6 SAMPLED-DATA CONTROL SYSTEMS 
continuous feedback systems. The problem of designing such networks 
is considerably more complex, however, because of the presence of the 
sampling operation. 
A configuration which is unique to sampled-data systems is one in 
which a digital controller is used, as shown in Fig. 1.5. In this system, 
the controller accepts a sequence of numbers and processes them, usually 
linearly, to produce an output number sequence. The latter sequence is 




Continuous Sampled 
error error 
Output 



Data 
reconstruction 

Continuous 
element 


Fia. 1.4. Typical error-sampled feedback control system. 
reconstructed into a continuous command signal and is applied to the 
plant. If the linear program of the digital controller is properly designed, 
the over-all system can be stabilized and its dynamical performance 
made to conform to fairly rigid specifications. The digital controller 
Data 
Sampled reconstruction 
Output 







Input i Bie 
Digital nen 
controller Sequence 

Continuous 
element 

Fic. 1.5. Sampled-data feedback control system using digital controller. 
may be implemented by digital-computer techniques or it may employ 
a mixture of analogue and digital components. Its main requirement 
is that it be capable of receiving a sequence of numbers equally spaced 
in time and of processing them in real time into a command signal. It 
will be shown later that controllers of this type can produce systems 
whose performance cannot be duplicated by all-continuous systems. 
The problems which must be studied in sampled-data feedback control 
systems include all those encountered in continuous systems. First, a 
criterion for stability must be derived and adapted for application to 
physical problems. Second, a means for relating the input and output 
which is as direct and simple as the Laplace transform in continuous 
systems must be developed, along with a means for shaping and compen- 
sating the system. A unique property of sampled-data systems is that 
the output will contain a small periodic output component which is the 
result of intermittency in the signal within the system caused by the 
sampling operation. This periodic variation is known as ripple, and 
methods for analyzing this component and reducing or controlling its 
magnitude are required. 
