Block Diagram Analysis of Sampled Data Systems

ME2025 Digital Control

Jee-Hwan Ryu

School of Mechanical Engineering

Korea University of Technology and Education

Laplace transform of sampled r(t)

We can prove it by Fourier series expansion

Zero Order Holder

ZOHr

T

r* hr

( ) ( ) ( ) ( )( ) ( ) ( ) ( )( )( ) ( ) ( )( )[ ]TktkTtkTx

TtTtTrTttrtr

k

h

111

211110

0

+−−−=

+−−−+−−=

∑∞

=

L

( ){ }

( ){ } ( ) ( )( )

( )∑

∑∞

=

−−

∞

=

+−−

−

−=

−==

=−

0

0

1

1

1

k

kTsTs

k

TskkTs

hh

kTs

ekTrs

es

eekTrsRtrL

s

ekTtL