APPLICATION OF CONVENTIONAL TECHNIQUES 135 
if the over-all pulse transfer function is to be given by (6.19). There is 
no unique continuous transfer function which satisfies (6.21). The time 
function corresponding to the transform NG/s must have a specified set 
of values at sample instants to satisfy (6.21) but may take any shape 
between sample values of time without affecting (6.21) at all. However, 
there are only a limited number of admissible or practical forms for NG/s. 
In order to exercise some control over the behavior of the output between 
sampling instants it is desirable that the selected continuous transform 
be as nearly “low-pass”? as possible. The simplest and most direct 
method of obtaining such a transform is to do a partial-fraction expansion 
of the pulse transform into elements which can be looked up in a table of 
transform pairs. For example, the poles of (6.21) are all located at unity, 
so that the continuous transform has all its poles at zero. Therefore, 
one should write ; 
ING Wapavucre (Chal) BTz Cz 
a ee eee gery wee) 
Simple matching of coefficients between (6.22) and (6.21) shows that in 
this case 
1 

A= oT 
3 
= oi 
Ce—s0 
and, consequently, associating the Laplace transforms and z transforms 
from the table in Appendix I and simplifying, 
N(s)G(s 1+ 37s 
SO = eS 62°) 
If the plant G(s) happens to be a pure integration then this problem is 
nicely solved with the compensation network 
N@) === (6.24) 
which is a practical transfer function. However, if G(s) has a greater 
excess of poles over zero than unity, then the compensation network will 
have more zeros than poles and the system will not be practical. In addi- 
tion to the difficulties attendant on the realization of networks having 
more zeros than poles, in the present case such a compensation network 
would cause impulses and possibly higher-order singularity functions to 
be applied to the plant. A possible way to increase the number of poles 
in the compensating network would be to add to the transform given by 
