z transform lecture
TRANSCRIPT
-
7/30/2019 z transform lecture
1/10
Automatic Control Systems
Prof. Abdel Latif Elshafei
Electric Power and Machines Department
Cairo University
-
7/30/2019 z transform lecture
2/10
Digital ControlProf. A.L. Elshafei
Components of a digital control system
Pre-filter A/D Computer D/ASmoothing
filter
PLANT
SensorAnt-aliasing
filter
A/D
R
U Y
-
7/30/2019 z transform lecture
3/10
Digital ControlProf. A.L. Elshafei
The z-transform
The Laplace transform of a sampled signal corresponds to the
z-transform of the continuous signal.
-
7/30/2019 z transform lecture
4/10
Digital ControlProf. A.L. Elshafei
Z-transform
( ) ( ) ( )
( )
( )
( )zR
zkTr
ekTr
dtekTtkTrsR
k
k
k
kTs
k
st
=
=
=
=
=
=
=
0
0
0 0
The Laplace transform of a sampled signal corresponds to the
z-transform of the continuous signal.
-
7/30/2019 z transform lecture
5/10
Digital ControlProf. A.L. Elshafei
Example
-
7/30/2019 z transform lecture
6/10
Digital ControlProf. A.L. Elshafei
Relations between s-plane and z-plane
sTez =
-
7/30/2019 z transform lecture
7/10
Digital ControlProf. A.L. Elshafei
Mapping of constant damping frequency lines
-
7/30/2019 z transform lecture
8/10
Digital ControlProf. A.L. Elshafei
Mapping of constant sigma lines
-
7/30/2019 z transform lecture
9/10
Digital ControlProf. A.L. Elshafei
Mapping of constant zeta lines
-
7/30/2019 z transform lecture
10/10
Digital ControlProf. A.L. Elshafei
Example: Find the impulse response