114 SAMPLED-DATA CONTROL SYSTEMS 
ing frequency-response curve. It is seen that the response to a unit step 
input is slow and that there is considerable overshoot. 
In the other frequency-response functions plotted in Fig. 5.21, there is 
a distinct correlation between the frequency-response characteristics and 
the time-domain response. Relatively flat frequency response indicates a 
time-domain response with relatively little overshoot, as seen in Fig. 5.21c 
and d. Peaked frequency response at the high end of the spectrum indi- 
cates some overshoot, with oscillation at higher frequencies. It is empha- 
sized that while it is theoretically possible to deduce the performance of a 
sampled-data system from the com- 
plete frequency-response character- 
istics, this can rarely be done in 
Giziplane practice. Only qualitative ideas of 
how the system is likely to behave 
can be obtained from the more ob- 
vious features of the frequency re- 
sponse. Because of the relative 
ease with which time-domain per- 
formance can be obtained for sam- 
pled systems using methods of long 
division or other machine computa- 
tion, the frequency response is 
rarely plotted. Asa concept, how- 
ever, it serves the useful purpose of 
Fia. 5.22. Relation of pulse transfer locus tying together the time domain, 
to frequency-response function. pole and zero locations, and fre- 
quency characteristics. As will be seen later, design in the time domain 
is feasible in sampled-data systems. 
The foregoing discussion serves also to substantiate the statement that 
the proximity of the pulse transfer locus to the critical point (—1,0) is 
indicative of a tendency of the system to have an oscillatory, though 
stable, response. This can be seen by reference to Fig. 5.22, where a 
typical pulse transfer locus is sketched. Each point on the pulse transfer 
locus represents a point on the unit circle of the z plane. Viewed from 
the frequency domain, each point on the unit circle represents a particular 
frequency. It is recalled that for a unity feedback system, the over-all 
pulse transfer function K(z) is 
KG) = 

G(z) 
From Fig. 5.22, it is seen that K(z) can be obtained for various values of 
frequency by taking the ratio of the sinors indicated. Now, if the pulse 
transfer locus passes close to the critical point (—1,0), the sinor 1 + G(z) 
