192 SAMPLED-DATA CONTROL SYSTEMS 
prevent this form of overshoot, the sampling frequency is increased and 
the effect is reduced. 
7.12 Effect of Disturbances on Digitally Controlled Systems 
In the previous discussions, it was assumed that the only excitation of 
the control system was at the input, where it was subtracted from the 
output to form an error signal. Such systems are classed as servo- 
mechanisms or duplicator feedback control systems. In practical sys- 
tems, inputs may be experienced elsewhere in the system and are usually 

Fia. 7.23. Digitally stabilized system with disturbances. 
in the form of disturbances to which the system should not respond. A 
pure regulator system has a fixed reference or set point, and the only 
dynamic effects are the result of disturbances which the controller 
attempts to neutralize. In regulator-system design, these inputs are the 
important ones, and the controller design is dictated by them rather than 
response to set-point changes. 
A general discussion of regulator-system design is not entirely possible, 
because the disturbances may enter almost anywhere in a system. For 
purposes of discussion, however, the system shown in Fig. 7.23 will be 
used. In this system a disturbance input is assumed to enter the system 
just before the plant and after the data hold of the digital controller. 
This input N is assumed to be systematic, that is, it is a definable func- 
tion, such asa step. The reference input R is assumed to be a constant 
and, since the system is linear, only that component of the output caused 
by the disturbance need be considered since it can be superimposed on 
any other outputs produced by other sources of excitation. The relations 
which hold in this system are 
C(s) = N(s)G(s) + Ei(s)G(s) (7.83) 
and E,(s) = E%¥(s) D*(s)H(s) (7.84) 
Also, since the input R is assumed to be zero for this development, 
E}(s) = —C*(s) (7.85) 
Combining (7.83), (7.84), and (7.85), 
C(s) = N(s)G(s) — C*(s) D*(s)H(s)G(s) (7.86) 
