3. Placing poles in the plane of the complex variable z , root locus method

In this paragraph, we'll use the z-transform representation of discrete systems to develop methods very similar to those derived in the case of continuous systems, where we've considered the behavior of a system in the plane of the complex variable p . Here, we will consider correction in the plane of the complex variable z .

Two classes of correctors will be studied:

• one corresponding to the traditional correctors found for continuous systems: phase advance, integral action, PI, PID, and for which the corrector structure is simple;

• the second, for which the simplification of poles and zeros is practiced, and which leads to correctors that are generally more complex but, conversely, to a simpler open-loop transfer function and therefore to a root locus that is easier to interpret....