Feedback Systems
Description
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 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. 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.
- Covers the mathematics needed to model, analyze, and design feedback systems
- Serves as an introductory textbook for students and a self-contained resource for researchers
- Includes exercises at the end of every chapter
- Features an electronic solutions manual
- Offers techniques applicable across a range of disciplines
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Content
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
