Robust and Adaptive Control With Aerospace Applications

✍ Scribed by Lavretsky, Eugene; Wise, Kevin A

• Publisher: Springer
• Year: 2013
• Tongue: English
• Leaves: 462
• Category: Library

✦ Synopsis

Part I: Robust and Optimal Control of Linear Systems.- Introduction to Control of Aerial Vehicles.- Command Tracking and Servomechanism Design.0 Optimal Control and Linear Quadratic Regulator (LQR).- H-infinity Optimal Control.- Stability Margins and Frequency Domain Consideration.- Projective Control.- Linear Quadratic Gaussian with Loop-transfer Recovery (LQG/LTR) Control.- Simulation Examplse and Case Studies.- Exercises.- Part II: Model Reference Adaptive Control.- Motivation.- Lyapunov Stability Theory: Introduction and Overview.- Adaptive Control Architectures: Direct vs. Indirect.- MRAC and Model Matching Conditions.- Adaptive Dynamic Inversion.- Persistency of Excitation.- Enforcing Robustness in MRAC Systems.- Approximation-based MRAC.- Adaptive Augmentation of a Linear Baseline Controller.- Simulation Examples and Case Studies.- Exercises.- Part III: MRAC Design Extensions.- Limited-authority Adaptive Control.- Predictor-based Control.- Combined/Composite MRAC.- Filtered MRAC Design.- MRAC Design Using Output Feedback.- Simulation Examples and Case Studies.- Conclusions, Future Work and Flight Control Challenges

