# Chapter three

Introduction to feedback

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:

Core skills include:

Why would I create such a feedback loop?

How do such closed-loop systems behave?

Are there generic analysis tools for assessing the behaviour?

Are there generic design tools for ensuring the behaviour meets specifications?

It is implicit that students have core competence in some mathematical topics such as polynomials, roots, complex numbers, exponentials, modelling, behaviours and Laplace.

### Rapid summary

Relatively quick overview videos introducing the core topics.

Introduction to feedback video and notes summary (PDF, 782KB). What do we do when the open-loop behaviour is poor?

Introduction to feedback loop analysis video - block diagrams, closed-loop transfer functions and some analysis with low order systems.

Introduction to proportional feedback video. Analysis of behaviours as proportional feedback varies and insights.

Introduction to integral feedback video. Analysis of behaviours as integral feedback varies and insights.

Introduction to PI design using heuristic rules video.

Summary of common MATLAB commands for loop analysis (PDF, 592KB).

A few summary case studies of applying simple control strategies to:

House temperature (PDF, 914KB)

Car cruise control (PDF, 252KB)

Aeroplane roll (PDF, 662KB)

DC servo (PDF, 345KB)

Heat exchanger (PDF, 344KB)

## Sections in chapter three

### Section one: Introductory concepts

What is feedback and why would I do it? What is the impact of feedback on behaviour? This section includes illustrations and motivation for more systematic design approaches.

### Section two: Basic analysis of feedback loops

How do I determine a transfer function to represent the behaviour of a closed-loop system? How do I infer behaviour from the closed-loop transfer functions? This section includes concepts of closed-loop poles and offset.

### Section three: Block diagrams

How do I define the closed-loop transfer functions for block diagrams with several components, nested loops, multiple inputs including disturbances and parallel paths?

### Section four: Introduction to PID

PID compensators are the most widely used approach globally. How are these defined and tuned? The focus here is on simple insights and tuning as befits a first course.

### Section five: Dealing with uncertainty

A core role of feedback is to handle the uncertainty in the real world. This section gives a brief introduction and demonstration of how feedback loops allow performance to be retained, notwithstanding ongoing disturbances in a system.

### Section six: Introduction to feedback with MATLAB

Much of control analysis and design requires tedious numerical manipulations. Therefore, it is best handled using computer tools. This section gives an overview of some basic MATLAB tools.