102 SAMPLED-DATA CONTROL SYSTEMS 
In plotting pulse transfer loci, the parameter which is varied from point 
to point is the angle 6 of the complex variable z since the magnitude of the 
latter is unity. The usual practice is to mark the various corresponding 
values of 0, as shown in Fig. 5.11. It is seen that GH(z) has conjugate 
values for positive and negative values of @ of equal magnitude. For 
pulse transfer functions which are the ratio of rational polynomials in 2, 

Im 
95 GH(z)-plane 

85 

Re 
9-5 
Fia. 5.11. The pulse transfer locus. 
the reason for this is that each of the component terms of GH (z) is itself a 
conjugate and the sums and ratios of conjugate terms are conjugates. 
As a result of this condition, only half of the pulse transfer locus is plotted 
in practice. 
In most practical applications found in feedback control systems, the 
feedforward pulse transfer function G(z) contains one or more integra- 
tors among the continuous elements. For instance, a typical continuous 
feedforward transfer function has the form 
A rete Sian 
si + Tis) --- 
This transfer function is expanded into partial fractions in the usual 
manner, 
G(s) = (5.52) 
Gs) = “2+, + (5.53) 
Taking the z transform corresponding to G(s), there results 
Ao Ai/T, 
1— 2-1 ris 1 — e-?/tz-1 

Ge) = (5.54) 
It is seen that a pole at the origin of the s plane contained by the continu- 
ous transfer function G(s) leads to a pulse transfer function G(z) having a 
pole at (1,0) in the z plane. The presence of this pole would cause a dis- 
