210 SAMPLED-DATA CONTROL SYSTEMS 
EXAMPLE 
To illustrate the method, the system shown in Fig. 8.8 will be used. 
Here the plant is a simple integrator, and the data hold is an RC circuit 

Fia. 8.9. System used in example expanded into partial fractions. 
as shown. In this case, the over-all plant transfer function including 
the data hold is 
1 
SON s(s + 1) 
which can be expanded into the partial fractions 
1 1 
Seren aren 
thus giving two elementary paths, as shown in Fig. 8.9. Referring to 
the corresponding z transforms G(z) and G2(z) as follows: 

1 
Gi(z) = ae 
fe 1 
i Se 
in Giese 
s+l 
ty 1 
et ee ee 
The significance of these transfer functions is better seen in Fig. 8.9. 
