292 SAMPLED-DATA CONTROL SYSTEMS 
which is, from the table in Appendix I, 
ay be ih 0.3679 + 0.264227} 
BO aae (ochre 
The term HBG(z) is given by 
ie a eee 
which is, from the table in Appendix I, 
O32) 4 OAI9Sz5 0080225" 
HBG(z) = (= 06) 

Substituting the component terms in (11.8), Ca(z) becomes 
0.36792-! + 0.26422-? 
1.1821 — 2.08022—! + 1.39622-? — 0.44812 
This z transform is inverted by the method of long division, using a 
desk calculator, resulting in the sequence 
C.(z) = 0.382502-1 +- 0.83052-? + 1.12523 + 1.17212-* + 1.09425 
+ 1.0ll2—° -- 0.971825 
The coefficients of the various z~! terms are the values of the output at 
the sampling instants corresponding to the powers of z~!. The result- 

Ca(z) = 
Pa cn l(t) 
(pS SSse 
' 


so ee 
s(s+1) 


c(t) rit) calf) 
(a) (b) 
Fig. 11.7. (a) Closed-loop system used in example. (b) Sampled model of closed-loop 
system. 
ing points are plotted in Fig. 11.8a on the same graph with the continu- 
ous curve obtained from the direct inversion of C(s). The errors are 
not large, as is seen from this curve and from the error plot shown in 
Fig. 11.8b. The maximum error is 2 per cent, which is within the 
required accuracy for most engineering computations. 
One of the usual problems in the application of numerical methods to 
the solution of continuous systems lies in an estimation of the errors which 
are incurred. In the context of this discussion, it is desirable to obtain 
an estimate or possibly an upper bound to the error in the output at 
