Welcome to FBSwiki. This is the wiki for the Second Edition of text Feedback Systems by Karl J. Åström and Richard M. Murray.
This book provides an introduction to the basic principles and tools for the design and analysis of feedback systems. It is intended to serve a diverse audience of scientists and engineers who are interested in understanding and utilizing feedback in physical, biological, information and social systems. A major goal of this book is to present a concise and insightful view of the current knowledge in feedback and control systems. In developing this book, we have attempted to condense the current knowledge by emphasizing fundamental concepts. We believe that it is important to understand why feedback is useful, to know the language and basic mathematics of control and to grasp the key paradigms that have been developed over the past half century. It is also important to be able to solve simple feedback problems using backoftheenvelope techniques, to recognize fundamental limitations and difficult control problems and to have a feel for available design methods.
This page corresponds to the Second Edition of FBS. The first edition is also available. Copyright in this book is held by Princeton University Press, who have kindly agreed to allow us to keep the book available on the web.
Contents
 Chapter 1  Introduction (PDF, 24 Jul 2020)
 What Is Feedback?
 What is Feedforward?
 What Is Control?
 Use of Feedback and Control
 Feedback Properties
 Simple Forms of Feedback
 Combining Feedback with Logic
 Control System Architectures
 Chapter 2  Feedback Principles (PDF, 24 Jul 2020)
 Nonlinear Static Models
 Linear Dynamical Models
 Using Feedback to Improve Disturbance Attenuation
 Using Feedback to Track Reference Signals
 Using Feedback to Provide Robustness
 Positive Feedback
 Feedback and Feedforward
 Chapter 3  System Modeling (PDF, 24 Jul 2020)
 Modeling Concepts
 State Space Models
 Modeling Methodology
 Modeling Examples
 Chapter 4  Examples (PDF, 24 Jul 2020)
 Cruise Control
 Bicycle Dynamics
 Operational Amplifier Circuits
 Computing Systems and Networks
 Atomic Force Microscopy
 Drug Administration
 Population Dynamics
 Chapter 5  Dynamic Behavior (PDF, 24 Jul 2020)
 Solving Differential Equations
 Qualitative Analysis
 Stability
 Lyapunov Stability Analysis
 Parametric and Nonlocal Behavior
 Chapter 6  Linear Systems (PDF, 24 Jul 2020)
 Basic Definitions
 The Matrix Exponential
 Input/Output Response
 Linearization
 Chapter 7  State Feedback (PDF, 24 Jul 2020)
 Reachability
 Stabilization by State Feedback
 State Feedback Design
 Integral Action
 Chapter 8  Output Feedback (PDF, 24 Jul 2020)
 Observability
 State Estimation
 Control Using Estimated State
 Kalman Filtering
 A General Controller Structure

 Chapter 9  Transfer Functions (PDF, 24 Jul 2020)
 Frequency Domain Modeling
 Derivation of the Transfer Function
 Block Diagrams and Transfer Functions
 The Bode Plot
 Laplace Transforms
 Chapter 10  Frequency Domain Analysis (PDF, 24 Jul 2020)
 The Loop Transfer Function
 The Nyquist Criterion
 Stability Margins
 Bode’s Relations and Minimum Phase Systems
 Generalized Notions of Gain and Phase
 Chapter 11  PID Control (PDF, 17 Aug 2019)
 Basic Control Functions
 Simple Controllers for Complex Systems
 PID Tuning
 Integrator Windup
 Implementation
 Chapter 12  Frequency Domain Design (PDF, 24 Jul 2020)
 Sensitivity Functions
 Feedforward Design
 Performance Specifications
 Feedforward Design
 Feedback Design via Loop Shaping
 The RootLocus Method
 Design Example
 Chapter 13  Robust Performance (PDF, 24 Jul 2020)
 Modeling Uncertainty
 Stability in the Presence of Uncertainty
 Performance in the Presence of Uncertainty
 Design for Robust Performance
 Chapter 14  Fundamental Limits (PDF, 24 Jul 2020)
 Effects of Design Decisions
 Nonlinear Effects
 Bode’s Integral Formula
 Gain Crossover Frequency Inequality
 The Maximum Modulus Principle
 Robust Pole Placement
 Chapter 15  Architecture and System Design (PDF, 24 Jul 2020)
 Introduction
 Systems and Control Design
 TopDown Architectures
 BottomUp Architectures
 Interaction
 Adaptation, Learning and Cognition
 Control Design in Common Application Fields
Other versions
 Complete book (PDF, 24 Jul 2020)  single PDF file (35 MB)
 iPad version (not yet available)  reduced margins
