
å
¥
=
=
or
Laplacing
Page 5


Pulse Transfer Function
Analysis of Discrete-Time Systems
1. The sampling process
2. z-transform
3. Properties of z-transforms
4. Analysis of open-loop and closed-loop discrete
time systems
5. Design of discrete-time controllers
n Continuous signal and its discrete-time representation with different sampling rates
3
t (sec)
y
*
6
9 12
3
t (sec)
1
y
7 9 11 5 3
t (sec)
1
y
*
6
9 12
y y
*
Continuous
signal
Disontinuous
signal
Dt
t = nT t
y
*
Dt
t = nT t
y
*
t = nT t
y
*
( ) nT area Impulse Ñ º
n From the response of a real sampler to the response of an ideal impulse sample
(a)
(b)
(c)
(a) (b)
(c)
T = 1 sec
T = 3 sec
The Sampling Process
1. At sampling times, strength of impulse is equal to value of input signal.
2. Between sampling times, it is zero.
( )
å
¥
=
=
+ + + + =
0 n
*
nT) - (t y(nT)
... nT) - (t y(nT) .... T) - (t y(T) (t) y(0) t y
d
d d d
Impulse
Sampler
y (t) y
*
nT)] - (t [ y(nT) (s) y
0 n
*
d L
å
¥
=
=
nTs -
0 n
*
e y(nT) (s) y
å
¥
=
=
or
Laplacing
The Hold Process :
From Discrete to Continuous Time
n Zero – Order Hold :
m
*
(t) m (t)
Continuous
output
discrete
impulses
Hold Device
( ) t d
t
m
*
(t)
T
m (t)
1
n Transfer Function :
Response of an impulse input : d (t)
( )
Ts -
-Ts
e - 1
s
1
s
e
-
s
1
H(s) = =
1)T (n t nT for (t) m m(t)
*
+ < £ =