Ashish Tewari is a Professor of Aerospace Engineering at the Indian Institute of Technology, Kanpur. He specializes in Flight Mechanics and Control, and is the single author of five previous books, including Aeroservoelasticity – Modeling and Control  (Birkhäuser, Boston, 2015) and Advanced Control of Aircraft, Spacecraft, and Rockets (Wiley, Chichester, 2011). He is also the author of several research papers in aircraft and spacecraft dynamics and control systems. He is an Associate Fellow of the American Institute of Aeronautics and Astronautics (AIAA), and a Senior Member of the Institution of Electrical and Electronics Engineers (IEEE). Prof. Tewari holds Ph.D.  and M.S. degrees in Aerospace Engineering from the University of Missouri-Rolla, and a B.Tech. degree in Aeronautical Engineering from the Indian Institute of Technology, Kanpur.

About the Author xv

Series Editor’s Preface xvii

Preface xix

1 Introduction 1

1.1 Aeroservoelasticity 1

1.2 Unsteady Aerodynamics 4

1.3 Linear Feedback Design 7

1.4 Parametric Uncertainty and Variation 11

1.5 Adaptive Control Design 13

1.5.1 Adaptive Control Laws 15

1.6 Organization 20

References 21

2 Linear Control Systems 23

2.1 Notation 23

2.2 Basic Control Concepts 23

2.3 Input–Output Representation 26

2.3.1 Gain and Stability 26

2.3.2 Small Gain Theorem 27

2.4 Input–Output Linear Systems 28

2.4.1 Laplace Transform and Transfer Function 30

2.5 Loop Shaping of Linear Control Systems 33

2.5.1 Nyquist Theorem 34

2.5.2 Gain and Phase Margins 36

2.5.3 Loop Shaping for Single Variable Systems 38

2.5.4 Singular Values 40

2.5.5 Multi-variable Robustness Analysis: Input–Output Model 42

2.6 State-Space Representation 42

2.6.1 State-Space Theory of Linear Systems 43

2.6.2 State Feedback by Eigenstructure Assignment 49

2.6.3 Linear Observers and Output Feedback Compensators 50

2.7 Stochastic Systems 52

2.7.1 Ergodic Processes 57

2.7.2 Filtering of Random Noise 59

2.7.3 Wiener Filter 60

2.7.4 Kalman Filter 61

2.8 Optimal Control 65

2.8.1 Euler–Lagrange Equations 65

2.8.2 Linear, Quadratic Optimal Control 67

2.9 Robust Control Design by LQG/LTR Synthesis 71

2.10 H2/H∞ Design 77

2.10.1 H2 Design Procedure 79

2.10.2 H∞ Design Procedure 80

2.11 𝜇-Synthesis 81

2.11.1 Linear Fractional Transformation 83

References 86

3 Aeroelastic Modelling 87

3.1 Structural Model 88

3.1.1 Statics 88

3.1.2 Dynamics 91

3.1.3 Typical Wing Section 93

3.2 Aerodynamic Modelling Concepts 98

3.2.1 Governing Equations for Unsteady Flow 99

3.2.2 Full-Potential Equation 100

3.2.3 Transonic Small-Disturbance Equation 104

3.3 Baseline Aerodynamic Model 106

3.3.1 Integral Equation Formulation 108

3.3.2 Subsonic Unsteady Aerodynamics 109

3.3.3 Supersonic Unsteady Aerodynamics 114

3.4 Preliminary Aeroelastic Modelling Concepts 115

3.5 Ideal Flow Model for Typical Section 120

3.6 Transient Aerodynamics of Typical Section 125

3.7 State-Space Model of the Typical Section 126

3.8 Generalized Aeroelastic Plant 128

References 135

4 Active Flutter Suppression 139

4.1 Single Degree-of-Freedom Flutter 141

4.2 Bending-Torsion Flutter 146

4.3 Active Suppression of Single Degree-of-Freedom Flutter 147

4.4 Active Flutter Suppression of Typical Section 153

4.4.1 Open-Loop Flutter Analysis 154

4.5 Linear Feedback Stabilization 157

4.5.1 Pole-Placement Regulator Design 157

4.5.2 Observer Design 160

4.5.3 Robustness of Compensated System 162

4.6 Active Flutter Suppression of Three-Dimensional Wings 164

References 168

5 Self-Tuning Regulation 171

5.1 Introduction 171

5.2 Online Plant Identification 172

