●Contents
1 Introduction 1
1.1 Problem Description 1
1.2 Research Significance 2
1.3 Research Progress 4
References 8
2 Mathematical Fundamentals 11
2.1 Regular Perturbation Method 11
2.2 Singular Perturbation Method 13
2.3 Spectral Decomposition Method 16
2.3.1 Idempotent Matrix 16
2.3.2 Spectral Decomposition Theorem 16
2.3.3 Inference 17
2.3.4 Example 19
2.4 Pseudospectral Method 19
2.4.1 Introduction of Method 19
2.4.2 Pseudospectral Discrete Process 23
2.5 Linear Gauss Pseudospectral Model Predictive Control 33
References 38
3 Mathematical Modeling for Hypersonic Glide Problem 41
3.1 The Coordinate System Adopted in This Book 41
3.1.1 Geocentric Inertial Coordinate System (I) 41
3.1.2 Geographic Coordinate System (T) 41
3.1.3 Orientation Coordinate System (O) 42
3.1.4 Velocity Coordinate System (V) 42
3.1.5 Half-Velocity Coordinate System (H) 42
3.1.6 Body Coordinate System (B) 43
3.2 Transformation Between Coordinate Systems 43
3.2.1 Transformation Between the Orientation Coordinate System and the Half-Velocity Coordinate System 43
3.2.2 Transformation Between the Velocity Coordinate System and the Half-Velocity Coordinate System 43
3.2.3 Transformation Between the Velocity Coordinate System and the Body Coordinate System 44
3.2.4 Transformation Between the Body Coordinate System and the Half-Velocity Coordinate System 45
3.3 Dynamic Equations of Hypersonic Vehicle in Half-Velocity Coordinate System 45
3.3.1 Dynamics Equations of the Center of Mass in Half-Velocity Coordinate System 45
3.3.2 The Dynamic Equations of the Center of Mass of the Vehicle 48
3.3.3 Dynamic Equations of Hypersonic Gliding Vehicle Based on BTT Control 48
3.3.4 Dynamic Equations of Hypersonic Vehicle in Vertical Plane 49
3.3.5 Atmospheric Model 50
3.3.6 Aerodynamic Model 50
3.3.7 The Stagnation Point Heat Flow，Overload and Dynamic Pressure 50
4 Mathematical Description of Glide-Trajectory Optimization Problem 53
4.1 Mathematical Description for Optimal Control Problem 53
4.1.1 Performance Index of Optimal Control Problem 53
4.1.2 Description of Optimal Control Problem 54
4.1.3 The Minimum Principle 55
4.1.4 Final Value Performance Index of Time-Invariant Systems 56
4.1.5 Integral Performance Index of Time-Invariant Systems 57
4.1.6 Optimal Control Problem with Inequality Constraints 58
4.1.7 Methods for Solving Optimal Control Problems 58
4.2 Mathematical Description of Optimal Control Problem for Hypersonic Vehicle Entry Glide 61
4.2.1 Maximum Final Speed Problem 61
4.2.2 Maximum Range Problem 62
4.2.3 Shortest Time Problem 62
4.2.4 Optimal Trajectory Problem with Heating Rate Constraint 63
4.2.5 Optimal Trajectory Problem with Heating Rate and Load Factor Constraints 64
5 Indirect Approach to the Optimal Glide Trajectory Problem 65
5.1 Combined Optimization Strategy for Solving the Optimal Gliding Trajectory of Hypersonic Aircraft 67
5.1.1 Mathematical Model of Hypersonic Gliding 67
5.1.2 Necessary Conditions for Optimal Gliding Trajectory 68
5.1.3 Solving Two-Point Boundary Value Problem by Combination Optimization Strategy 69
5.1.4 Numerical Calculation Results 70
5.1.5 Conclusion 73
5.2 Trajectory Optimization of Transition Section of Gliding Hypersonic Flight Vehicle 74
5.2.1 Aerodynamic Data for the Transition Section 74
