CHAPTER 7 
DIGITAL COMPENSATION OF SAMPLED-DATA SYSTEMS 
In the preceding chapter, the stabilization and compensation of sam- 
pled-data systems are accomplished by the insertion of a continuous ele- 
ment in cascade with the plant. This element is not separated by a 
sampler, so that its effect is that of altering the continuous transfer func- 
tion to produce some over-all desirable characteristic in the sampled-data 
system. This procedure is relatively obvious since it is analogous to that 
employed in completely continuous systems. Analytically, it is difficult 
to apply, mainly because the over-all pulse transfer function is not simply 
related to the cascaded continuous transfer functions. This difficulty is, 
of course, no justification to seek other means of compensation, but it so 
happens that better results can be achieved by means of pulsed or digital 
compensators. Such compensators can be pulsed networks, that is, net- 
works having a sampler at both their input and output. Alternatively, 
active linear digital controllers can be designed such that they accept a 
number sequence and deliver a processed number sequence at their out- 
put. Such a controller has a sampler at both its input and output, and 
its performance is described by a pulse transfer function. In general, any 
active or passive compensating device which is preceded and followed by 
synchronous samplers is referred to here as a digital controller. This 
chapter will be devoted to the theory and design of such digital controllers 
as compensators in sampled-data feedback control systems. 
7.1 The Digital Controller 
An approach to the concept underlying the digital compensation of 
sampled-data systems may be arrived at by the reasoning which follows. 
Referring to Fig. 7.1, it is seen that a continuous network is employed to 
compensate the sampled-data feedback system. In this case, the 
sampled error sequence H* is reconstructed into an approximation of the 
continuous error E by means of the data hold. The compensating net- 
work whose transfer function is N(s) then operates on the reconstructed 
error signal EH, to form the command input M, which is applied to the 
plant. The viewpoint taken here is that the error signal is first recon- 
structed and then altered by the compensating network to produce a 
desirable over-all system. 
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