Feedback Systems: An Introduction for Scientists and Engineers, Second Edition

**The essential introduction to the principles and applications of feedback systems―now fully revised and expanded** This textbook covers the mathematics needed to model, analyze, and design feedback systems. Now more user-friendly than ever, this revised and expanded edition of __Feedback Systems__ is a one-volume resource for students and researchers in mathematics and engineering. It has applications across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. Karl Åström and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. Åström and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. Contents Preface to the Second Edition Preface to the First Edition 1 Introduction 1.1 What Is Feedback? 1.2 What is Feedforward? 1.3 What Is Control? 1.4 Uses of Feedback and Control 1.5 Feedback Properties 1.6 Simple Forms of Feedback 1.7 Combining Feedback with Logic 1.8 Control System Architectures 1.9 Further Reading Exercises 2 Feedback Principles 2.1 Nonlinear Static Models 2.2 Linear Dynamical Models 2.3 Using Feedback to Attenuate Disturbances 2.4 Using Feedback to Track Reference Signals 2.5 Using Feedback to Provide Robustness 2.6 Positive Feedback 2.7 Further Reading Exercises 3 System Modeling 3.1 Modeling Concepts 3.2 State Space Models 3.3 Modeling Methodology 3.4 Modeling Examples 3.5 Further Reading Exercises 4 Examples 4.1 Cruise Control 4.2 Bicycle Dynamics 4.3 Operational Amplifier Circuits 4.4 Computing Systems and Networks 4.5 Atomic Force Microscopy 4.6 Drug Administration 4.7 Population Dynamics Exercises 5 Dynamic Behavior 5.1 Solving Differential Equations 5.2 Qualitative Analysis 5.3 Stability 5.4 Lyapunov Stability Analysis 5.5 Parametric and Nonlocal Behavior 5.6 Further Reading Exercises 6 Linear Systems 6.1 Basic Definitions 6.2 The Matrix Exponential 6.3 Input/Output Response 6.4 Linearization 6.5 Further Reading Exercises 7 State Feedback 7.1 Reachability 7.2 Stabilization by State Feedback 7.3 Design Considerations 7.4 Integral Action 7.5 Linear Quadratic Regulators 7.6 Further Reading Exercises 8 Output Feedback 8.1 Observability 8.2 State Estimation 8.3 Control Using Estimated State 8.4 Kalman Filtering 8.5 State Space Controller Design 8.6 Further Reading Exercises 9 Transfer Functions 9.1 Frequency Domain Modeling 9.2 Determining the Transfer Function 9.3 Laplace Transforms 9.4 Block Diagrams and Transfer Functions 9.5 Zero Frequency Gain, Poles, and Zeros 9.6 The Bode Plot 9.7 Further Reading Exercises 10 Frequency Domain Analysis 10.1 The Loop Transfer Function 10.2 The Nyquist Criterion 10.3 Stability Margins 10.4 Bode's Relations and Minimum Phase Systems 10.5 Generalized Notions of Gain and Phase 10.6 Further Reading Exercises 11 PID Control 11.1 Basic Control Functions 11.2 Simple Controllers for Complex Systems 11.3 PID Tuning 11.4 Integral Windup 11.5 Implementation 11.6 Further Reading Exercises 12 Frequency Domain Design 12.1 Sensitivity Functions 12.2 Performance Specifications 12.3 Feedback Design via Loop Shaping 12.4 Feedforward Design 12.5 The Root Locus Method 12.6 Design Example 12.7 Further Reading Exercises 13 Robust Performance 13.1 Modeling Uncertainty 13.2 Stability in the Presence of Uncertainty 13.3 Performance in the Presence of Uncertainty 13.4 Design for Robust Performance 13.5 Further Reading Exercises 14 Fundamental Limits 14.1 System Design Considerations 14.2 Bode's Integral Formula 14.3 Gain Crossover Frequency Inequality 14.4 The Maximum Modulus Principle 14.5 Robust Pole Placement 14.6 Nonlinear Effects 14.7 Further Reading Exercises 15 Architecture and System Design 15.1 Introduction 15.2 System and Control Design 15.3 Top-Down Architectures 15.4 Bottom-Up Architectures 15.5 Interaction 15.6 Adaptation and Learning 15.7 Control Design in Common Application Fields 15.8 Further Reading Bibliography Index The Essential Introduction To The Principles And Applications Of Feedback Systems--now Fully Revised And Expanded This Textbook Covers The Mathematics Needed To Model, Analyze, And Design Feedback Systems. Now More User-friendly Than Ever, This Revised And Expanded Edition Of Feedback Systems Is A One-volume Resource For Students And Researchers In Mathematics And Engineering. It Has Applications Across A Range Of Disciplines That Utilize Feedback In Physical, Biological, Information, And Economic Systems. Karl Åström And Richard Murray Use Techniques From Physics, Computer Science, And Operations Research To Introduce Control-oriented Modeling. They Begin With State Space Tools For Analysis And Design, Including Stability Of Solutions, Lyapunov Functions, Reachability, State Feedback Observability, And Estimators. The Matrix Exponential Plays A Central Role In The Analysis Of Linear Control Systems, Allowing A Concise Development Of Many Of The Key Concepts For This Class Of Models. Åström And Murray Then Develop And Explain Tools In The Frequency Domain, Including Transfer Functions, Nyquist Analysis, Pid Control, Frequency Domain Design, And Robustness. Features A New Chapter On Design Principles And Tools, Illustrating The Types Of Problems That Can Be Solved Using Feedback Includes A New Chapter On Fundamental Limits And New Material On The Routh-hurwitz Criterion And Root Locus Plots Provides Exercises At The End Of Every Chapter Comes With An Electronic Solutions Manual An Ideal Textbook For Undergraduate And Graduate Students Indispensable For Researchers Seeking A Self-contained Resource On Control Theory "In this updated and revised edition of the classic Feedback Systems (which Princeton University Press first published in 2008), Astrom and Murray provide a complete one-volume resource for students and researchers in mathematics and engineering. One of the primary comments from users of the first edition was that the use of control tools for design purposes occurred only after several chapters of analytical tools, leaving the instructor having to try to convince students that the techniques would soon be useful. Accordingly, the authors have re-structured the text to introduce design principles upfront. The text also includes a new chapter on fundamental limits, as well as additional updated material throughout. Drawing on examples from physics, computer science, and operations research, and more to introduce the basic principles and tools of feedback systems, the second edition of Feedback Systems will continue to serve as the ideal textbook for undergraduate and graduate students, as well as an indispensable reference for researchers"-- Provided by publisher