Control Engineering
An introduction with the use of Matlab
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About the book
Description
The book covers the basic aspects of linear single loop feedback control theory. Explanations of the mathematical concepts used in classical control such as root loci, frequency response and stability methods are explained by making use of MATLAB plots but omitting the detailed mathematics found in many textbooks. There is a chapter on PID control and two chapters provide brief coverage of state variable methods. The approach adopted allows more time to be devoted to controller design by different methods, to compare the results and also to examine the effects of plant parameter variations.
This free eBook can be read in combination with and in some cases instead of the following textbooks:
 Modern Control Engineering, by Katsuhiko Ogata
 Control Systems Engineering 6th edition, by Norman S Nise
 Modern Control Engineering 4th edition, by Katsuhiko Ogata
 Basic Control Systems Engineering 1st edition, by Paul H Lewis & Chang Yang
 Principles of Control Engineering 1st edition, by Fred White
 Modern Control Engineering 1st edition, by P N Paraskevopoulos
Preface
Preface to the second edition
It is almost four years since the first edition of this book so it seemed appropriate to reread it carefully again and make any suitable changes. Also during the intervening period I have added two further bookboon books one on ‘An Introduction to Nonlinearity in Control Systems’ and another very recently on ‘Control Engineering Problems with Solutions’. This later book contains worked examples and some problems with answers only, which cover the material in this book and ‘An Introduction to Nonlinearity in Control Systems’. It is hoped that the relevant chapters of ‘Control Engineering Problems with Solutions’ will help the reader gain a better understanding and deeper knowledge of the topics covered in this textbook.
Minor changes have been made to this second edition mainly with respect to a few changes in wording, but sadly despite repeated reading a few minor technical errors were found and corrected, for which I apologise. These were Figure 3.6 which had some incorrect markings and was not very clear due to the numbers chosen giving lines almost on top of each other. This has been corrected by choosing a different frequency for illustrating the frequency response calculation procedure. Further, some negative signs were omitted from equation (2.14), the units of H on page 50 were given incorrectly as were the subscripts on the a’s and a matrix in the material in section 10.5.1, page 131, on transforming to the controllable canonical form. Finally the cover page has been changed to contain a picture which is more relevant to the book.
Derek P Atherton
Brighton , June 2013.
Preface to the first edition
Control engineering courses have been given in universities for over fifty years. In fact it is just fifty years since I gave my first lectures on the subject. The basic theoretical topics taught in what is now often referred to as classical control have changed little over these years, but the tools which can be used to support theoretical analysis and the technologies used in control systems implementation have changed beyond recognition. I was lucky enough in the early days to have access to one of the first digital computers in a UK university, but programming was elementary, input was paper tape and output results, obtained often after a considerable delay, were just numbers on paper, which had to be laboriously plotted if one needed a graph. Simulations were done on analogue computers, which although having some nice features, had many deficiences. Today there are powerful digital simulation languages and specialised numerical software programs, which can be used on a desk top or lap top computer with excellent interaction and good graphical output. Although this book is not concerned with the technological implementation of control systems the technology has changed from components such as the vacuum tube, individual resistors and capacitors, and d.c commutator motors to integrated circuits, microprocessors, solid state power electronics and brushless machines. All of these are orders of magnitude cheaper, more robust, reliable and efficient.
The majority of students graduating from engineering courses in universities will go on to work in industry where employers, if the company is to survive, will provide their employees doing analytical control system design with computers with appropriate computational software. The role of the university lecturer should therefore be to teach courses in such a way that the student knows enough detail about the concepts used that he can see whether results obtained are plausible, whilst leaving the computer to do the detailed analytical calculations. This has the advantage that more realistic problems can be studied, comparisons can easily be made between the results produced by alternative design approaches and hopefully the student can learn more about control engineering than worrying about doing mathematics. Many students, without doubt, are ‘turned off’ control engineering because of the perceived mathematical content and whilst further study on the theoretical aspects is required for prospective research students, they will be a small proportion of the class in a first course on control engineering. There are difficulties in this approach, as I am strongly of the opinion that student’s weaknesses in algebra have been caused by them not having carried out traditional procedures in arithmetic due to the adoption of calculators. However, I’m also sure there is a ‘happy medium’ somewhere. The use of modern software with simulation facilities allows the student to practice the interesting philosophy about doing engineering put forward in the book ‘Think, Play, Do’ by Dodgson et al OUP,2005.
The material presented in this book has been set out with this philosophy in mind and it is hoped that it will enable the reader to obtain a sound knowledge of classical control system analytical design methods. Several software packages could have been used to support this approach but here MATLAB, which is the most widely used, has been employed. Sadly, however, if universities continue to use outdated examining methods where students are required to plot root locus, Nyquist diagrams etc. the reader may have to spend some additional time doing computations best done by a computer! Because I want to ‘get over’ ideas, understanding and concepts without detailed mathematics I have used words such as ‘it can be shown that’ to shorten some of the mathematical detail. This provides the reader interested in theory with the opportunity to do additional calculations.
The first chapter provides a brief introduction to feedback control and then has a section reviewing the contents of the book, which will therefore not be repeated here. I am indebted to my recent former students Ali Boz and Nusret Tan for providing me with some diagrams, assistance with computations, reading the text and doing some of the research which has provided information and results on some of the topics covered. For over forty years I have benefitted greatly from discussions with and input from many research students, who are too numerous to name here but have all helped to enrich the learning experience. Finally, I would like to acknowledge the efforts of my friend Dr Karl Jones in reading through the manuscript and providing me with constructive feedback. I trust that few errors remain in the text and I’d appreciate feedback from any reader who finds any or has any questions on the contents.
Derek P. Atherton
Brighton,
February 2009
Content
 Introduction
 What is Control Engineering?
 Contents of the Book
 References
 Mathematical Model Representations of Linear Dynamical Systems
 Introduction
 The Laplace Transform and Transfer Functions
 State space representations
 Mathematical Models in MATLAB
 Interconnecting Models in MATLAB
 Reference
 Transfer Functions and Their Responses
 Introduction
 Step Responses of Some Specific Transfer Functions
 Response to a Sinusoid
 Frequency Responses and Their Plotting
 Introduction
 Bode Diagram
 Nyquist Plot
 Nichols Plot
 The Basic Feedback Loop
 Introduction
 The Closed Loop
 System Specifications
 Stability
 More on Analysis of the Closed Loop System
 Introduction
 Time Delay
 The Root Locus
 Relative Stability
 M and N Circles
 Classical Controller Design
 Introduction
 Phase Lead Design
 Phase Lag Design
 PID Control
 References
 Parameter Optimisation for Fixed Controllers
 Introduction
 Some Simple Examples
 Standard Forms
 Control of an Unstable Plant
 Further Comments
 References
 Further Controller Design Considerations
 Introduction
 LagLead Compensation
 Speed Control
 Position Control
 A Transfer Function with Complex Poles
 The Effect of Parameter Variations
 References
 State Space Methods
 Introduction
 Solution of the State Equation
 A State Transformation
 State Representations of Transfer Functions
 State Transformations between Different Forms
 Evaluation of the State Transition Matrix
 Controllability and Observability
 Cascade Connection
 Some State Space Design Methods
 Introduction
 State Variable Feedback
 Linear Quadratic Regulator Problem
 State Variable Feedback for Standard Forms
 Transfer Function with Complex Poles