APPLICATION OF CONVENTIONAL TECHNIQUES 125 
approximation. The plots of the uncompensated gain and phase are 
shown in Fig. 6.7 for a value of loop gain constant of unity. For the 
purposes of this example let it be supposed that the objectives of the 
design are to maintain the low frequency gain at unity and to increase 
the phase margin from the indicated 17° to approximately 50° to 
ensure satisfactory performance. The time response will be checked 
to evaluate the final design in terms of overshoot and general transient 
behavior. 
Ris) 


(b) 
Fia. 6.5. A sampled-data system and the approximating continuous system. 
The first network one might apply for the stated purposes is a lag 
network. In general terms, one can say from a consideration of the 
Bode plot that greater benefit can be derived from a lag network than 
Rs) C(s) 

Fia. 6.6. Block diagram for illustrative example. 
from a lead network because of the very rapid increase in phase—fall of 
phase margin—as the linear phase from the delay e~*/? begins to be 
effective. A lead network has only limited effectiveness against this 
rapidly increasing lag angle. The exact location of the lag network and 
the separation of break frequencies are matters for individual judgment 
and component size requirements. As a first attempt, the network 
transfer function 
ovate Os2 
qa + 0.66 
will be tried. The modified plots of gain and phase are shown in Fig. 
6.8, where it may be observed that the phase margin at 0-db gain, 
“gain crossover,’”’ has been increased to about 47°. A slight addi- 
N(jw) = 0.3 
