DIGITAL COMPENSATION OF SAMPLED-DATA SYSTEMS 161 
conditions are acceptable, it is the fastest system in the respect noted. 
It was not possible to realize the minimal prototypes of the form listed 
in Table 7.1 because of the presence of a zero in G(z) outside of the unit 

4 
Time, sec. 
Fic. 7.9. Response of system in illustrative example to unit ramp input. 
Output 

Time, sec. 
Fic. 7.10. Response of system in illustrative example to unit step input. 
circle. 
The presence of this zero resulted in a settling time which was 
one sample time larger than the minimal system. 
The digital controller which is required to produce the over-all per- 
formance in this example is described by its pulse transfer function 
D(z), which is obtained by substitution in (7.5). This results in the 
