240 SAMPLED-DATA CONTROL SYSTEMS 



(1-0.1294)(1.5—z5}) 
0.9(1—25})2 



(a) 

(1—0.01 27} (2—27}) 
0.99(1—271)2 

(6) 
Fig. 9.10. Block diagrams of (a) double-rate and (b) single-rate systems designed to 
the same specifications. 
o Response of double rate system / 
x Response of single rate system A 
4 a 
Output c(t) 

T 2T 3T 4T 
Time 
Fig. 9.11. Ramp responses of double- and single-rate systems of Fig. 9.10. 
@ 
n 
G (zn) a 
to follow a step input with zero steady-state error at sampling instants 
is considered. In this case, the plant is open-loop unstable, and the 
design requires the application of the constraints expressed by (9.40), 
(9.41), (9.47), and (9.51). Combining these equations for the present 
example, it is found that the over-all pulse transfer function must 
