Using a "how to do it" approach with a strong emphasis on real-world design, this book provides comprehensive, single-source coverage of the full spectrum of control system design. Each of the book's 8 parts covers a specific area of control--ranging from signals and systems (Bode Diagrams, Root Locus, etc.), to SISO control (including PID and Fundamental Design Trade-offs) and MIMO systems (including Constraints, MPC, Decoupling, etc.). Features an abundance of real-world design examples drawn from the authors' direct experience, and many real-world case studies divided into Industrial case studies and Laboratory systems (several of which are supported by a virtual laboratory using Java Applets on the book's web page). All examples are supported by Matlab®. The Excitement of Control Engineering. Introduction to the Principles of Feedback. Modeling. Continuous Time Signals and Systems. Analysis of SISO Control Loops. Classical PID Control. Synthesis of SISO Controllers. Fundamental Limitations in SISO Control. Frequency Domain Design Limitations. Architectural Issues in SISO Control. Dealing with Constraints. Models for Sampled Data Systems. Digital Control. Hybrid Control. SISO Controller Parameterizations. Control Design Based on Optimization. Linear State Space Models. Synthesis via State Space Methods. Introduction to Nonlinear Control. Analysis of MIMO Control Loops. Exploiting SISO Techniques in MIMO Control. Design via Optimal Control Techniques. Model Predictive Control. Fundamental Limitations in MIMO Control. MIMO Controller Parameterizations. Decoupling. For anyone interested in Control System Design.
Goodwin (researcher in systems and control), Stefan Graebe (Schwechat refinery of OMV) and Mario Salgado (Universidad Tecnica Frederico Santa Maria) address the need to revitalize control education by providing a new approach to teaching control system design. They emphasize real-world design and cover essential aspects ranging from signals and systems (Bode diagrams, root locus, etc.) to SISO control (including PID and fundamental design tradeoffs), and MIMO systems (such as constraints, MPC, decoupling, and others). About 15 case studies range from distillation columns to satellite tracking. The accompanying CD-ROM contain MATLAB routines, PowerPoint lecture notes, and a Java Applet-driven virtual laboratory. Annotation c. Book News, Inc., Portland, OR (booknews.com)
GRAHAM GOODWIN has over 30 years of experience in the area of control engineering covering research, education and industry. He is the author of seven books, 500 papers and holds four patents. He was the foundation Chairman of a spin-off company and is currently Directory of a special research center dedicated to systems and control research.
STEFAN GRAEBE's career spans both academic and industrial positions. He was previously research coordinator in the Centre for Industrial Control Science at the University of Newcastle. He is currently head of the Department of Optimization and Automation for the Schwechat refinery of OMV—Austria.
MARIO SALGADO received a Maters degree in Control from Imperial College and a Ph.D. from the University of Newcastle. He is currently an academic in the Department of Electronics at the Universidad Tecnica Frederico Santa Maria, Valparaíso—Chile. His interests include signal processing and control systems design.
Control Engineering plays a fundamental role in modern technological systems. The benefits of improved control in industry can be immense. They include improved product quality, reduced energy consumption, minimization of waste material, increased safety levels, and reduction of pollution. A difficulty with the subject, however, is that some of the more advanced aspects depend on a sophisticated mathematical background. Arguably, mathematical systems theory is one of the most significant achievements of twentieth-century science, but its practical impact is only as important as the benefits it can bring. Thus, we include in this book a strong emphasis on design, ultimately striking a balance between theory and practice.
It was the authors' involvement in several industrial control-system design projects that provided part of the motivation to write this book. In a typical industrial problem, we found ourselves investigating fluid and thermal dynamics, experiencing the detrimental effects of nonconstant PLC scan rates, dealing with system integration and network communication protocols, building trust with plant operators, and investigating safe bumpless transfer schemes for testing tentative control designs on potentially dangerous plants. In short, we experienced the day-to-day excitement, frustration, set-backs, and progress in getting advanced control to contribute to a commercial company's bottom line. This is not an easy task. Success in this type of venture typically depends on the application of a wide range of multidisciplinary skills; however, it is rewarding and exciting work for those who do it.
One ofthe main aims of this book is to share this excitement with our readers. We hope to contribute to the development of skills and attitudes within readers and students that will better equip them to face the challenges of real-world design problems. The book is thus intended to contribute to the ongoing reform of the Control Engineering curriculum. This topic continues to receive considerable international attention as educators strive to convey the excitement and importance of control engineering. Indeed, entire issues of the IEEE Control Systems Magazine have been devoted to this theme.
Reforming the curriculum will not, however, be done by books alone. It will be done by people: students, teachers, researchers, practitioners, publication and grant reviewers, and by market pressures. Moreover, for these efforts to be efficient and sustainable, the control engineering community will need to communicate their experiences via a host of new books, laboratories, simulations, and web-based resources. Thus, there will be a need for several different and complementary approaches. In this context, the authors believe that this book will have been successful if it contributes, in some way, to the revitalization of interest by students in the exciting discipline of control engineering.
We stress that this is not a how-to book. On the contrary, we provide a comprehensive, yet condensed, presentation of rigorous control engineering. We employ, and thus require, mathematics as a means to model the process, analyze its properties under feedback, synthesize a controller with particular properties, and arrive at a design addressing the inherent trade-offs and constraints applicable to the problem.
In particular, we believe that success in control projects depends on two key ingredients: (i) having a comprehensive understanding of the process itself, gained by studying the relevant physics, chemistry, and so on; and (ii) by having mastery of the fundamental concepts of signals, systems, and feedback. The first ingredient typically occupies more than fifty per cent of the effort. It is an inescapable component of the complete design cycle; however, it is impractical for us to give full details of the processes to which control might be applied, because they cover chemical plants, electromechanical systems, robots, power generators, and so on. We thus emphasize the fundamental control engineering aspects that are common to all applications and we leave readers to complement this emphasis with process knowledge relevant to their particular problem. Thus, the book is principally aimed at the second ingredient of control engineering. Of course, we do give details of several real-world examples, so as to put the methods into a proper context.
The central theme of this book is continuous-time control; however, we also treat digital control in detail, because most modern control systems will usually be implemented on some form of computer hardware. This approach inevitably led to a book of larger volume than originally intended, but one with the advantage of providing a comprehensive treatment within an integrated framework. Naturally, there remain specialized topics that are not covered in the book; however, we trust that we provide a sufficiently strong foundation so that the reader can comfortably turn to the study of appropriate complementary literature. Goals
Thus, in writing this book we chose as our principal goals the following:
providing accessible treatment of rigorous material selected with applicability in mind;
giving early emphasis to design, including methods for dealing with fundamental trade-offs and constraints;
providing additional motivation through substantial interactive web-based support; and
demonstrating the relevance of the material through numerous industrial case studies.
Indeed, the material in the book is illustrated by numerous industrial case studies with which the authors have had direct involvement. Most of these case studies were carried out, in collaboration with industry, by the Centre for Integrated Dynamics and Control (CIDAC) (a Commonwealth Special Research Centre) at the University of Newcastle.
The projects that we have chosen to describe include the following:
satellite tracking
pH control
control of a continuous casting machine
sugar mill control
distillation column control
ammonia-synthesis plant control
zinc coating-mass estimation in a continuous-galvanizing line
BISRA gauge for thickness control in rolling mills
roll-eccentricity compensation in rolling mills
hold-up effect in reversing rolling mills
flatness control in steel rolling
vibration control
Design is a complex process, one that requires judgment and iteration. The design problem normally is incompletely specified, sometimes is ill-defined, and many times is without solution. A key element in design is an understanding of those factors that limit the achievable performance. This naturally leads to a viewpoint of control design that takes account of these fundamental limitations. This viewpoint is a recurring theme throughout the book.
Our objective is not to explore the full depth of mathematical completeness but instead to give enough detail so that a reader can begin applying the ideas as soon as possible. This approach is connected to our assumption that readers will have ready access to modern computational facilities, including the software package MATLAB-SIMULINK. This assumption allows us to put the emphasis on fundamental ideas rather than on the tools. Every chapter includes worked examples and problems for the reader. Overview of the Book
The book is divided into eight parts. A brief summary of each of the parts is given here.
