Speaker
Francois Bouvet
(SYNCHROTRON SOLEIL)
Description
Z-transform is an indispensable mathematical tool for the design and analysis of discrete-time systems. It is the discrete-time counter-part of the Laplace transform. The tutorial begins with the derivation of the Z-transform from the Laplace transform of a discrete-time signal. The main properties of the Z-transform are then listed. A useful aspect of the Laplace and the z-transforms is the representation of a system in terms of the location of the roots of the system transfer function in a complex plane. The correspondence between both planes is presented. The different ways to calculate the z-transfer function of a digitally controlled continuous-time transfer function are then listed. The poles and zeros of the resulting closed-loop transfer function provide useful insight into the system behavior and stability. The influence of the transfer function roots is detailed. The tutorial finishes with a quick description of the two ways to design a digital controller: emulation design and direct discrete-time design.
