# Chapter four

Classical control design techniques

## Section five: Classical Feedback Analysis Tools 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 supporting classical techniques such as root-loci, Bode and Nyquist. Some space is also given to the SISOTOOL environment which is very useful.

### 1. Root-loci tools and rlocus.m

• An introduction to rlocus.m video and notes (PDF, 644 KB).

• Introduction to trial and error design with root-locus using MATLAB, video and notes (PDF, 791 KB).

• Proportional design using MATLAB and root-locus, video and notes (PDF, 804 KB).

• A number of video illustrations.

### 2. Frequency response

For an introductory courses on control and frequency response, it is likely that the two files lsim.m and bode.m are sufficient to compute any information and plots needed on the frequency response parameters.

Notes on use of MATLAB (PDF, 588 KB)

### 3. Bode diagrams

Readers will only need to engage with a single file here, that is bode.m. The core skill is to understand what information this file can produce for you: numbers and graphs.

Notes on use of MATLAB (PDF, 739 KB)

### 4. Nyquist diagrams

Readers will only need to engage with a single file here, that is nyquist.m. The core skill is to understand what information this file can produce for you: numbers and graphs.

Notes on use of MATLAB (PDF, 636 KB)

### 5. Gain and phase margins

Once again there is one main file that readers need to compute gain and phase margins, and its use is relatively straightforward for basic computations.

Notes on use of MATLAB (PDF, 527 KB)

### 6. Sisotool

This tool integrates all the important analysis tools:

1. closed-loop step responses (input and output);

2. Root-loci (with and without compensation);

3. Bode diagrams and margin computations (with and without compensation);

4. Nyquist diagrams (with and without compensation).

Being integrated it supports fast and straightforward compensator design.

### 6a. Sisotool - an introduction

Introduces the main screen lay out and options in sisotool. Shows how to obtain plots that are not present automatically such as input responses and Nyquist diagrams. Also shows where some imbedded structural assumptions are accessed.

Concise notes (PDF, 885 KB)

YouTube video talking through the tool

### 6b. Sisotool - overlaying alternative compensators

A key task is to to compare and contrast different compensators. This resource shows how the new version of sisotool stores compensators and allows the user to overlay Bode, Nyquist and step responses for each of comparison.

Concise notes (PDF, 942 KB)

YouTube video talking through the tool

### 6c. Sisotool - proportional design

Begin a control design looking solely at proportional compensation. This resource shows how the drag facility in sisotool allows for easy tuning of a proportional, to at least get in the right range and using intuitive graphical based design approaches. Also shows how the compensator editor allows fine tuning if required.

Concise notes (PDF, 744 KB)

YouTube video talking through the tool

### 6d. Sisotool - lag compensator design

Sisotool has excellent functionality for entering and displaying compensator poles and zeros. This video shows how the drag and drop functions allow a quick graphical based design, without recourse to number crunching, which give a lag compensator close to an equivalent based on detailed algebra and computation.

Concise notes (PDF, 808 KB)

YouTube video talking through the tool

### 7. MATLAB live scripts to support proportional, lag, lead and lead-lag design

The 4 live scripts and in the zip file here.

1. Using phase margin criteria to design a proportional compensator.

2. Using phase margin and ramp error offset criteria to design a lag compensator.

3. Using phase margin and bandwidth criteria to design a lead compensator.

4. Using phase margin, bandwidth and ramp error offset criteria to design a lead-lag compensator.