Analysis of errors in sampled-data systems

THE system error ε(t) in a sampled-data feedback system is an important design parameter. It is defined as the difference between the actual output c(t) and the desired output c
d
(t), i.e.,
$\epsilon (t) \buildrel{\triangle}\over {=} c_{d}(t)-c(t)$
. The system error has two components: (1) organic error, due to system energy storages; and (2) ripple, due to the sampling process. Formulation of these errors is obtained through the use of z-transform
¹
and ordinary Laplace transform techniques. (z-transforms are merely Laplace transforms of pulsed data and are usually rational functions in ε
^sT
in which ε
^sT
has been replaced by z.)