194 SAMPLED-DATA CONTROL SYSTEMS 
The data hold is of the zero-order type, and its transfer function is 

since the sampling interval T is taken as 1 sec. The disturbance N is a 
unit step function so that 
Nie = 
The various pulse transfer functions required for substitution in (7.91) 
are 
OS682511) =- OF718zs%) 
(1 — 21)? — 0.368274) 

NG(z) = 
and 
i 
aa pears 
The system has been designed to respond to a unit step input with zero 
steady-state error, and the design for this condition leads to the result 
1 — K(z) = @ — 274) + 0.418273) 
Substituting these pulse transforms in (7.91), the disturbance pulse 
transfer function becomes 
0.3682-1(1 + 0.7182) (1 + 0.418273) 
1 — 0.36824 
It is seen that Ky(z) does not contain 1 — z~! as a factor so that it 
will not reduce the disturbance to zero. As a matter of fact if a unit 
step function is applied, the steady-state output (or error) is obtained 
by the usual final-value theorem and turns out to be 1.43. This is not 
good performance in reducing the effect of a disturbance; as a matter of 
fact, the output amplifies the disturbance. This result is not too sur- 
prising when it is recalled that regulating effect is produced by a high or 
infinite gain in the feedback line between the output of the plant and 
the point of application of the disturbance. The system design results 
in no integration in the digital controller since none is needed to respond 
to a step at the input. é 
To reduce the effect of the disturbance to zero in the steady state, it 
is necessary that 1 — K(z) contain an additional factor 1 — 2-1. Thus, 
for steady-state error suppression, it is necessary that the following be 
true: 
Ky(@) = 

1 — K(z) = 0 — 2)°F (2) 
if the error is caused by a step disturbance applied at N. This result 
causes the digital controller to supply an additional integration in the 
