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Control engineering An introductory course Jacqueline Wilkie, Michael Johnson and Reza Katebi Control engineering An introductory course Jacqueline Wilkie Michael Johnson Reza Katebi © Jacqueline Wilkie, Michael Johnson and Reza Katebi 2002 All rights reserved. No reproduction, copy or transmission of this publication may be made without written permission. No paragraph of this publication may be reproduced, copied or transmitted save with written permission or in accordance with the provisions of the Copyright, Designs and Patents Act 1988, or under the terms of any licence permitting limited copying issued by the Copyright Licensing Agency, 90 Tottenham Court Road, London W1P 0LP. Any person who does any unauthorised act in relation to this publication may be liable to criminal prosecution and civil claims for damages. The authors have asserted their right to be identified as the authors of this work in accordance with the Copyright, Designs and Patents Act 1988. First published 2002 by PALGRAVE Houndmills, Basingstoke, Hampshire RG21 6XS and 175 Fifth Avenue, New York, N. Y. 10010 Companies and representatives throughout the world PALGRAVE is the new global academic imprint of St. Martin’s Press LLC Scholarly and Reference Division and Palgrave Publishers Ltd (formerly Macmillan Press Ltd). ISBN 0–333–77129–X This book is printed on paper suitable for recycling and made from fully managed and sustained forest sources. A catalogue record for this book is available from the British Library. Typeset by Ian Kingston Editorial Services, Nottingham, UK 10 9 8 7 6 5 4 3 2 1 11 10 09 08 07 06 05 04 03 02 Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire To my husband, Patrick, for his continual supply of tea and understanding; to my daughters, Róisín and Erin, for not playing on mummy’s computer; and to my three-day-old son, Rory, who arrived just in time for this dedication. Jacqueline Wilkie For my mother and father – whose love and support have never failed me, and for my Glaswegian friend, Stanley. Michael Johnson To Raha and Imaon. Reza Katebi This page intentionally left blank Contents Dear Student xi 1 1 2 Introduction: Control engineering is a part of our life Wind turbine systems Wastewater treatment plant control Flight control systems Coordinate measuring machines Ship autopilot design Hot strip rolling mills in the steel industry Industrial heaters 3 4 6 8 10 11 14 Tools for the control engineer 16 How many ways of writing complex numbers are there? What is the complex exponential and how do I use it? I just want to know how to add, subtract, multiply and divide complex numbers. Is this easy? Control engineers talk about transfer functions. What is a transfer function? What are the magnitude or gain values of a complex number? How do I work out the phase of a complex number? I need to practise solving quadratic equations: are there some simple methods? Parameter dependent complex numbers! That sounds hard – what are they? How do I define a Laplace transform? What is the Laplace variable s and the s-plane? Where do the poles and zeros come from in a Laplace transform? How do I use transform tables? Oh dear, I need to work out Laplace transforms from first principles. How do I begin? The transforms get even harder: what are the exponential–trigonometric signals? When I multiply a signal by a constant, what happens to the Laplace transform? I need to transform a combinations of signals. How do I do this? What Laplace transform operations should I learn? Why is a differentiator like multiplying by s? How do we represent an integrator using Laplace transforms? 17 18 20 22 22 22 23 24 25 26 27 28 30 32 34 34 35 36 37 vi Contents I need to use Laplace