5.2.2 Unconstrained Trajectory of Maximum Terminal Velocity 75
5.2.3 Heat Flow Constrained Trajectory of Maximum Terminal Velocity 76
5.2.4 Solving the Two-Point Boundary Value Problem for the Transition Section 77
5.2.5 Optimizing the Transition Trajectory with Direct Method 77
5.2.6 Steps for Solving the Optimal Transition Trajectory 78
5.2.7 Transitional Trajectory Obtained by Indirect Method 81
5.3 The Maximum Range Gliding Trajectory of the Hypersonic Aircraft 84
5.3.1 Guess Initial Values for Optimal Control Problem by Direct Method 84
5.3.2 Indirect Method for Solving Optimal Control Problems 89
5.3.3 The Maximum Range Gliding Trajectory of the Hypersonic Aircraft 94
References 101
6 Direct Method for Gliding Trajectory Optimization Problem 103
6.1 Direct Method for Solving Optimal Control Problems 103
6.2 Direct Shooting Method 104
6.2.1 Direct ltiple Shooting Method 104
6.2.2 Direct Method of Discrete Control 105
6.2.3 Gradual Subdividing Optimization Strategy 106
6.3 Direct Collocation Method 107
6.3.1 General Form of Direct Collocation Method 107
6.3.2 Direct Transcription 108
6.3.3 Implicit Integral Method 109
6.3.4 Solving Optimal Trajectory Problems with NLP 110
6.4 Direct Collocating Method for Trajectory with Maximum Gliding Cross Range of Hypersonic Aircraft 111
6.4.1 Mathematical Model 111
6.4.2 Re-entry Flight Control Law with Given Angle of Attack Profile 113
6.4.3 Solution of Maximum Cross Range Problem by Direct Collocation Method 113
6.4.4 Optimization Example 116
6.4.5 Summary 118
6.5 Pseudospectral Method for the Optimal Trajectory of the Hypersonic Vehicle with the Longest Cross-Range 119
6.5.1 Introduction of Pseudospectral Method 119
6.5.2 Optimization Examples and Results 122
7 Concept of Steady Glide Reentry Trajectory and Stability of Its Regular Perturbation Solutions 125
7.1 Introduction 125
7.2 Kinetic Equations 126
7.3 Definition of the Steady Glide Trajectory 127
7.4 Effects of Control Variable on SGT 128
7.5 Effects of Initial Value on SGT 129
7.6 Analytical Solution of SGT 129
7.6.1 Altitude Dynamic Differential Equation 129
7.6.2 Analytical Steady Glide Altitude 131
7.6.3 Analytical Solutions of Flight-Path Angle and Vertical Acceleration 134
7.7 Dynamic Characteristics of SGT 135
7.7.1 Stability Analysis 135
7.7.2 Natural Frequency and Damping 137
7.8 Feedback Control of SGT 140
7.8.1 Feedback Design 140
7.8.2 Fixed-Damping Differential Feedback Method 144
7.9 Conclusions 147
References 147
8 Analytical Solutions of Steady Glide Reentry Trajectory in Three Dimensions and Their Application to Trajectory Planning 149
8.1 Introduction 149
8.2 Mathematical Model 150
8.2.1 Definition of Coordinate Frame 150
8.2.2 Kinematic Equations 150
8.2.3 Decoupling of Equations 152
8.3 Analytical Solution of Glide Trajectory 153
8.3.1 Analytical Solution of Altitude 153
8.3.2 Analytical Solution of Range 154
8.3.3 Analytical Solution of Heading Angle 154
8.3.4 Analytical Solution of Longitude and Latitude 155
8.3.5 Analytical Solution of Velocity 156
8.3.6 Optimal Initial Glide Angle 157
8.4 Simulation 157
8.4.1 Comparison Between Analytical Solution and Numerical Integral 157
8.4.2 Comparison with Bell Analytical Solution 157
8.4.3 Application of Analytic Solutions in Trajectory Planning 160
8.5 Summary 164