Part I: The Elements
This part covers basic continuous-time signals and systems and would be suitable for an introductory course on this topic. Alternatively, it could be used to provide review material before starting the study of control in earnest.
Part II: SISO Control Essentials
This part deals with basic single-input single-output (SISO) control, including classical proportional, integral and derivative (PID) tuning. This section, together with Part I, covers the content of many of the existing curricula for basic control courses.
Part III: SISO Control Design
This part covers design issues in SISO Control. We consider many of these ideas to be crucial to achieving success in practical control problems. In particular, we believe that the chapter dealing with constraints should be mentioned, if at all possible, in all introductory courses. Also, feedforward and cascade structures, which are covered in this part, are very frequently employed in practice.
Part IV: Digital Computer Control
This part covers material essential to the understanding of digital control. We go beyond traditional treatments of this topic by studying inter-sample issues.
Part V: Advanced SISO Control
This part could be the basis of a second course on control at an undergraduate level. It is aimed at the introduction of ideas that flow through to multi-input multi-output (MIMO) systems later in the book.
Part VI: MIMO Control Essentials
This part gives the basics required for a junior-level graduate course on MIMO control. In particular, this part covers basic MIMO system theory. It also shows how one can exploit SISO methods in some MIMO design problems.
Part VII: MIMO Control Design
This part describes tools and ideas that can be used in industrial MIMO design. In particular, it includes linear quadratic optimal control theory and optimal filtering. These two topics have major significance in applications. We also include a chapter on Model Predictive Control. We believe this to be important material, because of the widespread use of this technique in industrial applications.
Part VIII: Advanced MIMO Control
This final part of the book could be left for private study. It is intended to test the reader's understanding of the other material by examining advanced issues. Alternatively, instructors could use this part to extend parts VI and VII in a more senior graduate course on MIMO Control. Using this Book
This is a comprehensive book on control system design that can be used in many different course patterns. If one adopts the book for an early course on control, then the unused material is excellent reference material for later use in practice or for review. If one uses the book for a later course, then the early material gives an excellent summary of the basic building blocks on which the subject rests.
The book can be used for many different course patterns. Some suggested patterns are outlined as follows:
(i) Signals and Systems
This would be taught from Part I of the book.
(ii) Basic Control Theory
This would typically be taught for Part II of the book, together with some material for Part I (depending on the student's prior exposure to signals and systems) and some material from Part III. In particular, the chapter on design limitations (Chapter 8) requires only elementary knowledge of Laplace Transforms and gives students an understanding of those issues which limit achievable performance. This is an extremely important ingredient in all real-world control design problems. Also, Chapter 11 which deals with constraints is very important in practice. Finally, the ideas of feedforward and cascade architectures that are covered in Chapter 10 are central to solving real-world design problems.
(iii) Digital Control
This can be taught from Part IV. Indeed, we feel our treatment here is better focused on applications than many of the traditional treatments because of the emphasis we place on intersample behavior. In the various courses taught by the authors of this book some of the material on digital control is typically included in the Basic Control Theory Course. This is possible because the students are well prepared having taken a Signals and System course prior to the control course.
(iv) Second Course on Control
A second course on control typically includes an introduction to state space design, observers, and state-variable feedback. This material can be taught from Parts V to VII of the book. Part V is relatively straightforward and is intended to bridge the gap from single-input single-output systems (which are principally the focus of Parts I to IV) and multi-input multi-output systems (which are principally covered in Parts VI, VII, and VIII). We consider Chapter 22 on optimal control and filtering to be very important and have included in this chapter many real world design case studies. Also, Chapter 23 on Model Predictive Control is important as this technique is widely used in industrial control.
Two of the authors (Goodwin and Salgado) have taught undergraduate and postgraduate courses of the type mentioned above, using draft versions of this book, in Australia and South America.
Website
We have created a comprehensive website to support the book. This website contains the following:
Full Appendices (So that this material can be read at the same time as the printed text in the book.)
Full Matlab Support (This can be downloaded and used to reproduce all of the designs in the book.)
Interactive Java Laboratories (These illustrate the material in the book but can also be used for fun interaction.)
Selected Solutions for Problems (This allows students to see how certain key problems can be solved. Of course instructors adopting the book will be sent a copy of the comprehensive solutions manual that covers every problem set in the book.)
On-Line Forum (So that topics of general interest to control-system design can be raised and discussed.)
An Errata Section (This is used to give details of any errors occurring in the book.)
Extensive PowerPoint Slides (Approximately 2,500 slides are available for use with the book.)
We see the use of this material as follows: For the Instructor
We believe that the Matlab support and PowerPoint slides should be particularly helpful to an instructor. For example, it would be possible to teach the course entirely using the resources provided. Also, we have found that students enjoy using the Virtual Laboratories. These can be displayed in the classroom as part of a lecture or given to students to enhance their understanding of the material. For the Student
We believe that the PowerPoint slides are an excellent and easily understood summary of the book which by-passes all unnecessary technicalities. Even if your instructor does not use these slides in his/her presentations, we consider that they are an excellent summary for study purposes. If you print them out and annotate them, then remembering the material should be easy. Also, students should enjoy the Java Applets. If you can understand the case studies covered by these applets then you will be well on the way to understanding this exciting subject.
The website can be accessed at either of the following URLs: http://www.prenhall.com/goodwin and http://csd.newcastle.edu.au/control/
Alternatively, see the authors' home pages for a link. Also note that the website is under continuous development, so the resources provided will continue to grow and evolve as time proceeds.
Newcastle, Australia
Valparaiso, Chile
Vienna, Austria
(NOTE: Most chapters begin with a Preview and conclude with Summary, Further Reading, and Problems for the Reader.)
I. THE ELEMENTS.
1. The Excitement of Control Engineering.
Motivation for Control Engineering. Historical Periods of Control Theory. Types of Control-System Design. System Integration.
2. Introduction to the Principles of Feedback.
The Principal Goal of Control. A Motivating Industrial Example. Definition of the Problem. Prototype Solution to the Control Problem via Inversion. High-Gain Feedback and Inversion. From Open- to Closed-Loop Architectures. Trade-Offs Involved in Choosing the Feedback Gain. Measurements.
3. Modeling.
The Raison d'être for Models. Model Complexity. Building Models. Model Structures. State Space Models. Solution of Continuous-Time State Space Models. High-Order Differential and Difference-Equation Models. Modeling Errors. Linearization. Case Studies.
4. Continuous-Time Signals and Systems.
Linear Continuous-Time Models. Laplace Transforms. Laplace Transform. Properties and Examples. Transfer Functions. Stability of Transfer Functions. Impulse and Step Responses of Continuous-Time Linear Systems. Poles, Zeros, and Time Responses. Frequency Response. Fourier Transform. Models Frequently Encountered. Modeling Errors for Linear Systems. Bounds for Modeling Errors.
II. SISO CONTROL ESSENTIALS.
5. Analysis of SISO Control Loops.
Feedback Structures. Nominal Sensitivity Functions. Closed-Loop Stability Based on the Characteristic Polynomial. Stability and Polynomial Analysis. Root Locus (RL). Nominal Stability Using Frequency Response. Relative Stability: Stability Margins and Sensitivity Peaks. Robustness.
Polynomial Approach. PI and PID Synthesis Revisited by Using Pole Assignment. Smith Predictor.
III. SISO CONTROL DESIGN.
8. Fundamental Limitations in SISO Control.
Sensors. Actuators. Disturbances. Model-Error Limitations. Structural Limitations. An Industrial Application (Hold-Up Effect in Reversing Mill). Remedies. Design Homogeneity, Revisited.
9. Frequency-Domain Design Limitations.
Bode's Integral Constraints on Sensitivity. Integral Constraints on Complementary Sensitivity. Poisson Integral Constraint on Sensitivity. Poisson Integral Constraint on Complementary Sensitivity. Example of Design Trade-Offs.
