152 SAMPLED-DATA CONTROL SYSTEMS 
illustration, but in more complicated problems considerable care must be 
exercised to ensure that the approximation is near enough to the exact 
plot. A more practical design problem is given in the next example, 
where the sideband contribution is actually negligible. 
EXAMPLE Method 2 
The method of Linvill will be applied to the same system used for 
illustrating method 1. The block diagram of the system is shown in 
Fig. 6.6. The pulse transfer function for this system is given by 
ll a ay 1 
HG* (jw) » et a/ i? uae (6.13) 

where U, = w+ nwo. A plot of the first term in (6.13), which is 
H(jw)G(jw), is shown in Fig. 6.15, with points on the exact HG*(jw) 
indicated. From these points it is obvious that all sideband terms may 
be ignored in the design of the system. 

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Fic. 6.15. Polar plot for illustrative example 2. 




From the polar plot it is seen that a smaller frequency peak will 
require a lead network near 1 radian/sec, and a lag network, if added, 
should be at frequencies below about 0.3 radian/sec. The plot of the 
compensated system with the network 
(jo + 0.2) ja +1) ean 
AG) VN ea rarer ae 