5.2.1 Least-Squares Parameter Estimation 172

5.2.2 Least-Squares Method with Exponential Forgetting 174

5.2.3 Projection Algorithm 174

5.2.4 Autoregressive Identification 175

5.3 Design Methods for Stochastic Self-Tuning Regulators 176

5.4 Aeroservoelastic Applications 176

References 180

6 Nonlinear Systems Analysis and Design 181

6.1 Introduction 181

6.2 Preliminaries 182

6.2.1 Existence and Uniqueness of Solution 183

6.2.2 Expanded Solution 184

6.3 Stability in the Sense of Lyapunov 185

6.3.1 Local Linearization about Equilibrium Point 187

6.3.2 Lyapunov Stability Theorem 189

6.3.3 LaSalle Invariance Theorem 192

6.4 Input–Output Stability 192

6.4.1 Hamilton–Jacobi Inequality 193

6.4.2 Input-State Stability 194

6.5 Passivity 195

6.5.1 Positive Real Transfer Matrix 196

6.5.2 Stability of Passive Systems 198

6.5.3 Feedback Design for Passive Systems 200

References 201

7 Nonlinear Oscillatory Systems and Describing Functions 203

7.1 Introduction 203

7.2 Absolute Stability 205

7.2.1 Popov Stability Criteria 207

7.2.2 Circle Criterion 207

7.3 Describing Function Approximation 210

7.4 Applications to Aeroservoelastic Systems 212

7.4.1 Nonlinear and Uncertain Aeroelastic Plant 213

References 216

8 Model Reference Adaptation of Aeroservoelastic Systems 217

8.1 Lyapunov-Like Stability of Non-autonomous Systems 218

8.1.1 Uniform Ultimate Boundedness 219

8.1.2 Barbalat’s Lemma 220

8.1.3 LaSalle–Yoshizawa Theorem 220

8.2 Gradient-Based Adaptation 223

8.2.1 Least-Squared Error Adaptation 225

8.3 Lyapunov-Based Adaptation 225

8.3.1 Nonlinear Gain Evolution 228

8.3.2 MRAS for Single-Input Systems 231

8.4 Aeroservoelastic Applications 233

8.4.1 Reference Aeroelastic Model 234

8.4.2 Adaptive Flutter Suppression of Typical Section 236

8.4.3 Adaptive Stabilization of Flexible Fighter Aircraft 241

References 254

9 Adaptive Backstepping Control 255

9.1 Introduction 255

9.2 Integrator Backstepping 256

9.2.1 A Motivating Example 257

9.3 Aeroservoelastic Application 263

Reference 264

10 Adaptive Control of Uncertain Nonlinear Systems 265

10.1 Introduction 265

10.2 Integral Adaptation 266

10.2.1 Extension to Observer-Based Feedback 268

10.2.2 Modified Integral Adaptation with Observer 269

10.3 Model Reference Adaptation of Nonlinear Plant 273

10.4 Robust Model Reference Adaptation 275

10.4.1 Output-Feedback Design 285

10.4.2 Adaptive Flutter Suppression of a Three-Dimensional Wing 288

References 294

11 Adaptive Transonic Aeroservoelasticity 295

11.1 Steady Transonic Flow Characteristics 296

11.2 Unsteady Transonic Flow Characteristics 299

11.2.1 Thin Airfoil with Oscillating Flap 300

11.2.2 Supercritical Airfoil Oscillating in Pitch 308

11.3 Modelling for Transonic Unsteady Aerodynamics 310

11.3.1 Indicial Method 311

11.3.2 Volterra–Wiener Method 312

11.3.3 Describing Function Method 313

11.4 Transonic Aeroelastic Plant 316

11.5 Adaptive Control of Control-Surface Nonlinearity 317

11.5.1 Transonic Flutter Mechanism 319

11.6 Adaptive Control of Limit-Cycle Oscillation 322

References 330

Appendix A Analytical Solution for Ideal Unsteady Aerodynamics 331

A.1 Pure Heaving Oscillation 335

A.2 Küssner–Schwarz Solution for General Oscillation 336

References 337

Appendix B Solution to Possio’s Integral Equation for Subsonic, Unsteady

Aerodynamics 339

B.1 Dietze’s Iterative Solution 340

B.2 Analytical Solution by Fettis 341

B.3 Closed-Form Solution 344

References 345

Appendix C Flutter Analysis of Modified DAST-ARW1 Wing 347

References 357

Index 359

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