APPLICATION OF CONVENTIONAL TECHNIQUES 143 
infinity, so that a common factor z — a is added to give 


DO a= 
Can 
DAG) rer (6.43) 
The use of (6.38) and (6.39) is straightforward and leads to the results 
1 (d-aj)s+a 


ES) 1 a sta 
Q(s) = — = - (6.44) 
where e~*? = aas before. The selection of the time constant 1/a intro- 
duced in the procedure outlined above is arbitrary and can be chosen from 
the practical considerations of size and impedance level. It should be 
emphasized that the synthesis procedures given here for pulsed RC net- 
works require, in general, a gain factor in series with Q(s) and P(s). 
This additional gain can, in most practical situations, be associated with 
the zero-order-hold circuits which follow the two sampling switches. It 
should also be noticed that no restriction is placed by this design pro- 
cedure on the hold circuit which precedes the plant. In practice, one can 
frequently arrange the design so that all the zeros of N(z) are in the 
restricted range 0 < z < 1 and can be realized by a pulsed network with 
P(s) = 1. In this case, only one sampling switch and one hold circuit 
are required for the design. 
The complete development of specifications for digital controllers is 
given in the next chapter. Obviously, any of the designs given there can 
be realized by the pulsed networks described here if that is desirable. 
6.7 Summary 
This chapter has outlined five methods for the design of sampled-data 
control systems by the use of conventional servo techniques, which 
include the frequency-response methods associated with the names 
Nyquist, Bode, and Nichols, and the root-locus methods introduced by 
Evans. ‘The design of continuous tandem networks to provide the com- 
pensating action is difficult because of the complicated effects of such an 
element on the closed-loop pulse transfer function. The first three 
methods of design presented in this chapter are approximate methods 
which attempt to unscramble these effects or use only the most significant 
parts of them. The last two methods are exact design methods. The 
fourth method is a procedure for the specification of a continuous network 
to realize a time response specification. This method has great intuitive 
