PREFACE 
This book deals with the theory of sampled-data systems, a subject 
which has been of increasing interest and importance to engineers and 
scientists for the past decade. The science and art of communications 
have: profited from the realization and application of the fact that 
intelligence can be transmitted and stored in discrete pieces or as a 
sequence of numbers spaced in real time. As we hope to have shown 
in this book, the control systems field can similarly benefit by the utiliza- 
tion of this concept. Even though we treat sampled-data systems 
primarily from the viewpoint of the control function, it is not surprising 
that many concepts have been borrowed from the communications field. 
Control systems are essentially power devices which respond to intelli- 
gence that has been processed in subsystems similar to those in the 
communications field. Furthermore, the same body of theory can be 
used to describe the over-all performance of the control system, even 
though its primary function is the controlled actuation of power elements 
and processes. 
Sampled-data systems are characterized by the fact that the signal 
data appear at one or more points in the system as a sequence of pulses 
or numbers. A central problem in the theory of such systems is that of 
describing the response of linear continuous elements, or pulsed filters, 
as they are sometimes called, to pulse sequences applied to their input. 
The use of the z transformation and the all-important pulse transfer 
function of the pulsed filter makes this problem relatively straight- 
forward. A unique component found in sampled-data control systems 
is the digital controller, which is a computer that accepts a sequence of 
numbers at its input, processes it in accordance with some logical pro- 
gram, and applies the resultant sequence to the controlled element. In 
view of the operation of this type of controller, it is possible to implement 
it by means of a conventional digital computer or its equivalent in the 
form of a mixed or wholly analogue computer. If the numerical process 
programmed in the computer is linear, it can be expressed mathematically 
in terms of a recursion formula which is transformed into a generating 
function having similarity to the pulse transfer function of a pulsed 
linear filter. It is not unexpected to find the same general theory apply- 
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