BEHAVIOR OF SYSTEMS BETWEEN SAMPLING INSTANTS PAD 
The z transform of the first elementary output Ci(z) is given by 
_ R)Gi) 
ON) > TEE) 
and C’2(z) is given by 
_ R)G2() 
CAE) aeraies 
where G(z) is the loop pulse transfer function. G(z) is given by 
1 
GG) = BT) Ta) 
(1 — e-?)z7! 

re QS ey = oa) 
if, further, it is assumed that the input is a unit step function, so that 
R(Z) is 



1 
TE) = mane 
then, substituting the various expressions, C1(z) and C2(z) become 
1 Culem 
Cie) 1 —2z! + 1 — 2e-Tz-1 4 e-Tz-? 
and Co(z) = — : 
1 — 2e-Tz-! + e-Tz-? 
It will be assumed for purposes of illustration that the sampling 
interval T is such that e~7 is 0.5. Using this value and inverting Ci(z) 
and C2(z), 
ey(mT) = 1 + 2-”” sin mr/4 
comT) = —2-"/? (cos mr/4 + sin mr/4) 
In view of the fact that there are no higher-order poles than the first, 
the continuous output during the interval from mT to (m+ 1)T is 
given by 
6) = Ci(@ol) += eGo C2 
The continuous output c(t) can thus be obtained for any desired interval. 
For instance, supposing that it were desired to obtain the continuous 
function for the interval between 27 and 37, then c;(27) and c2(2T) are 
computed by substituting m = 2. Doing so results in the values 
GQ) = IW 
The continuous output function for the interval is 
c(t) = 1.5 — 0.5e—¢?”) 
