Robust and Adaptive Control: With Aerospace Applications

✍ Scribed by Eugene Lavretsky, Kevin A. Wise

• Publisher: Springer
• Year: 2024
• Tongue: English
• Leaves: 718
• Series: Advanced Textbooks in Control and Signal Processing
• Edition: 2
• Category: Library

✦ Synopsis

Robust and Adaptive Control (second edition) shows readers how to produce consistent and accurate controllers that operate in the presence of uncertainties and unforeseen events. Driven by aerospace applications, the focus of the book is primarily on continuous-time dynamical systems.

The two-part text begins with robust and optimal linear control methods and moves on to a self-contained presentation of the design and analysis of model reference adaptive control for nonlinear uncertain dynamical systems. Features of the second edition include:

• sufficient conditions for closed-loop stability under output feedback observer-based loop-transfer recovery (OBLTR) with adaptive augmentation;
• OBLTR applications to aerospace systems;
• case studies that demonstrate the benefits of robust and adaptive control for piloted, autonomous and experimental aerial platforms;
• realistic examples and simulation data illustrating key features of the methods described; and
• problem solutions for instructors and MATLAB^® code provided electronically.

The theory and practical applications address real-life aerospace problems, being based on numerous transitions of control-theoretic results into operational systems and airborne vehicles drawn from the authors’ extensive professional experience with The Boeing Company. The systems covered are challenging―often open-loop unstable with uncertainties in their dynamics―and thus require both persistently reliable control and the ability to track commands either from a pilot or a guidance computer.

Readers should have a basic understanding of root locus, Bode diagrams, and Nyquist plots, as well as linear algebra, ordinary differential equations, and the use of state-space methods in analysis and modeling of dynamical systems. The second edition contains a background summary of linear systems and control systems and an introduction to state observers and output feedback control, helping to make it self-contained.

Robust and Adaptive Control teaches senior undergraduate and graduate students how to construct stable and predictable control algorithms for realistic industrial applications. Practicing engineers and academic researchers will also find the book of great instructional value.

