Modelling, dynamics and control by Anthony Rossiter

# Introduction and Contents

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. This site introduces 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:
1. PDF files with basic notes summaries.
2. Video lectures which talk through topics in slower time (streamed from Youtube).
3. Tutorial sheets with worked solutions that students can use for self testing.
4. Occasional quick fire questions to test progress.
5. MATLAB files for core engineering problem analysis.

Content will cover a broad range of topics, mostly aimed at years 1 and 2 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? Some illustrative case studies indicate the use of these skills in practical engineering and to make the world a better place.

Introduction     Car cruise control     Diabetes management     Aeroplane autopilot     Climate control     Suspension systems     Multiple examples/overview

A number of videos available on Youtube introduce the core concepts and motivation. 1) Behaviours; 2) Weakness of open-loop control; 3) Human techniques for control; 4) PID feedback; 5) Content of a 1st course.

Chapter on mathematical skills: 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 on modelling physical systems and behaviours: Modelling principles and analogies, modelling of 1st and 2nd order systems, responses of 1st and 2nd order systems, classifying behaviours, case studies from various disciplines.

Chapter introduction to feedback: Block diagrams, impact of uncertainty, importance and impact of feedback, closed-loop offsets, simple design approaches.

Chapter introduction to discrete systems: what is a discrete system and why is it relevant. What mathematical tools do we need to describe, analysis and design discrete systems?

Chapter on control design and analysis: root-loci, Bode diagrams, Nyquist diagrams, gain/phase margins, lead and lag compensation.

Chapter on state space methods: beginning from definitions and equivalence to transfer function models and then moving through behaviours, controllability and observability, and finally an introduction to control design, observer design and optimal control.

The chapter on predictive control is more aimed at researchers but covers material that would appear in a final year option for undergraduates.

Chapter on use of MATLAB: 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, generic matlab coding skills.

About the Author: Dr John Anthony Rossiter has been an academic in UK universities for nearly 30 years and taught a huge variety of courses in that time, 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 and has been working in 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. Currently employed in the Department of Automatic Control and Systems Engineering: www.shef.ac.uk/acse.