Control of continuous linear systems

356 Pages·2006·1.44 MB·English

by  Kaddour Najim

Control of Continuous Linear Systems
Control of Continuous
Linear Systems

Kaddour Najim
First published in Great Britain and the United States in 2006 by ISTE Ltd

Apart from any fair dealing for the purposes of research or private study, or criticism or
review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may
only be reproduced, stored or transmitted, in any form or by any means, with the prior
permission in writing of the publishers, or in the case of reprographic reproduction in
accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction
outside these terms should be sent to the publishers at the undermentioned address:
ISTE Ltd ISTE USA
6 Fitzroy Square 4308 Patrice Road
London W1T 5DX Newport Beach, CA 92663
UK USA
www.iste.co.uk
© ISTE Ltd, 2006
The rights of Kaddour Najim to be identified as the author of this work has been asserted by
them in accordance with the Copyright, Designs and Patents Act 1988.
Library of Congress Cataloging-in-Publication Data

Najim, K.
Control of continuous linear systems / Kaddour Najim.
p. cm.
Includes bibliographical references and index.
ISBN-13: 978-1-905209-12-5
ISBN-10: 1-905209-12-6
1. Linear systems--Automatic control--Mathematics. 2. Linear control systems. 3. Calculus,
Operational. I. Title.
TJ220.N35 2006
629.8'32--dc22
2006009140

British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 10: 1-905209-12-6
ISBN 13: 978-1-905209-12-5
Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire.
Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Chapter1.OnProcessModeling . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.2. Modelclassification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.2.1. Heatandmassbalances . . . . . . . . . . . . . . . . . . . . . . . . 18
1.2.2. Mechanicalsystems . . . . . . . . . . . . . . . . . . . . . . . . . . 39
1.2.3. Electricalsystems . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
1.3. Linearization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Chapter2.LaplaceTransformsandBlockDiagrams . . . . . . . . . . . . . 67
2.1. TheLaplacetransform. . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
2.2. Transferfunctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
2.3. Laplacetransformcalculations . . . . . . . . . . . . . . . . . . . . . . . 72
2.4. Differentialandintegralequations . . . . . . . . . . . . . . . . . . . . . 87
2.5. Blockdiagrams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
2.6. Feedbacksystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Chapter3.Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
3.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
3.2. Stepresponses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
3.3. Systemidentification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
3.4. Frequencyresponse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Chapter4.StabilityandtheRootLocus . . . . . . . . . . . . . . . . . . . . 205
4.1. Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
4.1.1. TheRouth–Hurwitzcriterion . . . . . . . . . . . . . . . . . . . . . 207
4.1.2. Revers’scriterion . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
5
6 ControlofContinuousLinearSystems
4.2. Therootlocus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
Chapter5.RegulationandPIDRegulators . . . . . . . . . . . . . . . . . . . 255
5.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
5.2. Directdesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
5.3. PIDtuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
A. OnTheoreticalAspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
A.1. TheDiracimpulse . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
A.1.1. Residencetime . . . . . . . . . . . . . . . . . . . . . . . . . . 310
A.2. Theunitstep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
A.3. TheRouth–Hurwitzcriterion . . . . . . . . . . . . . . . . . . . . . 313
A.4. TheNyquistcriterion . . . . . . . . . . . . . . . . . . . . . . . . . . 320
A.5. Therootlocus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
A.6. ComputationofintegralsoftheformJ . . . . . . . . . . . . . . . 335
2
A.7. Onnon-linearsystems . . . . . . . . . . . . . . . . . . . . . . . . . 336
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349
Control of Continuous Linear Systems
This page intentionally left blank
Control of Continuous
Linear Systems

Kaddour Najim
First published in Great Britain and the United States in 2006 by ISTE Ltd

Apart from any fair dealing for the purposes of research or private study, or criticism or
review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may
only be reproduced, stored or transmitted, in any form or by any means, with the prior
permission in writing of the publishers, or in the case of reprographic reproduction in
accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction
outside these terms should be sent to the publishers at the undermentioned address:
ISTE Ltd ISTE USA
6 Fitzroy Square 4308 Patrice Road
London W1T 5DX Newport Beach, CA 92663
UK USA
www.iste.co.uk
© ISTE Ltd, 2006
The rights of Kaddour Najim to be identified as the author of this work has been asserted by
them in accordance with the Copyright, Designs and Patents Act 1988.
Library of Congress Cataloging-in-Publication Data

Najim, K.
Control of continuous linear systems / Kaddour Najim.
p. cm.
Includes bibliographical references and index.
ISBN-13: 978-1-905209-12-5
ISBN-10: 1-905209-12-6
1. Linear systems--Automatic control--Mathematics. 2. Linear control systems. 3. Calculus,
Operational. I. Title.
TJ220.N35 2006
629.8'32--dc22
2006009140

British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 10: 1-905209-12-6
ISBN 13: 978-1-905209-12-5
Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire.