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 ¿-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
