MISCELLANEOUS APPLICATIONS OF SAMPLED-DATA THEORY 293 
sampling instants produced by the sampled model. For engineering 
approximations, maximum advantage can be taken of the relationship 
which is established between the sampled model and the actual physical 
system. The definition of the computational error can best be under- 
stood by referring to Fig. 11.9, where the difference between the output 
Approximate solution c(t) 





Exact solution c(t) 
e(t) 0.6 
0.02 04 Exact error e(£) 
0.01 0.2 ‘o<— Approximate error e,(¢) 

Fic. 11.8. Exact and approximate response of system to unit step function. 
of the actual system c(¢) and the sampled model output c,(¢) is e(¢). For 
the linear system, the Laplace transform of the error e(s) is given by 
e(s) = C(s) — Ca(s) (11.9) 
The problem is to evaluate or approximate this transform. 
To approximate e(s), a number of steps are taken, the first of which is to 

Fic. 11.9. Block diagram for determination of computational error. 
note that the Laplace transform of the output C*(s) is given by the 
summation 
-) 
4 
if 
n=-—@2 
CAS) = Ca(s + njwo) (11.10) 
Taking only the central term of the summation as being an adequate 