References 164
9 Trajectory Damping Control Technique for Hypersonic Glide Reentry 167
9.1 Introduction 167
9.2 Guidance Scheme 168
9.2.1 Mathematical Proof 168
9.2.2 Command Flight-Path Angle for L/Dmax 170
9.2.3 Guidance Scheme for Range Maximization and Trajectory Damping Control 172
9.2.4 Extended Guidance Scheme for Glide Range Control 173
9.3 Hypersonic Vehicle Model 174
9.4 Results and Discussion 176
9.4.1 Performance of Guidance Scheme 176
9.4.2 Application of the Extended Guidance Scheme 183
9.5 Conclusions 189
References 189
10 Steady Glide Dynamic Modeling and Trajectory Optimization for High Lift-To-Drag Ratio Reentry Vehicle 191
10.1 Introduction 191
10.2 Dynamics and Vehicle Description 193
10.2.1 Entry Dynamics 193
10.2.2 Entry Trajectory Constraints 194
10.2.3 Vehicle Description and Model Assumption 194
10.3 Trajectory-Oscillation Suppressing Scheme 195
10.3.1 Generic Theory for the Oscillation Suppressing Scheme 195
10.3.2 Performance of the Trajectory-Oscillation Suppressing Scheme 197
10.4 Steady Glide Dynamic Modeling and Trajectory Optimization 198
10.4.1 Steady Glide Dynamic Modeling 199
10.4.2 Hp-Adaptive Gaussian Quadrature Collocation Method 200
10.4.3 Numerical Example of Trajectory Optimization Without Bank Reversal 201
10.4.4 Numerical Example of Trajectory Optimization with Bank Reversal 205
10.4.5 Verification of Feasibility for the Pseudospectral Solution 206
10.5 Conclusion 209
References 210
11 Singular Perturbation Guidance of Hypersonic Glide Reentry 213
11.1 Singular Perturbation Guidance for Range Maximization of a Hypersonic Glider 213
11.1.1 Problem Formulation (Dimensionless Model) 213
11.1.2 Reduced-Order System Solutions 215
11.1.3 Slow-Boundary Layer Solutions 216
11.1.4 Fast-Boundary Layer Solutions 218
11.1.5 Simulation Results 220
11.1.6 Comparison and Analysis 221
11.2 Improved Singular Perturbation Guidance for Maximum Glide Range 225
11.2.1 Dynamic Model and Solutions to the Reduced-Order System 226
11.2.2 Boundary Layer Correction 227
11.2.3 Slow Boundary-Layer Correction 227
11.2.4 Fast Boundary-Layer Correction 228
11.2.5 Guidance Law Derivation 228
11.2.6 Simulation Results and Analyses 229
11.3 Summary 232
References 232
12 3-D Reentry Guidance with Real-Time Planning of Reference Using New Analytical Solutions Based on Spectral Decomposition Method 233
12.1 Introduction 233
12.2 Equations of Motion 235
12.3 Entry Trajectory Constraints 237
12.3.1 Path Constraints 237
12.3.2 Terminal Conditions 237
12.4 Analytical Solutions to Hypersonic Gliding Problem 237
12.4.1 Auxiliary Geocentric Inertial (AGI) Frame 237
12.4.2 Linearization of the Equations of Motion 239
12.4.3 Analytical Solutions 241
12.4.4 Example for Accuracy Verification 245
12.5 Entry Guidance 248
12.5.1 Descent Phase 248
12.5.2 Quasi-Equilibrium Glide Phase 249
12.5.3 Altitude Adjustment Phase 260
12.5.4 Results and Discussion 262
12.5.5 Nominal Cases 262
12.6 Conclusions 273
Appendix 273
References 275
13 Omnidirecdonal Autonomous Reentry Guidance Based on 3-D Analytical Glide Formulae Considering Influence of Earth’s Rotation 277
13.1 Introduction 277
13.2 Entry Guidance Problem 280
13.2.1 Equations of Motion 280
13.2.2 Path Constraints 281
13.2.3 Terminal Conditions 282
13.3 Omnidirectional Autonomous Entry Guidance 282
