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Automatic Control Systems

Prof. Abdel Latif Elshafei

Electric Power and Machines Department

Cairo University

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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

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Digital ControlProf. A.L. Elshafei

The z-transform

The Laplace transform of a sampled signal corresponds to the

z-transform of the continuous signal.

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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.

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Example

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Digital ControlProf. A.L. Elshafei

Relations between s-plane and z-plane

sTez =

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Digital ControlProf. A.L. Elshafei

Mapping of constant damping frequency lines

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Digital ControlProf. A.L. Elshafei

Mapping of constant sigma lines

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Digital ControlProf. A.L. Elshafei

Mapping of constant zeta lines

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Digital ControlProf. A.L. Elshafei

Example: Find the impulse response