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Modern Anti-windup Synthesis

Book Description

This book provides a wide variety of state-space--based numerical algorithms for the synthesis of feedback algorithms for linear systems with input saturation. Specifically, it addresses and solves the anti-windup problem, presenting the objectives and terminology of the problem, the mathematical tools behind anti-windup algorithms, and more than twenty algorithms for anti-windup synthesis, illustrated with examples. Luca Zaccarian and Andrew Teel's modern method--combining a state-space approach with algorithms generated by solving linear matrix inequalities--treats MIMO and SISO systems with equal ease. The book, aimed at control engineers as well as graduate students, ranges from very simple anti-windup construction to sophisticated anti-windup algorithms for nonlinear systems.

  • Describes the fundamental objectives and principles behind anti-windup synthesis for control systems with actuator saturation
  • Takes a modern, state-space approach to synthesis that applies to both SISO and MIMO systems
  • Presents algorithms as linear matrix inequalities that can be readily solved with widely available software
  • Explains mathematical concepts that motivate synthesis algorithms
  • Uses nonlinear performance curves to quantify performance relative to disturbances of varying magnitudes
  • Includes anti-windup algorithms for a class of Euler-Lagrange nonlinear systems
  • Traces the history of anti-windup research through an extensive annotated bibliography

Table of Contents

  1. Cover Page
  2. Title Page
  3. Copyright Page
  4. Contents
  5. Preface
  6. Algorithms Summary
  7. Part I. Prepartion
    1. 1. The Windup Phenomenon and Anti-Windup Illustrated
      1. 1.1 Introduction
      2. 1.2 Illustrative Examples
      3. 1.3 Summary
      4. 1.4 Notes and References
    2. 2. Anti-Windup: Definitions, Objectives, and Architectures
      1. 2.1 Preliminaries
      2. 2.2 Qualitative Objectives
      3. 2.3 Anti-Windup Augmentation
      4. 2.4 Quantitative Performance Objectives
      5. 2.5 Notes and References
    3. 3. Analysis and Synthesis of Feedback Systems: Quadratic Functions and LMIs
      1. 3.1 Introduction
      2. 3.2 Unconstrained Feedback Systems
      3. 3.3 Linear Matrix Inequalities
      4. 3.4 Constrained Feedback Systems: Global Analysis
      5. 3.5 Constrained Feedback Systems: Regional Analysis
      6. 3.6 Analysis Examples
      7. 3.7 Regional Synthesis for External Stability
      8. 3.8 Notes and References
  8. Part II. Direct Linear Anti-Windup Augmentation
    1. 4. Static Linear Anti-Windup Augmentation
      1. 4.1 Overview
      2. 4.2 Key State-Space Representations
      3. 4.3 Algorithms Providing Global Guarantees
      4. 4.4 Algorithms Providing Regional Guarantees
      5. 4.5 Notes and References
    2. 5. Dynamic Linear Anti-Windup Augmentation
      1. 5.1 Overview
      2. 5.2 Key State-Space Representations
      3. 5.3 Factoring Rank-Deficient Matrices
      4. 5.4 Algorithms Providing Global Guarantees
      5. 5.5 Algorithms Providing Regional Guarantees
      6. 5.6 Notes and References
  9. Part III. Model Recovery Anti-Windup Augmentation
    1. 6. The MRAW Framework
      1. 6.1 Introduction
      2. 6.2 A Block Diagram/Transfer Function Description
      3. 6.3 A State-Space Description (Linearity not Needed)
      4. 6.4 Robust, Fragile, or Both?
      5. 6.5 Notes and References
    2. 7. Linear MRAW Synthesis
      1. 7.1 Introduction
      2. 7.2 Global Stability-Based Algorithms
      3. 7.3 Regional Stability and Performance Algorithms
      4. 7.4 Notes and References
    3. 8. Nonlinear MRAW Synthesis
      1. 8.1 Introduction
      2. 8.2 Switching and Scheduling Linear Controllers
      3. 8.3 Model Predictive Control for Anti-Windup Design
      4. 8.4 Global Designs for Non-Exponentially Unstable Plants
      5. 8.5 Designs for Exponentially Unstable Plants that Maximize the Basin of Attraction
      6. 8.6 Notes and References
    4. 9. The MRAW Structure Applied to Other Problems
      1. 9.1 Rate- and Magnitude-Saturated Plants
      2. 9.2 Anti-Windup for Dead-Time Plants
      3. 9.3 Bumpless Transfer in Multicontroller Schemes
      4. 9.4 Reliable Control via Hardware Redundancy
      5. 9.5 Notes and References
    5. 10. Anti-windup for Euler-Lagrange Plants
      1. 10.1 Fully Actuated Euler-Lagrange plants
      2. 10.2 Anti-Windup Construction and Selection of the Stabilizer
      3. 10.3 Simulation Examples
      4. 10.4 Notes and References
    6. 11. Annotated Bibliography
      1. 11.1 Overview
      2. 11.2 Problem Discovery
      3. 11.3 The First Constructive Techniques
      4. 11.4 Call for Systematization
      5. 11.5 Modern Anti-Windup Schemes
      6. 11.6 Additional References
  10. Index