10. Architectural Issues in SISO Control.
Models for Deterministic Disturbances and References. Internal Model Principle for Disturbances. Internal Model Principle for Reference Tracking. Feedforward. Industrial Applications of Feedforward Control. Cascade Control.
11. Dealing with Constraints.
Wind-Up. Anti-Wind-Up Scheme. State Saturation. Introduction to Model Predictive Control.
IV. DIGITAL COMPUTER CONTROL.
12. Models for Sampled-Data Systems.
Sampling. Signal Reconstruction. Linear Discrete-Time Models. The Shift Operator. Z-Transform. Discrete Transfer Functions. Discrete Delta-Domain Models. Discrete Delta-Transform. Discrete Transfer Functions (Delta Form). Transfer Functions and Impulse Responses. Discrete System Stability. Discrete Models for Sampled Continuous Systems. Using Continuous State Space Models. Frequency Response of Sampled-Data Systems.
13. Digital Control.
Discrete-Time Sensitivity Functions. Zeros of Sample-Data Systems. Is a Dedicated Digital Theory Really Necessary? Approximate Continuous Designs. At-Sample Digital Design. Internal Model Principle for Digital Control. Fundamental Performance Limitations.
14. Hybrid Control.
Hybrid Analysis. Models for Hybrid Control Systems. Analysis of Intersample Behavior. Repetitive Control Revisited. Poisson Summation Formula.
V. ADVANCED SISO CONTROL.
15. SISO Controller Parameterizations.
Open-Loop Inversion Revisited. Affine Parameterization: The Stable Case. PID Synthesis by Using the Affine Parameterization. Affine Parameterization for Systems Having Time Delays. Undesirable Closed-Loop Poles. Affine Parameterization: The Unstable Open-Loop Case. Discrete-Time Systems.
16. Control Design Based on Optimization.
Optimal Q (Affine) Synthesis. Robust Control Design with Confidence Bounds. Cheap Control Fundamental Limitations. Frequency-Domain Limitations Revisited.
17. Linear State Space Models.
Linear Continuous-Time State Space Models. Similarity Transformations. Transfer Functions Revisited. From Transfer Function to State Space Representation. Controllability and Stabilizability. Observability and Detectability. Canonical Decomposition. Pole-Zero Cancellation and System Properties.
18. Synthesis via State Space Methods.
Pole Assignment by State Feedback. Observers. Combining State Feedback with an Observer. Transfer-Function Interpretations. Reinterpretation of the Affine Parameterization of All Stabilizing Controllers. State Space Interpretation of Internal Model Principle. Trade-Offs in State Feedback and Observers. Dealing with Input Constraints in the Context of State-Estimate Feedback.
19. Introduction to Nonlinear Control.
Linear Control of a Nonlinear Plant. Switched Linear Controllers. Control of Systems with Smooth Nonlinearities. Static Input Nonlinearities. Smooth Dynamic Nonlineartiies for Stable and Stably Invertible Models. Disturbance Issues in Nonlinear Control. More General Plants with Smooth Nonlinearities. Nonsmooth Nonlinearities. Stability of Nonlinear Systems. Generalized Feedback Linearization for Nonstability-Invertible Plants.
VI. MIMO CONTROL ESSENTIALS.
20. Analysis of MIMO Control Loops.
Motivational Examples. Models for Multivariable Systems. The Basic MIMO Control Loop. Closed-Loop Stability. Steady-State Response for Step Inputs. Frequency-Domain Analysis. Robustness Issues.
21. Exploiting SISO Techniques in MIMO Control.
Completely Decentralized Control. Pairing of Inputs and Outputs. Robustness Issues in Decentralized Control. Feedforward Action in Decentralized Control. Converting MIMO Problems to SISO Problems. Industrial Case Study (Strip Flatness Control).
VII. MIMO CONTROL DESIGN.
22. Design via Optimal Control Techniques.
State-Estimate Feedback. Dynamic Programming and Optimal Control. The Linear Quadratic Regulator (LQR). Properties of the Linear Quadratic Optimal Regulator. Model Matching Based on Linear Quadratic Optimal Regulators. Discrete-Time Optimal Regulators. Connections to Pole Assignment. Observer Design. Linear Optimal Filters. State-Estimate Feedback. Transfer-Function Interpretation. Achieving Integral Action in LQR Synthesis. Industrial Applications.
23. Model Predictive Control.
Anti-Wind-Up Revisited. What Is Model Predictive Control? Stability. Linear Models with Quadratic Cost Function. State Estimation and Disturbance Prediction. Rudder Roll Stabilization of Ships.
24. Fundamental Limitations in MIMO Control.
Closed-Loop Transfer Function. MIMO Internal Model Principle. The Cost of the Internal Model Principle. RHP Poles and Zeros. Time-Domain Constraints. Poisson Integral Constraints on MIMO Complementary Sensitivity. Poisson Integral Constraints on MIMO Sensitivity. Interpretation. An Industrial Application: Sugar Mill. Nonsquare Systems. Discrete-Time Systems.
VIII. ADVANCED MIMO CONTROL.
25. MIMO Controller Parameterizations.
Affine Parameterization: Stable MIMO Plants. Achieved Sensitivities. Dealing with Model Relative Degree. Dealing with NMP Zeros. Affine Parameterization: Unstable MIMO Plants. State Space Implementation.
26. Decoupling.
Stable Systems. Pre- and PostDiagonalization. Unstable Systems. Zeros of Decoupled and Partially Decoupled Systems. Frequency-Domain Constraints for Dynamically Decouple Systems. The Cost of Decoupling. Input Saturation. MIMO Anti-Wind-Up Mechanism.
APPENDICES.
Appendix A: Notation, Symbols, and Acronyms.
Appendix B: Smith-McMillan Forms.
Polynomial Matrices. Smith Form for Polynomial Matrices. Smith-McMillan Form for Rational Matrices. Poles and Zeros. Matrix Fraction Descriptions (MFD).
Appendix C: Results from Analytic Function Theory.
Independence of Path. Simply Connected Domains. Functions of a Complex Variable. Derivatives and Differentials. Analytic Functions. Integrals Revisited. Poisson and Jensen Integral Formulas. Application of the Poisson-Jensen Formula to Certain Rational Functions. Bode's Theorems.
Appendix D: Properties of Continuous-Time Riccati Equations.
Solutions of the CTDRE. Solutions of the CTARE. The Stabilizing Solution of the CTARE. Convergence of Solutions of the CTARE to the Stabilizing Solution of the CTARE. Duality between Linear Quadratic Regulator and Optimal Linear Filter.
Control Engineering plays a fundamental role in modern technological systems. The benefits of improved control in industry can be immense. They include improved product quality, reduced energy consumption, minimization of waste material, increased safety levels, and reduction of pollution. A difficulty with the subject, however, is that some of the more advanced aspects depend on a sophisticated mathematical background. Arguably, mathematical systems theory is one of the most significant achievements of twentieth-century science, but its practical impact is only as important as the benefits it can bring. Thus, we include in this book a strong emphasis on design, ultimately striking a balance between theory and practice.
It was the authors' involvement in several industrial control-system design projects that provided part of the motivation to write this book. In a typical industrial problem, we found ourselves investigating fluid and thermal dynamics, experiencing the detrimental effects of nonconstant PLC scan rates, dealing with system integration and network communication protocols, building trust with plant operators, and investigating safe bumpless transfer schemes for testing tentative control designs on potentially dangerous plants. In short, we experienced the day-to-day excitement, frustration, set-backs, and progress in getting advanced control to contribute to a commercial company's bottom line. This is not an easy task. Success in this type of venture typically depends on the application of a wide range of multidisciplinary skills; however, it is rewarding and exciting work for those who do it.
One of the main aims of this book is to share this excitement with our readers. We hope to contribute to the development of skills and attitudes within readers and students that will better equip them to face the challenges of real-world design problems. The book is thus intended to contribute to the ongoing reform of the Control Engineering curriculum. This topic continues to receive considerable international attention as educators strive to convey the excitement and importance of control engineering. Indeed, entire issues of the IEEE Control Systems Magazine have been devoted to this theme.
