MULTIRATE SAMPLED SYSTEMS 247 
EXAMPLE 
As an example of the design principle outlined in this section, a 
second-order plant with zero-order hold is considered. The pertinent 
transfer function of the continuous element is 
i aes e7sT/n 1 
S s(s + 1) 
From previous calculations (see Sec. 7.8) it is known that the pulse 
transfer function of this system has two zeros, so that n = 2. UH, for 
Ro+ 1 
r s(s+1) 
G(s) = 

(9.86) 

Cc 

(a) 
c(t) 

Time 
(0) 
Fic. 9.14. (a) Block diagram and (b) step response of a multirate system designed 
for zero ripple. 
purposes of this example, 7’ is taken to be 2 sec, then the previously 
calculated pulse transfer function can be used, namely, 
0.3682.-1(1 + 0.718227) 


CO) = Sal = OR (ew) 
Substituting from (9.87) into (9.85), 
_ €=2790 = 03>) 
Ne) — TL =) 
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A block diagram of this system and the associated step response are 
shown in Fig. 9.14. 
It is possible to generalize the interpretation of the basic design equa- 
tion given as (9.82) considerably beyond the step-response case worked 
out in detail in (9.85). In some cases it is desirable, and for plants with 
