120 SAMPLED-DATA CONTROL SYSTEMS 
system cutoff frequency. In other words, from inspection of (6.2) and 
(6.3), the source of difficulty introduced by the sampling operation lies in 
the production of harmonics or sidebands at integral values of fo. If 
these sidebands are negligible, then the sampling can be ignored, and, 
conversely, the extent to which the sampling aspects of the problem must 
be considered depends upon the extent to which the sidebands are not 
negligible. 
In the present chapter a few examples will be studied and an attempt 
made to develop an experience and ‘‘feel”’ for the extent of the difficulty. 
6.2 Summary of Alternative Design Methods 
Before describing any of the design alternatives in detail it will be 
instructive to list the various possibilities and discuss briefly their impor- 
tant characteristics. Although the list which follows is by no means 
exhaustive, it is felt that the procedures included in this list hold the 
greatest promise for the practical applications of conventional techniques 
to the design problem presented by sampled-data control systems. 
Method 1. Approximation of sampled-data system with continuous 
system. 
Design step 1.1. Replace the sample and hold operations with a con- 
tinuous approximation. 
Design step 1.2. Design the approximate system on a continuous 
basis. 
Design step 1.3. Check the exact response of the compensated system 
by z-transform analysis techniques and repeat the design if necessary. 
This procedure for the design of sampled-data systems is the simplest 
possible approach for those familiar with continuous-control-system 
design, and the method is effective when the sampling rate is relatively 
high. The simplest approximation to take for the sampler and hold 
circuit is a through connection. In other words, when the sample rate is 
very high, one can ignore the fact that the system is sampled at all. This 
“approximation” is common practice, of course, in many pulsed radar 
systems and digital-computer or so-called numerical control loops, where 
it is fairly obvious that the data rate is sufficiently high to permit the 
designer to ignore the discrete character of some of the data in the system. 
The development and use of a more sophisticated approximation will be 
examined later, along with an example problem using the proposed 
method. 
Method 2. Approximation of the effects of the sampler by use of low- 
order sidebands only. 