✦ Table of Contents

Series Editor’s Foreword to the Second Edition
Preface to the Second Edition
Preface to the First Edition
Acknowledgments
Contents
Part IRobust Control
1 Introduction
1.1 Why Robust and Adaptive Control?
1.2 About This Book
1.3 Aircraft Flight Dynamics Equations of Motion
1.4 High-Fidelity Flight Simulation Environment
1.5 Simplified Flight Dynamics for Control Design
1.6 Summary
1.7 Exercises
References
2 Linear Time-Invariant Systems and Control
2.1 Model-Based Control Engineering
2.2 Control System Design Goals and Objectives
2.3 Feedback and Feedforward Control
2.4 State-Space Systems
2.4.1 Time and Frequency Domain Modeling of State-Space Systems
2.4.2 Control-Oriented Models for Linear Time-Invariant Systems
2.4.3 State-Space Similarity Transformations
2.4.4 Eigenvalues and Eigenvectors
2.4.5 Computing the State Transition Matrix
2.5 Stability, Controllability, and Observability
2.5.1 Stability of LTI Systems
2.5.2 Controllability of LTI Systems
2.5.3 Observability of LTI Systems
2.6 Norms of Vectors and Matrices in Euclidean Spaces
2.7 Summary
2.8 Exercises
References
3 Frequency Domain Analysis
3.1 Introduction
3.2 Transfer Functions and Transfer Function Matrices
3.3 Multivariable Stability Margins
3.3.1 Singular Values
3.3.2 Multivariable Nyquist Theory
3.3.3 Singular Value-Based Stability Margins for MIMO Systems
3.4 Control System Robustness Analysis
3.4.1 Analysis Models for Uncertain Systems
3.4.2 Singular Value Robustness Tests
3.4.3 Real Stability Margin
3.5 Conclusions
3.6 Exercises
References
4 Optimal Control and Linear Quadratic Regulators
4.1 Introduction
4.2 Optimal Control and the Hamilton–Jacobi–Bellman Equation
4.2.1 The HJB Equation for Nonlinear Systems Affine in Control
4.3 Linear Quadratic Regulator (LQR)
4.3.1 Infinite-Time LQR Problem
4.3.2 Guaranteed Stability Robustness for State Feedback LQR
4.3.3 LQR Design and Asymptotic Properties
4.4 Command Tracking and Robust Servomechanism Control
4.4.1 Servomechanism Control Design Model
4.4.2 Servomechanism Model Controllability
4.4.3 Servomechanism Control Design
4.5 Conclusions
4.6 Exercises
References
5 State Feedback H∞ Optimal Control
5.1 Introduction
5.2 Norms for Signals and Systems
5.3 Stability and Performance Specifications in the Frequency Domain
5.4 Loop Shaping Using Frequency-Dependent Weights
5.5 State Feedback H∞ Optimal Control
5.6 Controller Design Using γ-Iteration
5.7 Conclusions
5.8 Exercises
References
6 Output Feedback Control and State Observers
6.1 Output Feedback Using Projective Controls
6.2 Full-Order State Observers for Linear Time-Invariant Systems
6.2.1 The Separation Principle
6.2.2 Observer-Based Optimal Servomechanism Design
6.2.3 Asymptotic Properties of the Algebraic Riccati Equation
6.2.4 The Squaring-Up Method
6.3 Observer-Based Control with Loop Transfer Recovery
6.3.1 OBLTR Design Process and Examples
6.4 Summary
6.5 Exercises
References
Part IIRobust Adaptive Control
7 Direct Model Reference Adaptive Control: Motivation and Introduction
7.1 Model Reference Control: Motivational Example
7.2 Introduction to Direct Model Reference Adaptive Control
7.3 Direct Model Reference Adaptive Control of Scalar Linear Systems with Parametric Uncertainties
7.4 Historical Roots and Foundations of Model Reference Adaptive Control
7.5 Exercises
References
8 Lyapunov Stability of Motion
8.1 Dynamical Systems
8.2 Existence and Uniqueness of Solutions
8.3 System Equilibrium
8.4 Lyapunov Stability Definitions
8.5 Lyapunov Stability Theorems
8.6 Uniform Ultimate Boundedness
8.7 Barbalat’s Lemma
8.8 Summary and Historical Remarks
8.9 Exercises
References
9 State Feedback Direct Model Reference Adaptive Control
9.1 Introduction
9.2 Command Tracking
9.3 Direct MRAC Design for Scalar Systems
9.4 Dynamic Inversion MRAC Design for Scalar Systems
9.5 MRAC Design for Multi-Input–Multi-Output Systems
9.6 Summary
9.7 Exercises
References
10 Model Reference Adaptive Control with Integral Feedback Connections
10.1 Introduction
10.2 Control Design
10.3 MRAC Augmentation of an Optimal Baseline Controller
10.4 Summary
10.5 Exercises
References
11 Robust Adaptive Control
11.1 MRAC Design in the Presence of Bounded Disturbances
11.2 MRAC Design Modifications for Robustness
11.2.1 The Dead-Zone Modification
11.2.2 The σ-Modification
11.2.3 The e-Modification
11.3 The Projection Operator
11.4 Projection-Based MRAC Design
11.5 Summary and Discussion
11.6 Exercises
References
12 Approximation-Based Adaptive Control
12.1 Motivation
12.2 Basic Definitions
12.3 Approximation Properties of Feedforward Neural Networks
12.4 Adaptive Control with State Limiting Constraints
12.5 Summary
12.6 Exercises
References
13 Adaptive Control with Improved Transient Dynamics
13.1 Motivation
13.2 Asymptotic Orders and Singular Perturbations
13.3 Asymptotic Properties of the Algebraic Riccati Equation
13.4 System Dynamics and Control Problem Formulation
13.5 Observer-Like Model Reference Adaptive Control
13.6 Transient Dynamics Analysis
13.7 Summary
13.8 Exercises
References
14 Output Feedback Servomechanism with Observer-Based Loop Transfer Recovery and Adaptive Augmentation
14.1 Introduction
14.2 Optimal Control with “Cheap” Input and “Expensive” Output
14.3 Optimal Cost Asymptotic Analysis
14.4 ARE Asymptotic Analysis
14.5 Adaptive Output Feedback Design and Analysis
14.6 Adaptive Flight Control of a Flexible Transport Aircraft
14.7 Design Case Study: Control of the “Respect the Unstable” Dynamics
14.8 Design Case Study: (OBLTR + Adaptive) Flight Control of Aircraft MIMO Roll–Yaw Dynamics
14.9 Conclusions
14.10 Exercises
References
15 Robust and Adaptive Output Feedback Control for Square Non-Minimum Phase Systems
15.1 Introduction
15.2 Problem Motivation
15.3 The Squaring-Up Design for Non-Minimum Phase Systems with Arbitrary Relative Degree
15.4 Observer-Based Loop Transfer Recovery (OBLTR) Servo-Controller for Square Systems
15.5 Loop Transfer Recovery and OBLTR Stability Margins for Square Systems
15.6 OBLTR Adaptive Augmentation for Square Non-Minimum Phase Systems
15.7 Summary
15.8 Exercises
References
Appendix A: Aircraft Flight Simulation (aFltSim) Software
A.1 Aircraft Flight Dynamics Equations of Motion
A.2 High-Fidelity Flight Simulation Environment
A.3 Simplified Flight Dynamics for Control Design
A.4 aFltSim Block Diagram Architecture and Calling Sequence
References
Index