Reforming the curriculum will not, however, be done by books alone. It will be done by people: students, teachers, researchers, practitioners, publication and grant reviewers, and by market pressures. Moreover, for these efforts to be efficient and sustainable, the control engineering community will need to communicate their experiences via a host of new books, laboratories, simulations, and web-based resources. Thus, there will be a need for several different and complementary approaches. In this context, the authors believe that this book will have been successful if it contributes, in some way, to the revitalization of interest by students in the exciting discipline of control engineering.
We stress that this is not a how-to book. On the contrary, we provide a comprehensive, yet condensed, presentation of rigorous control engineering. We employ, and thus require, mathematics as a means to model the process, analyze its properties under feedback, synthesize a controller with particular properties, and arrive at a design addressing the inherent trade-offs and constraints applicable to the problem.
In particular, we believe that success in control projects depends on two key ingredients: (i) having a comprehensive understanding of the process itself, gained by studying the relevant physics, chemistry, and so on; and (ii) by having mastery of the fundamental concepts of signals, systems, and feedback. The first ingredient typically occupies more than fifty per cent of the effort. It is an inescapable component of the complete design cycle; however, it is impractical for us to give full details of the processes to which control might be applied, because they cover chemical plants, electromechanical systems, robots, power generators, and so on. We thus emphasize the fundamental control engineering aspects that are common to all applications and we leave readers to complement this emphasis with process knowledge relevant to their particular problem. Thus, the book is principally aimed at the second ingredient of control engineering. Of course, we do give details of several real-world examples, so as to put the methods into a proper context.
The central theme of this book is continuous-time control; however, we also treat digital control in detail, because most modern control systems will usually be implemented on some form of computer hardware. This approach inevitably led to a book of larger volume than originally intended, but one with the advantage of providing a comprehensive treatment within an integrated framework. Naturally, there remain specialized topics that are not covered in the book; however, we trust that we provide a sufficiently strong foundation so that the reader can comfortably turn to the study of appropriate complementary literature.
Goals
Thus, in writing this book we chose as our principal goals the following:
providing accessible treatment of rigorous material selected with applicability in mind;
giving early emphasis to design, including methods for dealing with fundamental trade-offs and constraints;
providing additional motivation through substantial interactive web-based support; and
demonstrating the relevance of the material through numerous industrial case studies.
Indeed, the material in the book is illustrated by numerous industrial case studies with which the authors have had direct involvement. Most of these case studies were carried out, in collaboration with industry, by the Centre for Integrated Dynamics and Control (CIDAC) (a Commonwealth Special Research Centre) at the University of Newcastle.
The projects that we have chosen to describe include the following:
satellite tracking
pH control
control of a continuous casting machine
sugar mill control
distillation column control
ammonia-synthesis plant control
zinc coating-mass estimation in a continuous-galvanizing line
BISRA gauge for thickness control in rolling mills
roll-eccentricity compensation in rolling mills
hold-up effect in reversing rolling mills
flatness control in steel rolling
vibration control
Design is a complex process, one that requires judgment and iteration. The design problem normally is incompletely specified, sometimes is ill-defined, and many times is without solution. A key element in design is an understanding of those factors that limit the achievable performance. This naturally leads to a viewpoint of control design that takes account of these fundamental limitations. This viewpoint is a recurring theme throughout the book.
Our objective is not to explore the full depth of mathematical completeness but instead to give enough detail so that a reader can begin applying the ideas as soon as possible. This approach is connected to our assumption that readers will have ready access to modern computational facilities, including the software package MATLAB-SIMULINK. This assumption allows us to put the emphasis on fundamental ideas rather than on the tools. Every chapter includes worked examples and problems for the reader.
Overview of the Book
The book is divided into eight parts. A brief summary of each of the parts is given here.
Part I: The Elements
This part covers basic continuous-time signals and systems and would be suitable for an introductory course on this topic. Alternatively, it could be used to provide review material before starting the study of control in earnest.
Part II: SISO Control Essentials
This part deals with basic single-input single-output (SISO) control, including classical proportional, integral and derivative (PID) tuning. This section, together with Part I, covers the content of many of the existing curricula for basic control courses.
Part III: SISO Control Design
This part covers design issues in SISO Control. We consider many of these ideas to be crucial to achieving success in practical control problems. In particular, we believe that the chapter dealing with constraints should be mentioned, if at all possible, in all introductory courses. Also, feedforward and cascade structures, which are covered in this part, are very frequently employed in practice.
Part IV: Digital Computer Control
This part covers material essential to the understanding of digital control. We go beyond traditional treatments of this topic by studying inter-sample issues.
Part V: Advanced SISO Control
This part could be the basis of a second course on control at an undergraduate level. It is aimed at the introduction of ideas that flow through to multi-input multi-output (MIMO) systems later in the book.
Part VI: MIMO Control Essentials
This part gives the basics required for a junior-level graduate course on MIMO control. In particular, this part covers basic MIMO system theory. It also shows how one can exploit SISO methods in some MIMO design problems.
Part VII: MIMO Control Design
This part describes tools and ideas that can be used in industrial MIMO design. In particular, it includes linear quadratic optimal control theory and optimal filtering. These two topics have major significance in applications. We also include a chapter on Model Predictive Control. We believe this to be important material, because of the widespread use of this technique in industrial applications.
Part VIII: Advanced MIMO Control
This final part of the book could be left for private study. It is intended to test the reader's understanding of the other material by examining advanced issues. Alternatively, instructors could use this part to extend parts VI and VII in a more senior graduate course on MIMO Control.
Using this Book
This is a comprehensive book on control system design that can be used in many different course patterns. If one adopts the book for an early course on control, then the unused material is excellent reference material for later use in practice or for review. If one uses the book for a later course, then the early material gives an excellent summary of the basic building blocks on which the subject rests.
The book can be used for many different course patterns. Some suggested patterns are outlined as follows:
(i) Signals and Systems
This would be taught from Part I of the book.
(ii) Basic Control Theory
This would typically be taught for Part II of the book, together with some material for Part I (depending on the student's prior exposure to signals and systems) and some material from Part III. In particular, the chapter on design limitations (Chapter 8) requires only elementary knowledge of Laplace Transforms and gives students an understanding of those issues which limit achievable performance. This is an extremely important ingredient in all real-world control design problems. Also, Chapter 11 which deals with constraints is very important in practice. Finally, the ideas of feedforward and cascade architectures that are covered in Chapter 10 are central to solving real-world design problems.
(iii) Digital Control
This can be taught from Part IV. Indeed, we feel our treatment here is better focused on applications than many of the traditional treatments because of the emphasis we place on intersample behavior. In the various courses taught by the authors of this book some of the material on digital control is typically included in the Basic Control Theory Course. This is possible because the students are well prepared having taken a Signals and System course prior to the control course.
(iv) Second Course on Control
A second course on control typically includes an introduction to state space design, observers, and state-variable feedback. This material can be taught from Parts V to VII of the book. Part V is relatively straightforward and is intended to bridge the gap from single-input single-output systems (which are principally the focus of Parts I to IV) and multi-input multi-output systems (which are principally covered in Parts VI, VII, and VIII). We consider Chapter 22 on optimal control and filtering to be very important and have included in this chapter many real world design case studies. Also, Chapter 23 on Model Predictive Control is important as this technique is widely used in industrial control.
Two of the authors (Goodwin and Salgado) have taught undergraduate and postgraduate courses of the type mentioned above, using draft versions of this book, in Australia and South America.
Website
We have created a comprehensive website to support the book. This website contains the following:
Full Appendices (So that this material can be read at the same time as the printed text in the book.)
Full Matlab Support (This can be downloaded and used to reproduce all of the designs in the book.)
Interactive Java Laboratories (These illustrate the material in the book but can also be used for fun interaction.)
Selected Solutions for Problems (This allows students to see how certain key problems can be solved. Of course instructors adopting the book will be sent a copy of the comprehensive solutions manual that covers every problem set in the book.)
On-Line Forum (So that topics of general interest to control-system design can be raised and discussed.)
An Errata Section (This is used to give details of any errors occurring in the book.)
