10 SAMPLED-DATA CONTROL SYSTEMS 
found, just as in the case of continuous systems. Techniques are avail- 
able to optimize the performance of sampled-data systems based on 
mean-square criteria used in the design of sampled-data feedback control 
systems and filters. 
1.6 Miscellaneous Uses of Sampled-data Theory 
If a linear system contains variables which are actually sampled, analy- 
sis by use of the z transformation is exact. Interestingly enough, the 
same theory can be applied approximately to models of continuous sys- 
tems in which sampling of the variable is introduced artificially as an 
aid to analysis. For instance, with the continuous feedback control 
system shown in Fig. 1.9a, it is often desired to obtain the response of the 

Data 
reconstruction 
(a) (b) 
Fria. 1.9. (a) Continuous feedback system. (b) Sampled model of feedback system 
for computation. 
system to an input in the time domain using ordinary inversion of the 
Laplace transform of the output variable. In principle, this is very 
simple and straightforward, but if an accurate solution is desired, the 
process can be quite laborious, requiring the use of calculating machines. 
It so happens that one of the techniques for inversion of the z transform 
is directly accomplished by routine numerical processes. This advantage 
can be applied to continuous systems by constructing a sampled model 
which gives solutions with tolerable error. Such a model for feedback 
systems often takes the form shown in Fig. 1.9b. By selecting the 
sampling rate high enough and using a sufficiently sophisticated data- 
reconstruction element, acceptable accuracy can be achieved. As a 
matter of comparison, the sampling interval is exactly analogous to the 
quadrature interval which would be selected in the numerical integration 
of a differential equation. The sampled-data approach has the advan- 
tage, however, that a physical interpretation of the process is readily 
seen. Having selected the sampled model of the continuous system, its 
analysis becomes one of numerical methods simply carried out by a desk 
calculator or digital-computer program. 
The use of a sampled model in this as well as other applications has 
the advantage of making clear just where the sampler should be placed 
