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.
1. Introduction
1.1 What is Control Engineering?
1.2 Contents of the Book
1.3 References
2. Mathematical Model Representations of Linear Dynamical Systems
2.1 Introduction
2.2 The Laplace Transform and Transfer Functions
2.3 State space representations
2.4 Mathematical Models in MATLAB
2.5 Interconnecting Models in MATLAB
2.6 Reference
3. Transfer Functions and Their Responses
3.1 Introduction
3.2 Step Responses of Some Specific Transfer Functions
3.3 Response to a Sinusoid
4. Frequency Responses and Their Plotting
4.1 Introduction
4.2 Bode Diagram
4.3 Nyquist Plot
4.4 Nichols Plot
5. The Basic Feedback Loop
5.1 Introduction
5.2 The Closed Loop
5.3 System Specifications
5.4 Stability
6. More on Analysis of the Closed Loop System
6.1 Introduction
6.2 Time Delay
6.3 The Root Locus
6.4 Relative Stability
6.5 M and N Circles
7. Classical Controller Design
7.1 Introduction
7.2 Phase Lead Design
7.3 Phase Lag Design
7.4 PID Control
7.5 References
8. Parameter Optimisation for Fixed Controllers
8.1 Introduction
8.2 Some Simple Examples
8.3 Standard Forms
8.4 Control of an Unstable Plant
8.5 Further Comments
8.6 References
9. Further Controller Design Considerations
9.1 Introduction
9.2 Lag-Lead Compensation
9.3 Speed Control
9.4 Position Control
9.5 A Transfer Function with Complex Poles
9.6 The Effect of Parameter Variations
9.7 References
10. State Space Methods
10.1 Introduction
10.2 Solution of the State Equation
10.3 A State Transformation
10.4 State Representations of Transfer Functions
10.5 State Transformations between Different Forms
10.6 Evaluation of the State Transition Matrix
10.7 Controllability and Observability
10.8 Cascade Connection
11. Some State Space Design Methods
11.1 Introduction
11.2 State Variable Feedback
11.3 Linear Quadratic Regulator Problem
11.4 State Variable Feedback for Standard Forms
11.5 Transfer Function with Complex Poles
About the Author
Professor Derek. P. Atherton
BEng, PhD, DSc, CEng, FIEE, FIEEE, HonFInstMC,
Derek Atherton studied at the universities of Sheffield ( BEng 1956)
and Manchester, obtaining a PhD in 1962 and DSc in 1975 from the latter.
He spent the period from 1962 to 1980 teaching and doing research in
Canada, first at McMaster University until 1964 and then at the
University of New Brunswick. Whilst in Canada he served on several
National Research Council committees including the Electrical
Engineering Grants Committee.
He took up the post of Professor of Control Engineering at the
University of Sussex in 1980 and is currently retired but has an office
at the university, gives some lectures, and has the title of Emeritus
Professor and Associate Tutor. He has been active with many professional
engineering bodies, serving as President of the Institute of
Measurement and Control in 1990, President of the IEEE Control Systems
Society in 1995, and as a member of the IFAC Council from 1990-96. He
was an Editor of the IEE Proceedings on Control Theory and Applications
(CTA) for several years until 2007 and was also formerly an editor for
the IEE Control Engineering Book Series. He has served EPSRC on
research panels and as an assessor for research grants for many years
and also served as a member of the Electrical Engineering Panel for the
Research Assessment Exercise in 1992.
His major research interests are in non-linear control theory,
computer aided control system design, simulation and target tracking. He
has written three books, is a co-author of two others [1-5] and has
published more than 350 papers in Journals and Conference Proceedings.
Professor Atherton has given invited lectures in many countries and
supervised over 30 Doctoral students.
1. Atherton D P,
Nonlinear Control Engineering: Describing Function Analysis and Design. London, Van Nostrand Reinhold, September 1975, 627 pages. (also abridged version) Atherton D P,
Nonlinear Control Engineering. Van Nostrand Reinhold, 1982, student edition, 470 pages
2. Atherton D P,
Stability of Nonlinear Systems. Research Studies Press, John Wiley,1981, 231 pages
3. Atherton, D.P. Control Engineering 2009 Bookboon publications at www.bookboon.com
4. Furuta K, Sano A and Atherton D P
State Variable Methods in Automatic Control. John Wiley, 1988, 212 pages.
5. Xue, D , Chen,Y and Atherton,D.P Linear Feedback Control;
Analysis and Design with MATLAB SIAM books, Philadelphia, USA, 2007, pp354.
Derek P. Atherton.
August 2010.
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