# Chapter three

Introduction to feedback

## Section six: Introduction to Feedback with MATLAB

This chapter is on the theme of linear feedback control, for example with G(s) representing a system, M(s) a compensator and d an input disturbance signal:

MATLAB tools are are valuable for modelling, simulating and analysing feedback loops. This section gives a brief introduction to the most important tools.

### 1. Solving ODEs and other skills

A number of resources are already provided on the main MATLAB resources page and moreover a concise feedback tool summary (PDF, 522 KB).

It is useful to be proficient with MATLAB syntax for handling polynomials, so some extra notes are provided here (PDF, 900 KB).

A MATLAB live script for doing modelling, analysis and PI control of a 1st order system.

### 2. Defining transfer function objects

MATLAB has a number of built in functions for handling the analysis of systems represented by transfer function objects, so creating these objects is a core skill.

Continuous time transfer functions video and notes (PDF, 918 KB).

Discrete time transfer functions notes (PDF, 708 KB).

Transfer functions with a delay notes (PDF, 655 KB).

### 3. Control analysis tools

A number of built in functions allow simple analysis of feedback-loops and transfer functions.

Closed-loop transfer functions video and notes (PDF, 575 KB).

Step responses (open- or closed-loop) video and notes (PDF, 558 KB).

Overlaying step-response plots (PDF, 687 KB) and code1 (M-file), code2 (M-file).

Closed-loop poles and iterative design notes (PDF, 739 KB).

### 4. Videos with useful illustrations

Demonstrates real time examples of MATLAB use to analyse and design feedback loops.

Responses with arbitrary inputs

Trial and error design: