Feedback Systems An Introduction for Scientists and Engineers

About this book

This book provides an introduction to the mathematics needed to model, analyze, and design feedback systems. It is an ideal textbook for undergraduate and graduate students, and is indispensable for researchers seeking a self-contained reference on control theory.

Unlike most books on the subject, "Feedback Systems" develops transfer functions through the exponential response of a system, and is accessible across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. Karl Astrom 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. Astrom and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. They provide exercises at the end of every chapter, and an accompanying electronic solutions manual is available.

"Feedback Systems" is a complete one-volume resource for students and researchers in mathematics, engineering, and the sciences. It covers the mathematics needed to model, analyze, and design feedback systems. It serves as an introductory textbook for students and a self-contained resource for researchers. It includes exercises at the end of every chapter. It features an electronic solutions manual. It offers techniques applicable across a range of disciplines.

Contents

Preface ix Chapter 1. Introduction 1 1.1 What Is Feedback? 1 1.2 What Is Control? 3 1.3 Feedback Examples 5 1.4 Feedback Properties 17 1.5 Simple Forms of Feedback 23 1.6 Further Reading 25 Exercises 25 Chapter 2. System Modeling 27 2.1 Modeling Concepts 27 2.2 State Space Models 34 2.3 Modeling Methodology 44 2.4 Modeling Examples 51 2.5 Further Reading 61 Exercises 61 Chapter 3. Examples 65 3.1 Cruise Control 65 3.2 Bicycle Dynamics 69 3.3 Operational Amplifier Circuits 71 3.4 Computing Systems and Networks 75 3.5 Atomic Force Microscopy 81 3.6 Drug Administration 84 3.7 Population Dynamics 89 Exercises 91 Chapter 4. Dynamic Behavior 95 4.1 Solving Differential Equations 95 4.2 Qualitative Analysis 98 4.3 Stability 102 4.4 Lyapunov Stability Analysis 110 4.5 Parametric and Nonlocal Behavior 120 4.6 Further Reading 126 Exercises 126 Chapter 5. Linear Systems 131 5.1 Basic Definitions 131 5.2 The Matrix Exponential 136 5.3 Input/Output Response 145 5.4 Linearization 158 5.5 Further Reading 163 Exercises 164 Chapter 6. State Feedback 167 6.1 Reachability 167 6.2 Stabilization by State Feedback 175 6.3 State Feedback Design 183 6.4 Integral Action 195 6.5 Further Reading 197 Exercises 197 Chapter 7. Output Feedback 201 7.1 Observability 201 7.2 State Estimation 206 7.3 Control Using Estimated State 211 7.4 Kalman Filtering 215 7.5 A General Controller Structure 219 7.6 Further Reading 226 Exercises 226 Chapter 8. Transfer Functions 229 8.1 Frequency Domain Modeling 229 8.2 Derivation of the Transfer Function 231 8.3 Block Diagrams and Transfer Functions 242 8.4 The Bode Plot 250 8.5 Laplace Transforms 259 8.6 Further Reading 262 Exercises 262 Chapter 9. Frequency Domain Analysis 267 9.1 The Loop Transfer Function 267 9.2 The Nyquist Criterion 270 9.3 Stability Margins 278 9.4 Bode's Relations and Minimum Phase Systems 283 9.5 Generalized Notions of Gain and Phase 285 9.6 Further Reading 290 Exercises 290 Chapter 10. PID Control 293 10.1 Basic Control Functions 293 10.2 Simple Controllers for Complex Systems 298 10.3 PID Tuning 302 10.4 Integrator Windup 306 10.5 Implementation 308 10.6 Further Reading 312 Exercises 313 Chapter 11. Frequency Domain Design 315 11.1 Sensitivity Functions 315 11.2 Feedforward Design 319 11.3 Performance Specifications 322 11.4 Feedback Design via Loop Shaping 326 11.5 Fundamental Limitations 331 11.6 Design Example 340 11.7 Further Reading 343 Exercises 344 Chapter 12. Robust Performance 347 12.1 Modeling Uncertainty 347 12.2 Stability in the Presence of Uncertainty 352 12.3 Performance in the Presence of Uncertainty 358 12.4 Robust Pole Placement 361 12.5 Design for Robust Performance 369 12.6 Further Reading 374 Exercises 374 Bibliography 377 Index 387

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Biography

Karl J. Astrom is professor of automatic control at the Lund Institute of Technology in Sweden. His books include "Adaptive Control". Richard M. Murray is professor of control and dynamical systems at the California Institute of Technology. He is the coauthor of "A Mathematical Introduction to Robotic Manipulation".