APPLICATION OF CONVENTIONAL TECHNIQUES 133 
is shown in dashed lines on Fig. 6.15. The compensation has reduced 
the frequency overshoot from 2.0 to approximately 1.25, which is prob- 
ably satisfactory. A transient response test could be made to deter- 
mine the exact nature of the system response to a particular type of 
input if that is necessary. For this example, the pertinent step 
responses are shown in Fig. 6.10. 
The two examples used here to illustrate Linvill’s method lie almost 
at opposite extremes as far as the applicability of the method is con- 
cerned. The first-order example plotted in Fig. 6.14 does not permit 
use of the method at all for reasonable ease and accuracy, and the second 
example required only one term for satisfactory accuracy. The evalua- 
tion of the method for any particular system can be quickly made by a 
comparison of the loop transfer function 1/TG(jw) with the exact pulse 
transfer function G*(jw). Without this check, the designer is not able to 
say with confidence that one or two or even ten terms satisfactorily 
approximate the true loop transfer function. 
Method 3, in which the continuous network N(s) is separated from the 
plant by a fictitious sampler and hold as shown in Fig. 6.3, is most useful 
only when the sampling period T’2 of the fictitious sampler is considerably 
smaller than that of the first actual sampler. If the sampling periods 
T and T, are the same, this technique is no more accurate than that of 
method 1. In choosing T» to be a fraction of 7, the system becomes a 
multirate system, which is treated in Chap. 9, so that no detailed example 
will be given until the theory is more fully developed. The design steps 
outlined in Sec. 6.3 are self-explanatory for the case of equal sampling 
periods and can be extended to the case of multirate systems using the 
techniques developed in Chap. 9. 
6.5 Design of Continuous Network by Time-domain Specifications. 
Method 4 
This design method is based upon the following calculations. For the 
single-loop feedback system shown in Fig. 6.2 one can write 
CO) Re ANGe) 

me) tlie ~“@ (elo) 
and, consequently, 
HNG(2) = es (6.16) 
If now, one were to specify K(z), the closed-loop pulse transfer function 
from input to output, then, from (6.16) one can calculate the open-loop 
transfer function NHG(z). From this open-loop pulse transfer function 
