126 SAMPLED-DATA CONTROL SYSTEMS 
tional improvement can be effected by the use of a lag-lead network as 
described by the transfer function 
(jo + 0.2)(jw + 1) 
(jo + 0.06) (jo + 3) 
The total gain and phase characteristics of the compensated system are 
shown in Fig. 6.9, where it is observed that the phase margin has 
Ni(s)e=20:9 

30 
- \_  —jw/2 1 
HG{ju)=e ste 
20 
3 
= 
& 
ms a 
= 10 g 
xq x 
° | 
8 s 
g ° ¢ 
o 
E 
cb] 
10 3 
a= 
oa 
—20 

Fic. 6.7. Bode plot for uncompensated system. 
been further increased to 60°. The introduction of networks having 
different transfer characteristics than those described above is easily 
accomplished on the gain and phase curves, and any conventional 
rules observed by a particular designer can be applied to this approxi- 
mate model. The ultimate limitation on the use of the method is 
exactly the same as that which applies to the use of frequency 
methods in the design of continuous systems. The designer does not 
know in advance the exact effect of a change in the frequency charac- 
teristics on the time response. The closed-loop step responses which 
correspond to the frequency plots of Figs. 6.7, 6.8, and 6.9 are sketched 
in Fig. 6.10. Examination of these time-response plots indicate that 
application of very simple conventional frequency-response ideas leads 
to an improvement in the time response but that the extent of the 
