216 SAMPLED-DATA CONTROL SYSTEMS 
where the parameters A and B are defined as follows: 
An Oe 
Be 05>) — 0 
This expression is inverted to yield the following impulse sequence: 
ed) = Ao) + (B 4 2A)s¢ — T) + CB 25400 = 2m 
+ (2.5B + 2.5A)e(i — 37) + (2.5B + 2.254)5¢ — 4) 
If the ripple in the sampling interval between 37 and 4T is desired, 
the fourth term in the expression for c(¢) is considered, so that 
e3(t) = 2.5(1 — 0.54) + 2.5(0.54 — 0.5) 
If A is taken as zero, the ordinary z-transform inversion is obtained, 
which gives the values of the pulse sequence at sampling instants. 
This sequence is 
e*(t) = 0.567 — T) + 1.06¢ — 2T) + 1.256 — 3T) 
+ 1.256¢ —4T)+--- 
The pulse sequence represented by c*(é) is plotted in Fig. 8.13, where 
it is seen that the values of the output at sampling instants as given by 
c*(t) are marked. The intersample instant ripple as given by c;(¢) is 
plotted in the third sampling interval by allowing the parameter A to 
vary between 0 and 1. The ripple at any other sampling interval 
could be obtained by a similar procedure, although the peak overshoot 
probably occurs in the interval shown. 
As with the methods discussed in previous sections, the use of advanced 
or delayed z transforms is relatively 
2.0 t straightforward theoretically, though 
somewhat complex to apply. This 
should be expected since the Laplace 
1.5 Ripple c(t) x 
S wee Phe transform of the continuous output 
EI is itself very complicated. The use 
2 of the advanced or modified z trans- 
form has the advantage of being 
orderly in form and of requiring the 
development of no new techniques 
for itsinversion. Tables of modified 
z transforms are used directly, just 
San Bine insteaua) as in the case of ordinary z trans- 
fie 18; Mo of cutput pple belveen’ forms, Because d appears usualy a 
example. an exponent in the resultant modi- 
fied z transform expressions, it is not 
readily evident how to synthesize systems having prescribed specifica- 

