Digital Control System Design

To design a digital control system, a z -domain transfer function or difference equation model of the controller that meets given design specifications, is seeked. The controller model can be obtained from the model of an analog controller that meets the same design specifications. Alternatively, the digital controller can be designed in the z -domain using procedures that are almost identical to s -domain analog controller design. This chapter elucidates both these approaches. It begins with an explanation of the z -domain root locus and describes the method of sketching the z -domain root locus for a digital control system or obtaining it using MATLAB. This approach is based on the relation between any time function and its s -domain poles and zeros. If the time function is sampled and the resulting sequence is z- transformed, the z -transform contains information about the transformed time sequence and the original time function. The poles of the z -domain function can therefore be used to characterize the sequence, and possibly the sampled continuous time function, without inverse z -transformation. However, this latter characterization is generally more difficult than characterization based on the s -domain functions.