DIGITAL COMPENSATION OF SAMPLED-DATA SYSTEMS 75) 
the over-all pulse transfer function by the usual methods, to give the 
following: 
Oe) K Gi(2)G2(z) 
Riz) 1+ Ky oGi(z)Ge(z) + KoKiGi(z) 
The procedure in design is to adjust the gain constants Ko and K, to 
obtain the desired over-all pulse transfer function K(z) which fulfills the 
design specifications. 

K(z) = (7.52) 

Fic. 7.20. System used to illustrate design of system with early feedback. 
It is seen from (7.52) that in view of (7.49), the numerator contains all 
the zeros of the plant pulse transfer function, thus fulfilling the require- 
ment for ripple-free operation. The other requirements on K(z) to cause 
the system to respond with zero error to a test input are fulfilled by adjust- 
ment of the gain constants, of which there are as many as the order of the 
system. It should be emphasized that ripple-free operation cannot be 
obtained unless there are a sufficient number of integrations in the feed- 
forward line to make this possible. For instance, to respond to input 
steps or ramps, at least one integration is required to make the design 
practical. Another point is that in order to implement such a system it 
is necessary that each state variable, as indicated in Fig. 7.17, be avail- 
able for instrumentation. If this is not the case, these variables must be 
generated by an auxiliary means. In the extreme, if only the final output 
of the plant is available, a complete analogue-computer simulation of the 
plant would have to be placed in parallel with the actual plant and syn- 
thetic state variables extracted from it. Such a system might be as 
complex as a full digitally controlled system. On the other hand, where 
most or some of the state variables are available, the system has many 
desirable features. This is illustrated most graphically by an example of 
a simple instrument servomechanism. 
EXAMPLE 
To illustrate the design procedure, a servomechanism whose basic 
block diagram is shown in Fig. 7.20 will be used. The system consists 
of a sampler in the error line, a zero-order data hold, and a transducer 
