300 SAMPLED-DATA CONTROL SYSTEMS 
The Laplace transform of the output C(s) is thus 
1 
OOS Sato 
Following the procedure which permits the use of the z forms given in 
Table 11.1, both numerator and denominator are divided by the highest 
order of s, resulting in 
g73 
C8) = Tari 
Substituting for each term the z form from Table 11.1, there results the 
equivalent z transform of the output C(z): 
C(z) 
J 6T2(2-1 + 2-2) 
~ G2 + 6r + 1) — G6 + 6T — 9TDz 
+ (36 — 6T — 9T2)z? — (12 — 6T + TAZ 
The sampling interval 7 is chosen on the basis of frequency-response 
considerations similar to those used in previous sections. In this case, 
T is chosen as 1 sec, based on the criterion that frequency components 
below —30 db are negligible. If 7 is taken as 1 sec, then 
a) Ogg em 
OO) Se eens eae 
Inverting C(z) by the process of long division there results the 
sequence 
Ce) = 0:3162-! + 0.864¢ + 1.152-* + 1.1'62-* + 1 0Gze" 
+ 0.9872-§ + -- - 
The computed response at sampling instants is given by the coefficients 
of the terms of this sequence. These are plotted as the marked points 
cm Huge eS. 
To show how a reduction of sampling interval can improve accuracy, 
a sampling interval 7 of 0.5 sec is used in the expression for C(z). The 
result is 
Go = ethan ibe 
15125 = 36) (be5 S80 bees 02a 
which, upon expansion by long division, becomes 
C(z) = 0.09842-! + 0.3352-? + 0.610z2—* + 0.85324 + = == 
It is noted that every second term in this expression corresponds to 
that of the sequence obtained for a 1-sec sampling interval. These 
