# Modelling, dynamics and control

How do we model the world around us and use this to understand its behaviour?

How does behaviour depend upon the engineering choices we make and therefore how do we undertake design to achieve desirable behaviour?

Can we create common forms or representations and thus represent a wide range of engineering systems with a single mathematical approach?

How do we quantify behaviours so we can undertake systematic comparison and design?

How do we influence the behaviour to achieve what we would like?

In practice we ‘control’ or influence behaviour by continuously manipulating (or choosing) the system input. We introduce simple engineering techniques for ensuring this ‘control’ is effective and delivers the behaviour we want, including common control structures such as PID.

This website is intended to be used like a textbook, either as a reference for checking specific topics or to learn topics from scratch. It is made up of a combination of

PDF files with basic notes summaries.

Video lectures which talk through topics in slower time (streamed from YouTube).

Tutorial sheets with worked solutions that students can use for self testing.

Occasional quick fire questions to test progress.

MATLAB files for core engineering problem analysis.

Content will cover a broad range of topics, mostly aimed at years one and two of engineering undergraduate degrees. Many of the videos on Youtube have been viewed by a global audience and received extremely positive feedback. Follow the left hand links for more detail.

### Introduction

Why is an understanding of modelling, behaviours and feedback important for all engineers?

Illustrative case studies indicate the use of these skills in practical engineering and to make the world a better place:

Introduction (PDF, 583KB)

Car cruise control (PDF, 176KB)

Diabetes management (PDF, 497KB)

Aeroplane autopilot (PDF, 176KB)

Climate control (PDF, 474KB)

Suspension systems (PDF, 361KB)

Multiple examples/overview (PDF, 486KB) and more varied examples.

A number of videos are available on YouTube that introduce the core concepts and motivation:

There are also enumerable resources developed by others on the power and relevance of control engineering to the modern world problems, for example: i) How much modelling and control is needed to make this flight happen? ii) What about self-driving cars which could be our future? iii) Platooning trucks saves huge amounts of fuel - modelling and control is core. iv) What about robots in the operating theatre - do you trust the control design on your body? v) How about an artifical pancreas for diabetes which works on closed-loop control. vi) What about stabilising roll in ships; vii) Auto-pilot systems. viii) Satellite attitude control.

### Chapter overviews

Chapter one: Mathematical skills

This chapter looks at roots of polynomials, Laplace transforms, inverse Laplace, complex numbers, logarithms and exponentials, binomial expansions for A Level, logarithms for A Level, trigonometry for A Level, simultaneous equations, matrices and determinants.

Chapter two: Modelling and behaviour

This chapter looks at modelling principles and analogies, modelling of first and second order systems, responses of first and second order systems, classifying behaviours and case studies from various disciplines.

Chapter three: Introduction to feedback

This chapter looks at block diagrams, impact of uncertainty, importance and impact of feedback, closed-loop offsets and simple design approaches.

Chapter four: Classical control design techniques

This chapter looks at root-loci, Bode diagrams, Nyquist diagrams, gain and phase margins, and lead and lag compensation.

Chapter five: Discrete models and Z-transforms

This chapter explores what a discrete system is and why it is relevant. It looks at what mathematical tools we need to describe, analysis and design discrete systems.

Chapter six: MATLAB resources

This chapter looks at solving ODEs, creating transfer functions, closed-loop transfer functions, analysing transfer functions, step responses, closed-loop offsets, trial and error design for offset, poles and loop analysis and generic MATLAB coding skills.

Chapter seven: State space methods

This chapter begins with definitions and equivalence to transfer function models. It then moving through behaviours, controllability and observability. Finally, it looks at an introduction to control design, observer design and optimal control.

Chapter eight: Predictive control

This chapter is more aimed at researchers, but covers material that would appear in a final year option for undergraduates.

Other resources:

Popular YouTube channel by Brian Douglas and his resourcium site with learning journeys.

UNILABS (from Spanish control community: virtual and remote laboratories)

### About the author

Dr John Anthony Rossiter has been an academic in UK universities for nearly 30 years. In that time, he has taught a huge variety of courses, but with special interest in the topics of modelling, analysis and control.

He was educated at Oxford University where he was also awarded his doctorate in 1990. He has been working at the University of Sheffield since 2001. He has a number of prizes for teaching as well as publishing extensively in the academic literature, mainly in the field of predictive control.

Dr John Anthony Rossiter is currently employed in the Department of Automatic Control and Systems Engineering.

### About the resources

Dr Rossiter's perception of education is that the world is changing and in particular the historical reliance on conventional text books and didactic lectures is already outdated. Moving into a world that encourages and supports independent and flexible learning, it is important that students have suitable resources.

A full suite of learning resources will include laboratories, quizzes, question and answer sessions, interactive resources and so on. However, it is still necessary to have at the core some didactic material students can use for their first exposure to topics and for reference where necessary.

Consequently, these videos are intended to act like lectures, partially didactic and partially with worked examples. Students can view these offline to get to grips with a topic. Videos can be paused and restarted and even reviewed over and over again and thus, through repetition and/or active engagement, students' understanding will improve. In several places they are supplemented with tutorial sheets students can use to test their progress.

The material will cover topics and content which could be presented anywhere within the first three years of an engineering undergraduate degree; years two and three would be more typical.

The presentation of material is such that many chapters are standalone, so students do not need to view all the preceding chapters in order to find them useful. However, within the chapters themselves there are often references back to earlier videos, so it is advisable to view the chapter videos in order.