Extensive PowerPoint Slides (Approximately 2,500 slides are available for use with the book.)
We see the use of this material as follows:
For the Instructor
We believe that the Matlab support and PowerPoint slides should be particularly helpful to an instructor. For example, it would be possible to teach the course entirely using the resources provided. Also, we have found that students enjoy using the Virtual Laboratories. These can be displayed in the classroom as part of a lecture or given to students to enhance their understanding of the material.
For the Student
We believe that the PowerPoint slides are an excellent and easily understood summary of the book which by-passes all unnecessary technicalities. Even if your instructor does not use these slides in his/her presentations, we consider that they are an excellent summary for study purposes. If you print them out and annotate them, then remembering the material should be easy. Also, students should enjoy the Java Applets. If you can understand the case studies covered by these applets then you will be well on the way to understanding this exciting subject.
The website can be accessed at either of the following URLs: http://www.prenhall.com/goodwin and http://csd.newcastle.edu.au/control/
Alternatively, see the authors' home pages for a link. Also note that the website is under continuous development, so the resources provided will continue to grow and evolve as time proceeds.
Newcastle, Australia
Valparaiso, Chile
Vienna, Austria
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More About This Textbook
Overview
Using a "how to do it" approach with a strong emphasis on real-world design, this book provides comprehensive, single-source coverage of the full spectrum of control system design. Each of the book's 8 parts covers a specific area of control--ranging from signals and systems (Bode Diagrams, Root Locus, etc.), to SISO control (including PID and Fundamental Design Trade-offs) and MIMO systems (including Constraints, MPC, Decoupling, etc.). Features an abundance of real-world design examples drawn from the authors' direct experience, and many real-world case studies divided into Industrial case studies and Laboratory systems (several of which are supported by a virtual laboratory using Java Applets on the book's web page). All examples are supported by Matlab®. The Excitement of Control Engineering. Introduction to the Principles of Feedback. Modeling. Continuous Time Signals and Systems. Analysis of SISO Control Loops. Classical PID Control. Synthesis of SISO Controllers. Fundamental Limitations in SISO Control. Frequency Domain Design Limitations. Architectural Issues in SISO Control. Dealing with Constraints. Models for Sampled Data Systems. Digital Control. Hybrid Control. SISO Controller Parameterizations. Control Design Based on Optimization. Linear State Space Models. Synthesis via State Space Methods. Introduction to Nonlinear Control. Analysis of MIMO Control Loops. Exploiting SISO Techniques in MIMO Control. Design via Optimal Control Techniques. Model Predictive Control. Fundamental Limitations in MIMO Control. MIMO Controller Parameterizations. Decoupling. For anyone interested in Control System Design.
Editorial Reviews
Booknews
Goodwin (researcher in systems and control), Stefan Graebe (Schwechat refinery of OMV) and Mario Salgado (Universidad Tecnica Frederico Santa Maria) address the need to revitalize control education by providing a new approach to teaching control system design. They emphasize real-world design and cover essential aspects ranging from signals and systems (Bode diagrams, root locus, etc.) to SISO control (including PID and fundamental design tradeoffs), and MIMO systems (such as constraints, MPC, decoupling, and others). About 15 case studies range from distillation columns to satellite tracking. The accompanying CD-ROM contain MATLAB routines, PowerPoint lecture notes, and a Java Applet-driven virtual laboratory. Annotation c. Book News, Inc., Portland, OR (booknews.com)Product Details
Related Subjects
Meet the Author
GRAHAM GOODWIN has over 30 years of experience in the area of control engineering covering research, education and industry. He is the author of seven books, 500 papers and holds four patents. He was the foundation Chairman of a spin-off company and is currently Directory of a special research center dedicated to systems and control research.
STEFAN GRAEBE's career spans both academic and industrial positions. He was previously research coordinator in the Centre for Industrial Control Science at the University of Newcastle. He is currently head of the Department of Optimization and Automation for the Schwechat refinery of OMV—Austria.
MARIO SALGADO received a Maters degree in Control from Imperial College and a Ph.D. from the University of Newcastle. He is currently an academic in the Department of Electronics at the Universidad Tecnica Frederico Santa Maria, Valparaíso—Chile. His interests include signal processing and control systems design.
Read an Excerpt
PREFACE Introduction to Control Engineering
Control Engineering plays a fundamental role in modern technological systems. The benefits of improved control in industry can be immense. They include improved product quality, reduced energy consumption, minimization of waste material, increased safety levels, and reduction of pollution. A difficulty with the subject, however, is that some of the more advanced aspects depend on a sophisticated mathematical background. Arguably, mathematical systems theory is one of the most significant achievements of twentieth-century science, but its practical impact is only as important as the benefits it can bring. Thus, we include in this book a strong emphasis on design, ultimately striking a balance between theory and practice.
It was the authors' involvement in several industrial control-system design projects that provided part of the motivation to write this book. In a typical industrial problem, we found ourselves investigating fluid and thermal dynamics, experiencing the detrimental effects of nonconstant PLC scan rates, dealing with system integration and network communication protocols, building trust with plant operators, and investigating safe bumpless transfer schemes for testing tentative control designs on potentially dangerous plants. In short, we experienced the day-to-day excitement, frustration, set-backs, and progress in getting advanced control to contribute to a commercial company's bottom line. This is not an easy task. Success in this type of venture typically depends on the application of a wide range of multidisciplinary skills; however, it is rewarding and exciting work for those who do it.
One ofthe main aims of this book is to share this excitement with our readers. We hope to contribute to the development of skills and attitudes within readers and students that will better equip them to face the challenges of real-world design problems. The book is thus intended to contribute to the ongoing reform of the Control Engineering curriculum. This topic continues to receive considerable international attention as educators strive to convey the excitement and importance of control engineering. Indeed, entire issues of the IEEE Control Systems Magazine have been devoted to this theme.
Reforming the curriculum will not, however, be done by books alone. It will be done by people: students, teachers, researchers, practitioners, publication and grant reviewers, and by market pressures. Moreover, for these efforts to be efficient and sustainable, the control engineering community will need to communicate their experiences via a host of new books, laboratories, simulations, and web-based resources. Thus, there will be a need for several different and complementary approaches. In this context, the authors believe that this book will have been successful if it contributes, in some way, to the revitalization of interest by students in the exciting discipline of control engineering.
We stress that this is not a how-to book. On the contrary, we provide a comprehensive, yet condensed, presentation of rigorous control engineering. We employ, and thus require, mathematics as a means to model the process, analyze its properties under feedback, synthesize a controller with particular properties, and arrive at a design addressing the inherent trade-offs and constraints applicable to the problem.
In particular, we believe that success in control projects depends on two key ingredients: (i) having a comprehensive understanding of the process itself, gained by studying the relevant physics, chemistry, and so on; and (ii) by having mastery of the fundamental concepts of signals, systems, and feedback. The first ingredient typically occupies more than fifty per cent of the effort. It is an inescapable component of the complete design cycle; however, it is impractical for us to give full details of the processes to which control might be applied, because they cover chemical plants, electromechanical systems, robots, power generators, and so on. We thus emphasize the fundamental control engineering aspects that are common to all applications and we leave readers to complement this emphasis with process knowledge relevant to their particular problem. Thus, the book is principally aimed at the second ingredient of control engineering. Of course, we do give details of several real-world examples, so as to put the methods into a proper context.
The central theme of this book is continuous-time control; however, we also treat digital control in detail, because most modern control systems will usually be implemented on some form of computer hardware. This approach inevitably led to a book of larger volume than originally intended, but one with the advantage of providing a comprehensive treatment within an integrated framework. Naturally, there remain specialized topics that are not covered in the book; however, we trust that we provide a sufficiently strong foundation so that the reader can comfortably turn to the study of appropriate complementary literature. Goals
Thus, in writing this book we chose as our principal goals the following:
Indeed, the material in the book is illustrated by numerous industrial case studies with which the authors have had direct involvement. Most of these case studies were carried out, in collaboration with industry, by the Centre for Integrated Dynamics and Control (CIDAC) (a Commonwealth Special Research Centre) at the University of Newcastle.
