212 SAMPLED-DATA CONTROL SYSTEMS 
This output is plotted in Fig. 8.10 in the interval in question. The out- 
put samples in this plot at other sampling instants are obtained by 
inversion of C(z) in the normal manner. 
It is seen that the application of this technique is relatively straight- 
forward, though it can be tedious in the case of more complex systems of 

Output c(é) 
(T=In 2) 

0 T al eye 4T 5T 6T 
Time 
Fic. 8.10. Continuous response in third interval for unit step input in example. 
higher order containing a data hold such as the zero-order type. On the 
other hand, it has the advantage of giving the continuous time function 
at any chosen sampling interval without requiring the computation of the 
function at other intervals. Thus, if a peak overshoot is being investi- 
gated, its position to one sampling interval is readily estimated, and the 
continuous time function computed for that interval only. The method 
is exact, so that no hidden effects will be unnoticed. Finally, the expan- 
sion of the system into its partial-fraction form permits an evaluation as 
to which terms in the expression contribute most to the ripple. 
8.4 Use of Advanced or Modified Z Transforms 
Advanced or modified z transforms can be applied to the problem of 
determining the ripple at the output of a sampled-data system.!?:??-74 
The application of the modified z transform is best shown by referring to 
the block diagram of Fig. 8.11. A fictitious negative delay or advance 
AT is placed in cascade with the plant whose ripple output is to be studied. 
If the output of the system containing this fictitious time advance is 
sampled at synchronous rate, the output samples will be displaced in time 
from the input samples by atime AJ’. If A is taken as a number ranging 
