# Chapter five

Discrete models and Z-transforms

## section three: discrete time models

This chapter is on the theme of discrete time linear models, for example:

y_{k}+a_{1}y_{k-1} + ...+ a_{n}y_{k-n} = b_{1}u_{k-1} + ...+ b_{n}u_{k-n}

where y(t) is the output, u(t) the input and a_{i }, b_{i} are model parameters. The subscript 'k' denotes the sampling index.

This section focuses on an introduction to discrete time models, that is models which represent or encompass continuous time systems but have discrete input and output signals.

### 1. Introduction to the zero order hold

Continuous time systems need continuous inputs. A discrete signal can be converted to a continuous signal using a zero order hold (ZOH).

ZOH basics (PDF, 810 KB)

### 2. Realisation of a ZOH

In order to facilitate modelling, analysis and control design, a mathematical interpretation of a ZOH is needed.

Mathematical representation of a ZOH (PDF, 829 KB)

### 3. Find a discrete model

Examples of how to compute the discrete model G(z) from a continuous model G(s) with a ZOH and sampler.

Discrete model computations (PDF, 786 KB)

Tutorial sheets for chapter five

Online quizzes for chapter five