The projects that we have chosen to describe include the following:
Design is a complex process, one that requires judgment and iteration. The design problem normally is incompletely specified, sometimes is ill-defined, and many times is without solution. A key element in design is an understanding of those factors that limit the achievable performance. This naturally leads to a viewpoint of control design that takes account of these fundamental limitations. This viewpoint is a recurring theme throughout the book.
Our objective is not to explore the full depth of mathematical completeness but instead to give enough detail so that a reader can begin applying the ideas as soon as possible. This approach is connected to our assumption that readers will have ready access to modern computational facilities, including the software package MATLAB-SIMULINK. This assumption allows us to put the emphasis on fundamental ideas rather than on the tools. Every chapter includes worked examples and problems for the reader. Overview of the Book
The book is divided into eight parts. A brief summary of each of the parts is given here.
Part I: The Elements
This part covers basic continuous-time signals and systems and would be suitable for an introductory course on this topic. Alternatively, it could be used to provide review material before starting the study of control in earnest.
Part II: SISO Control Essentials
This part deals with basic single-input single-output (SISO) control, including classical proportional, integral and derivative (PID) tuning. This section, together with Part I, covers the content of many of the existing curricula for basic control courses.
Part III: SISO Control Design
This part covers design issues in SISO Control. We consider many of these ideas to be crucial to achieving success in practical control problems. In particular, we believe that the chapter dealing with constraints should be mentioned, if at all possible, in all introductory courses. Also, feedforward and cascade structures, which are covered in this part, are very frequently employed in practice.
Part IV: Digital Computer Control
This part covers material essential to the understanding of digital control. We go beyond traditional treatments of this topic by studying inter-sample issues.
Part V: Advanced SISO Control
This part could be the basis of a second course on control at an undergraduate level. It is aimed at the introduction of ideas that flow through to multi-input multi-output (MIMO) systems later in the book.
Part VI: MIMO Control Essentials
This part gives the basics required for a junior-level graduate course on MIMO control. In particular, this part covers basic MIMO system theory. It also shows how one can exploit SISO methods in some MIMO design problems.
Part VII: MIMO Control Design
This part describes tools and ideas that can be used in industrial MIMO design. In particular, it includes linear quadratic optimal control theory and optimal filtering. These two topics have major significance in applications. We also include a chapter on Model Predictive Control. We believe this to be important material, because of the widespread use of this technique in industrial applications.
Part VIII: Advanced MIMO Control
This final part of the book could be left for private study. It is intended to test the reader's understanding of the other material by examining advanced issues. Alternatively, instructors could use this part to extend parts VI and VII in a more senior graduate course on MIMO Control. Using this Book
This is a comprehensive book on control system design that can be used in many different course patterns. If one adopts the book for an early course on control, then the unused material is excellent reference material for later use in practice or for review. If one uses the book for a later course, then the early material gives an excellent summary of the basic building blocks on which the subject rests.
The book can be used for many different course patterns. Some suggested patterns are outlined as follows:
This would be taught from Part I of the book.
This would typically be taught for Part II of the book, together with some material for Part I (depending on the student's prior exposure to signals and systems) and some material from Part III. In particular, the chapter on design limitations (Chapter 8) requires only elementary knowledge of Laplace Transforms and gives students an understanding of those issues which limit achievable performance. This is an extremely important ingredient in all real-world control design problems. Also, Chapter 11 which deals with constraints is very important in practice. Finally, the ideas of feedforward and cascade architectures that are covered in Chapter 10 are central to solving real-world design problems.
This can be taught from Part IV. Indeed, we feel our treatment here is better focused on applications than many of the traditional treatments because of the emphasis we place on intersample behavior. In the various courses taught by the authors of this book some of the material on digital control is typically included in the Basic Control Theory Course. This is possible because the students are well prepared having taken a Signals and System course prior to the control course.
A second course on control typically includes an introduction to state space design, observers, and state-variable feedback. This material can be taught from Parts V to VII of the book. Part V is relatively straightforward and is intended to bridge the gap from single-input single-output systems (which are principally the focus of Parts I to IV) and multi-input multi-output systems (which are principally covered in Parts VI, VII, and VIII). We consider Chapter 22 on optimal control and filtering to be very important and have included in this chapter many real world design case studies. Also, Chapter 23 on Model Predictive Control is important as this technique is widely used in industrial control.
Two of the authors (Goodwin and Salgado) have taught undergraduate and postgraduate courses of the type mentioned above, using draft versions of this book, in Australia and South America.
We have created a comprehensive website to support the book. This website contains the following:
We see the use of this material as follows: For the Instructor
We believe that the Matlab support and PowerPoint slides should be particularly helpful to an instructor. For example, it would be possible to teach the course entirely using the resources provided. Also, we have found that students enjoy using the Virtual Laboratories. These can be displayed in the classroom as part of a lecture or given to students to enhance their understanding of the material. For the Student
We believe that the PowerPoint slides are an excellent and easily understood summary of the book which by-passes all unnecessary technicalities. Even if your instructor does not use these slides in his/her presentations, we consider that they are an excellent summary for study purposes. If you print them out and annotate them, then remembering the material should be easy. Also, students should enjoy the Java Applets. If you can understand the case studies covered by these applets then you will be well on the way to understanding this exciting subject.
The website can be accessed at either of the following URLs:
http://www.prenhall.com/goodwin and http://csd.newcastle.edu.au/control/
Alternatively, see the authors' home pages for a link. Also note that the website is under continuous development, so the resources provided will continue to grow and evolve as time proceeds.
Newcastle, Australia
Valparaiso, Chile
Vienna, Austria
Table of Contents
I. THE ELEMENTS.
1. The Excitement of Control Engineering.
Motivation for Control Engineering. Historical Periods of Control Theory. Types of Control-System Design. System Integration.
2. Introduction to the Principles of Feedback.
The Principal Goal of Control. A Motivating Industrial Example. Definition of the Problem. Prototype Solution to the Control Problem via Inversion. High-Gain Feedback and Inversion. From Open- to Closed-Loop Architectures. Trade-Offs Involved in Choosing the Feedback Gain. Measurements.
3. Modeling.
The Raison d'être for Models. Model Complexity. Building Models. Model Structures. State Space Models. Solution of Continuous-Time State Space Models. High-Order Differential and Difference-Equation Models. Modeling Errors. Linearization. Case Studies.
4. Continuous-Time Signals and Systems.
Linear Continuous-Time Models. Laplace Transforms. Laplace Transform. Properties and Examples. Transfer Functions. Stability of Transfer Functions. Impulse and Step Responses of Continuous-Time Linear Systems. Poles, Zeros, and Time Responses. Frequency Response. Fourier Transform. Models Frequently Encountered. Modeling Errors for Linear Systems. Bounds for Modeling Errors.
II. SISO CONTROL ESSENTIALS.
5. Analysis of SISO Control Loops.
Feedback Structures. Nominal Sensitivity Functions. Closed-Loop Stability Based on the Characteristic Polynomial. Stability and Polynomial Analysis. Root Locus (RL). Nominal Stability Using Frequency Response. Relative Stability: Stability Margins and Sensitivity Peaks. Robustness.
6. Classical PID Control.
PID Structure. Empirical Tuning. Ziegler-Nichols (Z-N) Oscillation Method. Reaction Curve Based Methods. Lead-Lag Compensators. Distillation Column.
7. Synthesis of SISO Controllers.
Polynomial Approach. PI and PID Synthesis Revisited by Using Pole Assignment. Smith Predictor.
III. SISO CONTROL DESIGN.
8. Fundamental Limitations in SISO Control.
Sensors. Actuators. Disturbances. Model-Error Limitations. Structural Limitations. An Industrial Application (Hold-Up Effect in Reversing Mill). Remedies. Design Homogeneity, Revisited.
9. Frequency-Domain Design Limitations.
Bode's Integral Constraints on Sensitivity. Integral Constraints on Complementary Sensitivity. Poisson Integral Constraint on Sensitivity. Poisson Integral Constraint on Complementary Sensitivity. Example of Design Trade-Offs.
