Modelling and control by Anthony Rossiter

# INTRODUCTION TO FEEDBACK - HOW AND WHY?

This is a section in the chapter on introduction to the importance and impact of feedback. Use the left hand toolbar to access the other chapters and themes.

 It is implicit in several of these chapters that students have core competence in some mathematical topics such as polynomials, roots, complex numbers, exponentials and Laplace. More information on these can be found in the Mathematics theme on the left hand toobar.

This section contains the following topics. Under each topic there are hardcopy (pdf) notes, a video talk through of key derivations with example problems and also a tutorial sheet for users to test themselves.

## Introduction to feedback 1 - open-loop

This set of videos introduces feedback concepts and demonstrates how feedback design has a huge and important impact on the world around us. Specifically, feedback allows us to moderate the behaviours of systems to ensure that the behaviour is desirable. The first video demonstrates the weaknesses in allowing systems to behave with so called open-loop dynamics, that is with no feedback.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

#### Quick test question

Open-loop control is good because:
A. It is robust to uncertainty..
B. Stability and convergence can be assured.
C. Gauarantees offset free tracking.
D. None of the above.

## Introduction to feedback 2 - why feedback?

This set of videos introduces feedback concepts and demonstrates how feedback design has a huge and important impact on the world around us. The second video introduces the concepts of feedback by demonstrating that this is implicit in human behaviour and is a key mechanism that enables us to control the world around us.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

#### Quick test question

A key component of feedback is:
A. The input choice primarily depends upon the target.
B. Measurement followed by corresponding action at the output.
C. Measurement followed by corresponding action at the input.
D. None of the above.

## Introduction to feedback 3 - how feedback?

This set of videos introduces feedback concepts and demonstrates how feedback design has a huge and important impact on the world around us. The third video looks at how feedback can be automated, that is how do we remove the human from the process.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

## Introduction to feedback 4 - impact of feedback

This set of videos introduces feedback concepts and demonstrates how feedback design has a huge and important impact on the world around us. The fourth video introduces concepts of how feedback moderates behaviour and shows that there are many types of feedback and they result in different behaviours. This is introduced in a qualitative fashion.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

## Introduction to feedback 5 - quantifying the impact of feedback

This set of videos introduces feedback concepts and demonstrates how feedback design has a huge and important impact on the world around us. The fifth video begins the task of quantifying the effect of feedback on behaviours by focussing on proportional feedback with first order systems. This quantification is needed to enable design, that is the selection of feedback to achieve the desired system behaviour.

## Introduction to feedback 6 - quantifying the impact of feedback for 1st order systems

This set of videos introduces feedback concepts and demonstrates how feedback design has a huge and important impact on the world around us. The sixth video continues the focus on quantifying more explicitly the effect of proportional feedback on 1st order behaviours and looks at this for a generic system.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

#### Quick test question

Proportional feedback achieves the following for a stable 1st order process.
A. The offset can be removed.
B. The time constant can be speeded up.
C. Acceptable overall behaviour can be achieved.
D. None of the above.

## Introduction to feedback 7 - quantifying the impact of feedback for 2nd order systems

This set of videos introduces feedback concepts and demonstrates how feedback design has a huge and important impact on the world around us. The seventh video continues the focus on quantifying the effect of proportional feedback on behaviours and here focuses on second order systems.

## Introduction to feedback 8 - quantifying the impact of feedback for high order systems

This set of videos introduces feedback concepts and demonstrates how feedback design has a huge and important impact on the world around us. The eighth video continues the focus on quantifying the effect of proportional feedback on behaviours and here focuses on high order systems. As the algebra gets difficult, MATLAB will be needed much more.

• A talk through video is on youtube.

## Introduction to feedback 9 - tutorial sheet on 1st order systems with proportional feedback

This set of videos introduces feedback concepts and demonstrates how feedback design has a huge and important impact on the world around us. The ninth video provides a number of tutorial questions on quantifying the effect of proportional feedback on behaviours of 1st order systems. The video also provides worked solutions, several of which are backed up by MATLAB demonstrations.

## Introduction to feedback 10 - tutorial sheet on 2nd order systems with proportional feedback

This set of videos introduces feedback concepts and demonstrates how feedback design has a huge and important impact on the world around us. The tenth video provides a number of tutorial questions on quantifying the effect of proportional feedback on behaviours of 2nd order systems. The video also provides worked solutions, several of which are backed up by MATLAB demonstrations.

## Introduction to feedback 11 - tutorial sheet on high order systems with proportional feedback

This set of videos introduces feedback concepts and demonstrates how feedback design has a huge and important impact on the world around us. The 11th video provides a number of tutorial questions on quantifying the effect of proportional feedback on behaviours of high order systems. The video also provides worked solutions, all of which utlise MATLAB demonstrations, as the associated algebra is non-trivial.