DIGITAL COMPENSATION OF SAMPLED-DATA SYSTEMS 195 
‘feedforward loop so that the system will not only reduce the effect of a 
step disturbance applied at N to zero in the steady state but will also 
make the system capable of responding to a ramp at the input. 
7.13 Implementation of Digital Controllers 
A linear digital controller is characterized by a pulse transfer function, 
which was shown in Sec. 4.6 to represent a linear recursion formula in the 
time domain. The output sample of the controller is the weighted sum of 
a number of past input and output samples. This process requires a 
storage function which holds the past samples and an arithmetic operation 
which carries out the weighting and summing. Such a program can be 
implemented by a digital computer which is programmed to carry out the 
necessary operation. Schematically, the operation of the computer is 
shown in Fig. 4.10, where the sequence of operations is shown. From a 
practical viewpoint, however, digital controllers need not be in the form 
of digital computers. For instance, it is possible to implement the con- 
troller using completely analogue techniques. 
A typical analogue implementation* is shown in Fig. 7.24a, where the 
two groups of eight dials operate potentiometers which adjust the weight- 
ing coefficients applied to eight input and eight output samples. Lower- 
order pulse transfer functions are realized by setting some of these 
coefficients to zero. The sequence of operations is controlled by a set of 
stepping switches actuated by a central timer. The latter is a constant 
adjustable speed drive which operates a set of cams and microswitches. 
It is possible to obtain sampling intervals ranging from 1 to 20 sec with 
this system. This unit is strictly for experimental laboratory use and 
was not designed for field applications. 
One of the disadvantages of a fully analogue unit is the drift which 
occurs in the storage units. The use of condensers, and the mechanical 
switching involved, leads to leakage problems. It is more advantageous 
to use drift-free storage elements, such as digital registers, for data stor- 
age. On the other hand, the simplicity of analogue methods to perform 
the arithmetic operations and the fact that the plant must be supplied 
with an analogue command signal suggests that a mixed system of this 
type is optimum from a practical point of view. Such a system shown in 
Fig. 7.24b has been designed and constructed.+ If a digital computer is 
used for other functions in a complex system, it can be programmed to 
give real-time command signals to the plant at sampling intervals. 
Digital control, whether it be by the use of a complete analogue imple- 
* This unit was constructed at the Department of Electrical Engineering, Columbia 
University, New York. 
} Department of Electrical Engineering, Columbia University, New York. 
