DIGITAL COMPENSATION OF SAMPLED-DATA SYSTEMS 193 
Taking the z transform of both sides of the equation, 
C(z) = NG(z) — C(z) D(z)GH() (7.87) 
Solving for C(z), 
uf NG(z) 
It is seen that an over-all pulse transfer function relating the output to 
the disturbance cannot be obtained because it is not possible to separate 
N(z) from NG(z). 
Using an approach similar to that of the previous section, a quasi-over- 
all pulse transfer function is obtained as follows: 
NG(z)/N(z) 
i) ame ETI) 
(7.89) 
This pulse transfer function is meaningful only for a particular N(z) and 
must be used in that manner. 
Recalling that the over-all pulse transfer function for excitation at the 
input F is given by 

Ee VOGHe 
It is readily ascertained that 
Kw) = 37S - KO) 7.91) 
If the system is to regulate to cancel out a disturbance N (z), it is necessary 
that Ky(z) have a form which produces zero steady-state error for the 
particular N(z) for which it is designed. 
As an example, if N(z) is a step-function disturbance such as that pro- 
duced by the sudden closure of a valve in a process control system, then 
to cancel out this effect in the steady state it is necessary that 
Kl) = (lh oN) (7.92) 
where F(z) is an unspecified polynomial ratio in z. In many cases it is 
seen from (7.91) that this is automatically satisfied since the same require- 
ment may have been put on1 — K(z). There is the possibility, however, 
that the term NG(z)/N(z) may affect the result. 
EXAMPLE 
The example relates to the system whose block diagram is shown in 
Fig. 7.23. The plant transfer function G(s) is 
1 
ENS) ea) 