10. Architectural Issues in SISO Control.
Models for Deterministic Disturbances and References. Internal Model Principle for Disturbances. Internal Model Principle for Reference Tracking. Feedforward. Industrial Applications of Feedforward Control. Cascade Control.
11. Dealing with Constraints.
Wind-Up. Anti-Wind-Up Scheme. State Saturation. Introduction to Model Predictive Control.
IV. DIGITAL COMPUTER CONTROL.
12. Models for Sampled-Data Systems.
Sampling. Signal Reconstruction. Linear Discrete-Time Models. The Shift Operator. Z-Transform. Discrete Transfer Functions. Discrete Delta-Domain Models. Discrete Delta-Transform. Discrete Transfer Functions (Delta Form). Transfer Functions and Impulse Responses. Discrete System Stability. Discrete Models for Sampled Continuous Systems. Using Continuous State Space Models. Frequency Response of Sampled-Data Systems.
13. Digital Control.
Discrete-Time Sensitivity Functions. Zeros of Sample-Data Systems. Is a Dedicated Digital Theory Really Necessary? Approximate Continuous Designs. At-Sample Digital Design. Internal Model Principle for Digital Control. Fundamental Performance Limitations.
14. Hybrid Control.
Hybrid Analysis. Models for Hybrid Control Systems. Analysis of Intersample Behavior. Repetitive Control Revisited. Poisson Summation Formula.
V. ADVANCED SISO CONTROL.
15. SISO Controller Parameterizations.
Open-Loop Inversion Revisited. Affine Parameterization: The Stable Case. PID Synthesis by Using the Affine Parameterization. Affine Parameterization for Systems Having Time Delays. Undesirable Closed-Loop Poles. Affine Parameterization: The Unstable Open-Loop Case. Discrete-Time Systems.
16. Control Design Based on Optimization.
Optimal Q (Affine) Synthesis. Robust Control Design with Confidence Bounds. Cheap Control Fundamental Limitations. Frequency-Domain Limitations Revisited.
17. Linear State Space Models.
Linear Continuous-Time State Space Models. Similarity Transformations. Transfer Functions Revisited. From Transfer Function to State Space Representation. Controllability and Stabilizability. Observability and Detectability. Canonical Decomposition. Pole-Zero Cancellation and System Properties.
18. Synthesis via State Space Methods.
Pole Assignment by State Feedback. Observers. Combining State Feedback with an Observer. Transfer-Function Interpretations. Reinterpretation of the Affine Parameterization of All Stabilizing Controllers. State Space Interpretation of Internal Model Principle. Trade-Offs in State Feedback and Observers. Dealing with Input Constraints in the Context of State-Estimate Feedback.
19. Introduction to Nonlinear Control.
Linear Control of a Nonlinear Plant. Switched Linear Controllers. Control of Systems with Smooth Nonlinearities. Static Input Nonlinearities. Smooth Dynamic Nonlineartiies for Stable and Stably Invertible Models. Disturbance Issues in Nonlinear Control. More General Plants with Smooth Nonlinearities. Nonsmooth Nonlinearities. Stability of Nonlinear Systems. Generalized Feedback Linearization for Nonstability-Invertible Plants.
VI. MIMO CONTROL ESSENTIALS.
20. Analysis of MIMO Control Loops.
Motivational Examples. Models for Multivariable Systems. The Basic MIMO Control Loop. Closed-Loop Stability. Steady-State Response for Step Inputs. Frequency-Domain Analysis. Robustness Issues.
21. Exploiting SISO Techniques in MIMO Control.
Completely Decentralized Control. Pairing of Inputs and Outputs. Robustness Issues in Decentralized Control. Feedforward Action in Decentralized Control. Converting MIMO Problems to SISO Problems. Industrial Case Study (Strip Flatness Control).
VII. MIMO CONTROL DESIGN.
22. Design via Optimal Control Techniques.
State-Estimate Feedback. Dynamic Programming and Optimal Control. The Linear Quadratic Regulator (LQR). Properties of the Linear Quadratic Optimal Regulator. Model Matching Based on Linear Quadratic Optimal Regulators. Discrete-Time Optimal Regulators. Connections to Pole Assignment. Observer Design. Linear Optimal Filters. State-Estimate Feedback. Transfer-Function Interpretation. Achieving Integral Action in LQR Synthesis. Industrial Applications.
23. Model Predictive Control.
Anti-Wind-Up Revisited. What Is Model Predictive Control? Stability. Linear Models with Quadratic Cost Function. State Estimation and Disturbance Prediction. Rudder Roll Stabilization of Ships.
24. Fundamental Limitations in MIMO Control.
Closed-Loop Transfer Function. MIMO Internal Model Principle. The Cost of the Internal Model Principle. RHP Poles and Zeros. Time-Domain Constraints. Poisson Integral Constraints on MIMO Complementary Sensitivity. Poisson Integral Constraints on MIMO Sensitivity. Interpretation. An Industrial Application: Sugar Mill. Nonsquare Systems. Discrete-Time Systems.
VIII. ADVANCED MIMO CONTROL.
25. MIMO Controller Parameterizations.
Affine Parameterization: Stable MIMO Plants. Achieved Sensitivities. Dealing with Model Relative Degree. Dealing with NMP Zeros. Affine Parameterization: Unstable MIMO Plants. State Space Implementation.
26. Decoupling.
Stable Systems. Pre- and PostDiagonalization. Unstable Systems. Zeros of Decoupled and Partially Decoupled Systems. Frequency-Domain Constraints for Dynamically Decouple Systems. The Cost of Decoupling. Input Saturation. MIMO Anti-Wind-Up Mechanism.
APPENDICES.
Appendix A: Notation, Symbols, and Acronyms.
Appendix B: Smith-McMillan Forms.
Polynomial Matrices. Smith Form for Polynomial Matrices. Smith-McMillan Form for Rational Matrices. Poles and Zeros. Matrix Fraction Descriptions (MFD).
Appendix C: Results from Analytic Function Theory.
Independence of Path. Simply Connected Domains. Functions of a Complex Variable. Derivatives and Differentials. Analytic Functions. Integrals Revisited. Poisson and Jensen Integral Formulas. Application of the Poisson-Jensen Formula to Certain Rational Functions. Bode's Theorems.
Appendix D: Properties of Continuous-Time Riccati Equations.
Solutions of the CTDRE. Solutions of the CTARE. The Stabilizing Solution of the CTARE. Convergence of Solutions of the CTARE to the Stabilizing Solution of the CTARE. Duality between Linear Quadratic Regulator and Optimal Linear Filter.
Appendix E: MATLAB Support.
Preface
PREFACE
Introduction to Control Engineering
Control Engineering plays a fundamental role in modern technological systems. The benefits of improved control in industry can be immense. They include improved product quality, reduced energy consumption, minimization of waste material, increased safety levels, and reduction of pollution. A difficulty with the subject, however, is that some of the more advanced aspects depend on a sophisticated mathematical background. Arguably, mathematical systems theory is one of the most significant achievements of twentieth-century science, but its practical impact is only as important as the benefits it can bring. Thus, we include in this book a strong emphasis on design, ultimately striking a balance between theory and practice.
It was the authors' involvement in several industrial control-system design projects that provided part of the motivation to write this book. In a typical industrial problem, we found ourselves investigating fluid and thermal dynamics, experiencing the detrimental effects of nonconstant PLC scan rates, dealing with system integration and network communication protocols, building trust with plant operators, and investigating safe bumpless transfer schemes for testing tentative control designs on potentially dangerous plants. In short, we experienced the day-to-day excitement, frustration, set-backs, and progress in getting advanced control to contribute to a commercial company's bottom line. This is not an easy task. Success in this type of venture typically depends on the application of a wide range of multidisciplinary skills; however, it is rewarding and exciting work for those who do it.
One of the main aims of this book is to share this excitement with our readers. We hope to contribute to the development of skills and attitudes within readers and students that will better equip them to face the challenges of real-world design problems. The book is thus intended to contribute to the ongoing reform of the Control Engineering curriculum. This topic continues to receive considerable international attention as educators strive to convey the excitement and importance of control engineering. Indeed, entire issues of the IEEE Control Systems Magazine have been devoted to this theme.
