142 SAMPLED-DATA CONTROL SYSTEMS 
tors are . 
D2) =1 
1 
D(z) = 5 
Although all the factors of D(z) have been used, the reciprocal of D;(z) is 
not bounded at infinity, so that a common factor must be added, such as 
z— a. One such factor is sufficient, and the final results are 


D2) o> ea 
Dy(z) = == (6.40) 
From (6.38), 
vata: 
s (¢—1)(¢- a) 
il zZ 1 Zz 




'1@) ea ee nade 
fisy (ad ae Ae Sacee 
iG) == | (6.41) 
l—as+a 
where a = e—°7. 
From (6.39), 
oes Z a 
Ss Zi lace a 
er: = Z ) 
Bila. a eee 
and Q(s) = == = (6.42) 
fora = e777. 
As a second example consider D(z) = z/(z — 1), which is a pure inte- 
grator. In this case the transfer function has a zero at the origin which 
must be assigned to D,(z) and a pole at unity which must be assigned to 
D;(z). Therefore, after the first step, 
Die) =z 
Dj@) = 4 
Neither of these preliminary functions has satisfactory behavior at 