✦ Table of Contents

Cover......Page 1
Robust and Adaptive Control......Page 4
Series Editors’ Foreword......Page 6
Preface......Page 8
Acknowledgments......Page 12
Contents......Page 14
1.1 Why Robust and Adaptive Control?......Page 20
1.2 About This Book......Page 21
1.3 Aircraft Flight Dynamics Equations of Motion......Page 22
1.4 Simplified Flight Dynamics for Control Design......Page 27
1.4.1 Longitudinal Dynamics......Page 29
1.4.2 Lateral-Directional Dynamics......Page 31
1.4.3 Model Generalizations for Adaptive Control Design......Page 33
1.5 Control-Oriented Models for Linear-Time-Invariant Systems......Page 35
1.6 Norms of Vectors and Matrices in Euclidean Spaces......Page 38
1.7 Summary......Page 40
1.8 Exercises......Page 41
References......Page 42
2.1 Introduction......Page 43
2.2 Optimal Control and the Hamilton-Jacobi-Bellman Equation......Page 44
2.2.1 The Hamilton-Jacobi-Bellman Equation......Page 45
2.2.2 Summary......Page 49
2.3 Linear Quadratic Regulator......Page 51
2.4 Infinite-Time LQR Problem......Page 53
2.4.1 Summary......Page 55
2.5 Guaranteed Stability Margins for State Feedback LQR......Page 58
2.6 LQR Design and Asymptotic Properties......Page 60
2.7 Conclusions......Page 63
2.8 Exercises......Page 64
References......Page 66
3.1 Introduction......Page 67
3.2 The Servomechanism Design Model......Page 68
3.2.1 Controllability of the Servomechanism Design Model......Page 72
3.3 The Robust Servomechanism LQR......Page 74
3.3.1 Summary......Page 78
3.5 Exercises......Page 87
References......Page 88
4.1 Introduction......Page 89
4.2.1 Power Signals......Page 91
4.2.2 Norms for Systems......Page 92
4.2.3 Computing Norms for Systems......Page 94
4.2.4 Well-Posedness and Stability......Page 95
4.3 Stability and Performance Specifications in the Frequency Domain......Page 96
4.4 Loop Shaping Using Frequency-Dependent Weights......Page 98
4.5 State Feedback H Optimal Control......Page 101
4.6 Controller Design Using gamma-Iteration......Page 104
4.6.1 Summary......Page 106
References......Page 112
5.1 Introduction......Page 113
5.2 Transfer Functions and Transfer Function Matrices......Page 114
5.3.1 Singular Values......Page 119
5.3.2 Singular Value Properties......Page 122
5.3.3 Multivariable Nyquist Theory......Page 123
5.3.4 Stability Margins for Multi-Input Multi-Output Systems......Page 128
5.3.5 A+B Argument......Page 131
5.3.6 Singular Value Stability Margins......Page 134
5.4 Control System Robustness Analysis......Page 141
5.4.1 Analysis Models for Uncertain Systems......Page 142
5.4.1.1 Real-Parameter Uncertainties......Page 145
5.4.2 Singular Value Robustness Tests......Page 149
5.4.2.2 The Structured Singular Value mu......Page 150
5.4.3 Real Stability Margin......Page 159
5.4.3.2 Upper Bound on the Stability Margin km......Page 163
5.4.3.3 Comment......Page 164
5.4.3.4 Convergence to km......Page 165
5.4.3.5 Computing the Real Margin......Page 168
5.5 Conclusions......Page 173
5.6 Exercises......Page 174
References......Page 176
6.1 Output Feedback Using Projective Controls......Page 177
6.2 Linear Quadratic Gaussian with Loop Transfer Recovery......Page 192
6.2.1 Summary......Page 196
6.3 Loop Transfer Recovery Using the Lavretsky Method......Page 206
6.3.1 Summary......Page 211
6.5 Exercises......Page 221
References......Page 223
7.1 Model Reference Control: Motivational Example......Page 225
7.2 Introduction to Direct Model Reference Adaptive Control......Page 229
7.3 Direct Model Reference Adaptive Control of Scalar Linear Systems with Parametric Uncertainties......Page 234
7.4 Historical Roots and Foundations of Model Reference Adaptive Control......Page 235
7.5 Exercises......Page 236
References......Page 237
8.1 Dynamical Systems......Page 238
8.2 Existence and Uniqueness of Solutions......Page 240
8.3 System Equilibrium......Page 246
8.4 Lyapunov Stability Definitions......Page 248
8.5 Lyapunov Stability Theorems......Page 253
8.6 Uniform Ultimate Boundedness......Page 260
8.7 Barbalat´s Lemma......Page 267
8.9 Exercises......Page 272
References......Page 274
9.1 Introduction......Page 275
9.2 Command Tracking......Page 276
9.3 Direct MRAC Design for Scalar Systems......Page 277
9.4 Dynamic Inversion MRAC Design for Scalar Systems......Page 286
9.5 MRAC Design for Multi-Input Multi-Output Systems......Page 293
9.7 Exercises......Page 303
References......Page 304
10.1 Introduction......Page 305
10.2 Control Design......Page 307
10.3 MRAC Augmentation of an Optimal Baseline Controller......Page 315
10.5 Exercises......Page 326
References......Page 327
11.1 MRAC Design in the Presence of Bounded Disturbances......Page 328
11.2.1 The Dead-Zone Modification......Page 330
11.2.2 The σ-Modification......Page 334
11.3 The e-Modification......Page 338
11.4 The Projection Operator......Page 340
11.5 Projection-Based MRAC Design......Page 348
11.6 Summary and Discussions......Page 361
11.7 Exercises......Page 362
References......Page 363
12.1 Motivation......Page 365
12.2 Basic Definitions......Page 366
12.3 Approximation Properties of Feedforward Neural Networks......Page 370
12.4 Adaptive Control with State Limiting Constraints......Page 372
12.5 Summary......Page 393
12.6 Exercises......Page 394
References......Page 395
13.1 Motivation......Page 396
13.2 Asymptotic Orders and Singular Perturbations......Page 403
13.3 Asymptotic Properties of the Algebraic Riccati Equation......Page 408
13.4 System Dynamics and Control Problem Formulation......Page 415
13.5 Observer-Like Model Reference Adaptive Control......Page 417
13.6 Transient Dynamics Analysis......Page 421
13.7 Summary......Page 424
References......Page 425
14.1 Introduction......Page 426
14.2 Mathematical Preliminaries......Page 428
14.3 System Dynamics and Control Problem Formulation......Page 430
14.4 Adaptive Output Feedback Design and Analysis......Page 433
14.5 Adaptive Flight Control of a Flexible Transport Aircraft......Page 444
14.6 Conclusions......Page 456
14.7 Exercises......Page 457
References......Page 458
Index......Page 459

✦ Subjects

Транспорт;Аэрокосмическая техника;