Reforming the curriculum will not, however, be done by books alone. It will be done by people: students, teachers, researchers, practitioners, publication and grant reviewers, and by market pressures. Moreover, for these efforts to be efficient and sustainable, the control engineering community will need to communicate their experiences via a host of new books, laboratories, simulations, and web-based resources. Thus, there will be a need for several different and complementary approaches. In this context, the authors believe that this book will have been successful if it contributes, in some way, to the revitalization of interest by students in the exciting discipline of control engineering.
We stress that this is not a how-to book. On the contrary, we provide a comprehensive, yet condensed, presentation of rigorous control engineering. We employ, and thus require, mathematics as a means to model the process, analyze its properties under feedback, synthesize a controller with particular properties, and arrive at a design addressing the inherent trade-offs and constraints applicable to the problem.
In particular, we believe that success in control projects depends on two key ingredients: (i) having a comprehensive understanding of the process itself, gained by studying the relevant physics, chemistry, and so on; and (ii) by having mastery of the fundamental concepts of signals, systems, and feedback. The first ingredient typically occupies more than fifty per cent of the effort. It is an inescapable component of the complete design cycle; however, it is impractical for us to give full details of the processes to which control might be applied, because they cover chemical plants, electromechanical systems, robots, power generators, and so on. We thus emphasize the fundamental control engineering aspects that are common to all applications and we leave readers to complement this emphasis with process knowledge relevant to their particular problem. Thus, the book is principally aimed at the second ingredient of control engineering. Of course, we do give details of several real-world examples, so as to put the methods into a proper context.
The central theme of this book is continuous-time control; however, we also treat digital control in detail, because most modern control systems will usually be implemented on some form of computer hardware. This approach inevitably led to a book of larger volume than originally intended, but one with the advantage of providing a comprehensive treatment within an integrated framework. Naturally, there remain specialized topics that are not covered in the book; however, we trust that we provide a sufficiently strong foundation so that the reader can comfortably turn to the study of appropriate complementary literature.
Goals
Thus, in writing this book we chose as our principal goals the following:
Indeed, the material in the book is illustrated by numerous industrial case studies with which the authors have had direct involvement. Most of these case studies were carried out, in collaboration with industry, by the Centre for Integrated Dynamics and Control (CIDAC) (a Commonwealth Special Research Centre) at the University of Newcastle.
The projects that we have chosen to describe include the following:
Design is a complex process, one that requires judgment and iteration. The design problem normally is incompletely specified, sometimes is ill-defined, and many times is without solution. A key element in design is an understanding of those factors that limit the achievable performance. This naturally leads to a viewpoint of control design that takes account of these fundamental limitations. This viewpoint is a recurring theme throughout the book.
Our objective is not to explore the full depth of mathematical completeness but instead to give enough detail so that a reader can begin applying the ideas as soon as possible. This approach is connected to our assumption that readers will have ready access to modern computational facilities, including the software package MATLAB-SIMULINK. This assumption allows us to put the emphasis on fundamental ideas rather than on the tools. Every chapter includes worked examples and problems for the reader.
Overview of the Book
The book is divided into eight parts. A brief summary of each of the parts is given here.
Part I: The Elements
This part covers basic continuous-time signals and systems and would be suitable for an introductory course on this topic. Alternatively, it could be used to provide review material before starting the study of control in earnest.
Part II: SISO Control Essentials
This part deals with basic single-input single-output (SISO) control, including classical proportional, integral and derivative (PID) tuning. This section, together with Part I, covers the content of many of the existing curricula for basic control courses.
Part III: SISO Control Design
This part covers design issues in SISO Control. We consider many of these ideas to be crucial to achieving success in practical control problems. In particular, we believe that the chapter dealing with constraints should be mentioned, if at all possible, in all introductory courses. Also, feedforward and cascade structures, which are covered in this part, are very frequently employed in practice.
Part IV: Digital Computer Control
This part covers material essential to the understanding of digital control. We go beyond traditional treatments of this topic by studying inter-sample issues.
Part V: Advanced SISO Control
This part could be the basis of a second course on control at an undergraduate level. It is aimed at the introduction of ideas that flow through to multi-input multi-output (MIMO) systems later in the book.
Part VI: MIMO Control Essentials
This part gives the basics required for a junior-level graduate course on MIMO control. In particular, this part covers basic MIMO system theory. It also shows how one can exploit SISO methods in some MIMO design problems.
Part VII: MIMO Control Design
This part describes tools and ideas that can be used in industrial MIMO design. In particular, it includes linear quadratic optimal control theory and optimal filtering. These two topics have major significance in applications. We also include a chapter on Model Predictive Control. We believe this to be important material, because of the widespread use of this technique in industrial applications.
Part VIII: Advanced MIMO Control
This final part of the book could be left for private study. It is intended to test the reader's understanding of the other material by examining advanced issues. Alternatively, instructors could use this part to extend parts VI and VII in a more senior graduate course on MIMO Control.
Using this Book
This is a comprehensive book on control system design that can be used in many different course patterns. If one adopts the book for an early course on control, then the unused material is excellent reference material for later use in practice or for review. If one uses the book for a later course, then the early material gives an excellent summary of the basic building blocks on which the subject rests.
The book can be used for many different course patterns. Some suggested patterns are outlined as follows:
This would be taught from Part I of the book.
This would typically be taught for Part II of the book, together with some material for Part I (depending on the student's prior exposure to signals and systems) and some material from Part III. In particular, the chapter on design limitations (Chapter 8) requires only elementary knowledge of Laplace Transforms and gives students an understanding of those issues which limit achievable performance. This is an extremely important ingredient in all real-world control design problems. Also, Chapter 11 which deals with constraints is very important in practice. Finally, the ideas of feedforward and cascade architectures that are covered in Chapter 10 are central to solving real-world design problems.
This can be taught from Part IV. Indeed, we feel our treatment here is better focused on applications than many of the traditional treatments because of the emphasis we place on intersample behavior. In the various courses taught by the authors of this book some of the material on digital control is typically included in the Basic Control Theory Course. This is possible because the students are well prepared having taken a Signals and System course prior to the control course.
A second course on control typically includes an introduction to state space design, observers, and state-variable feedback. This material can be taught from Parts V to VII of the book. Part V is relatively straightforward and is intended to bridge the gap from single-input single-output systems (which are principally the focus of Parts I to IV) and multi-input multi-output systems (which are principally covered in Parts VI, VII, and VIII). We consider Chapter 22 on optimal control and filtering to be very important and have included in this chapter many real world design case studies. Also, Chapter 23 on Model Predictive Control is important as this technique is widely used in industrial control.
Two of the authors (Goodwin and Salgado) have taught undergraduate and postgraduate courses of the type mentioned above, using draft versions of this book, in Australia and South America.
Website
We have created a comprehensive website to support the book. This website contains the following:
We see the use of this material as follows:
For the Instructor
We believe that the Matlab support and PowerPoint slides should be particularly helpful to an instructor. For example, it would be possible to teach the course entirely using the resources provided. Also, we have found that students enjoy using the Virtual Laboratories. These can be displayed in the classroom as part of a lecture or given to students to enhance their understanding of the material.
For the Student
We believe that the PowerPoint slides are an excellent and easily understood summary of the book which by-passes all unnecessary technicalities. Even if your instructor does not use these slides in his/her presentations, we consider that they are an excellent summary for study purposes. If you print them out and annotate them, then remembering the material should be easy. Also, students should enjoy the Java Applets. If you can understand the case studies covered by these applets then you will be well on the way to understanding this exciting subject.
The website can be accessed at either of the following URLs:
http://www.prenhall.com/goodwin and http://csd.newcastle.edu.au/control/
Alternatively, see the authors' home pages for a link. Also note that the website is under continuous development, so the resources provided will continue to grow and evolve as time proceeds.
Newcastle, Australia
Valparaiso, Chile
Vienna, Austria