BEHAVIOR OF SYSTEMS BETWEEN SAMPLING INSTANTS Pa \\I5) 
EXAMPLE 
To demonstrate the application of the method of modified pulse trans- 
forms, the same problem which was considered in the previous section 
will be used. The basic system is shown in block form in Fig. 8.8, 
where it is seen that the feedforward transfer function G(s) is 
I 
Os S\(Speree) 
Inserting the time advance in this feedforward element, 
G eATs 
(s,A) a s(s al. 1) 
From the tables of advanced z transforms in Appendix IT, the advanced 
pulse transfer function G(z,A) is 
b= Gk LG We = GE) 
Oe) = (Gs BC ote) 

If A is set equal to zero, the ordinary z transform for the feedforward 
element results. 
Substituting G(z,A) in (8.31), the advanced output pulse transform 
becomes 
in Gd =e) BAe’ = 
UA) = Cae lS Ee) Bed Se) ) 

If, for the sake of illustration, T is chosen as In 2 so that e-? = i, 
C(z,A) becomes 
mee A il AN fees 
GEA) = a OO" = 270.8 0.5) 
z)(1 — 0.52-1) + 0.5271 

R(z) 
If, for purposes of illustration, it is assumed that the input is a unit 
step function, then 
IL 
L =o 
in) 
Substituting this expression in the delayed z transform of the output 
and simplifying, there results 

(1 = 0. 2710s = 0.8) 
= St ies Sa 
This transform can be inverted by long division by expanding C(z,A) 
into a power series in z~! as follows: 
Ciz,A) = A+ (B+ 2A)z1+4+ QB 4 2.5A)2? + (2.5B 4+ 2.5A)z°3 
se (5/8) = CAA ea ao 0s 