13.3.1 Overview 282
13.3.2 Descent Phase 285
13.33 Steady Glide Phase 286
13.4 Altitude Adjustment Phase 300
13.4.1 Correction of Baseline AOA Profile and Second Bank Reversal 300
13.4.2 Baseline Bank Angle in AAP 304
13.4.3 AOA and Bank Angle Commands in AAP 305
13.5 Results and Discussion 306
13.5.1 Nominal Cases 306
13.5.2 Monte Carlo Simulations 309
13.6 Conclusions 314
Appendix 1: Generalized States of Motion 315
Appendix 2: Generalized Aerodynamic Forces 318
References 319
14 Analytical Steady-Gliding Guidance Employing Pseudo-Aerodynamic Profiles 323
14.1 Introduction 323
14.2 Entry Guidance Problem 325
14.2.1 Equations of Motion 325
14.2.2 Path Constraints 326
14.2.3 Terminal Conditions 327
14.3 Analytical Entry Guidance Design 327
14.3.1 Descent Phase 328
14.3.2 Steady Glide Phase 328
14.3.3 Altitude Adjustment Phase 344
14.4 Results and Discussion 349
14.4.1 Nominal Cases 349
14.4.2 Monte Carlo Simulations 354
14.5 Conclusions 361
References 364
15 Linear Pseudospectral Guidance Method for Eliminating General Nominal Effort Miss Distance 365
15.1 Introduction 365
15.2 Generic Theory of LGPMPC 366
15.2.1 Linearization of Nonlinear Dynamic System and Formulation of Linear Optimal Control Problem 367
15.2.2 Linear Gauss Pseudospectral Method 369
15.2.3 Singularity of Differential Approximation Matrices for Different Pseudospctral Methods 374
15.2.4 Boundary Control of Linear Gauss Pseudospctral Method 374
15.2.5 Implementation of LGPMPC 375
15.3 Application to Terminal Guidance 377
15.3.1 Terminal Guidance Problem and Three-Dimensional Mode 377
15.3.2 Initial Guess and Target Model 379
15.3.3 Cases for Target with Straight-Line Movements 380
15.3.4 Comparison with Adaptive Terminal Guidance 384
15.4 Conclusion 386
Appendix 387
References 388
16 Linear Pseudospectral Reentry Guidance with Adaptive Flight Phase Segmentation and Eliminating General Nominal Effort Miss Distance 389
16.1 Introduction 389
16.2 Entry Dynamics, Entry Trajectory Constraints and Vehicle Description 391
16.2.1 Entry Dynamics 391
16.2.2 Entry Trajectory Constraints 392
16.2.3 Vehicle Description and Model Assumption 393
16.2.4 Auxiliary Geocentric Inertial Frame and Emotion Dynamics 393
16.3 Linear Pseudospectral Model Predictive Entry Guidance 394
16.3.1 Descent Phase Guidance 395
16.3.2 Glide Phase Entry Guidance 395
16.3.3 Terminal Adjustment Phase 411
16.3.4 Implementation of the Proposed Method 416
16.4 Numeric Results and Discussion 417
16.4.1 Normal Cases for Various Destinations 417
16.4.2 Monte Carlo Simulations 423
16.5 Conclusion 430
References 431
17 Trajectory-shaping Guidance with Final Speed and Load Factor Constraints 433
17.1 Introduction 433
17.2 Equations of Motion 435
17.3 Guidance Law Overview 437
17.4 Trajectory Shaping Guidance 437
17.4.1 Guidance Form 437
17.4.2 Generalized Closed Form Solutions for TSG 438
17.4.3 Stability Domain of Guidance Coefficients 448
17.5 Final Speed Control Scheme 452
17.6 Model of CAV-H 453
11.1 Results and Discussion 454
17.8 Conclusions 460
References 460

本書從平穩滑翔的概念和基本理論－運動學、動力學和控制方程－平穩滑翔彈道的動態特性-平穩滑翔彈道的設計－基於平穩滑翔理論的制導方法全面繫統地介紹高超聲速飛行器再入平穩機動滑翔動力學與制導技術，在理論深度和應用參考性方面有自己的特色。主要內容包括：平穩滑翔再入動力學模型；平穩滑翔彈道動態特性；彈道阻尼控制技術；基於平穩滑翔的彈道優化技術；基於平穩滑翔的線性偽譜廣義標控脫靶量制導；平穩滑翔彈道解析解；平穩機動滑翔突防彈道設計。