Steady Glide Dynamics and Guidance of Hypersonic Vehicle

Preface
Contents
Abbreviations
List of Figures
List of Tables
1 Introduction
1.1 Problem Description
1.2 Research Significance
1.3 Research Progress
References
2 Mathematical Fundamentals
2.1 Regular Perturbation Method
2.2 Singular Perturbation Method
2.3 Spectral Decomposition Method
2.3.1 Idempotent Matrix
2.3.2 Spectral Decomposition Theorem
2.3.3 Inference
2.3.4 Example
2.4 Pseudospectral Method
2.4.1 Introduction of Method
2.4.2 Pseudospectral Discrete Process
2.5 Linear Gauss Pseudospectral Model Predictive Control
References
3 Mathematical Modeling for Hypersonic Glide Problem
3.1 The Coordinate System Adopted in This Book
3.1.1 Geocentric Inertial Coordinate System (I)
3.1.2 Geographic Coordinate System (T)
3.1.3 Orientation Coordinate System (O)
3.1.4 Velocity Coordinate System (V)
3.1.5 Half-Velocity Coordinate System (H)
3.1.6 Body Coordinate System (B)
3.2 Transformation Between Coordinate Systems
3.2.1 Transformation Between the Orientation Coordinate System and the Half-Velocity Coordinate System
3.2.2 Transformation Between the Velocity Coordinate System and the Half-Velocity Coordinate System
3.2.3 Transformation Between the Velocity Coordinate System and the Body Coordinate System
3.2.4 Transformation Between the Body Coordinate System and the Half-Velocity Coordinate System
3.3 Dynamic Equations of Hypersonic Vehicle in Half-Velocity Coordinate System
3.3.1 Dynamics Equations of the Center of Mass in Half-Velocity Coordinate System
3.3.2 The Dynamic Equations of the Center of Mass of the Vehicle
3.3.3 Dynamic Equations of Hypersonic Gliding Vehicle Based on BTT Control
3.3.4 Dynamic Equations of Hypersonic Vehicle in Vertical Plane
3.3.5 Atmospheric Model
3.3.6 Aerodynamic Model
3.3.7 The Stagnation Point Heat Flow, Overload and Dynamic Pressure
4 Mathematical Description of Glide-Trajectory Optimization Problem
4.1 Mathematical Description for Optimal Control Problem
4.1.1 Performance Index of Optimal Control Problem
4.1.2 Description of Optimal Control Problem
4.1.3 The Minimum Principle
4.1.4 Final Value Performance Index of Time-Invariant Systems
4.1.5 Integral Performance Index of Time-Invariant Systems
4.1.6 Optimal Control Problem with Inequality Constraints
4.1.7 Methods for Solving Optimal Control Problems
4.2 Mathematical Description of Optimal Control Problem for Hypersonic Vehicle Entry Glide
4.2.1 Maximum Final Speed Problem
4.2.2 Maximum Range Problem
4.2.3 Shortest Time Problem
4.2.4 Optimal Trajectory Problem with Heating Rate Constraint
4.2.5 Optimal Trajectory Problem with Heating Rate and Load Factor Constraints
5 Indirect Approach to the Optimal Glide Trajectory Problem
5.1 Combined Optimization Strategy for Solving the Optimal Gliding Trajectory of Hypersonic Aircraft
5.1.1 Mathematical Model of Hypersonic Gliding
5.1.2 Necessary Conditions for Optimal Gliding Trajectory
5.1.3 Solving Two-Point Boundary Value Problem by Combination Optimization Strategy
5.1.4 Numerical Calculation Results
5.1.5 Conclusion
5.2 Trajectory Optimization of Transition Section of Gliding Hypersonic Flight Vehicle
5.2.1 Aerodynamic Data for the Transition Section
5.2.2 Unconstrained Trajectory of Maximum Terminal Velocity
5.2.3 Heat Flow Constrained Trajectory of Maximum Terminal Velocity
5.2.4 Solving the Two-Point Boundary Value Problem for the Transition Section
5.2.5 Optimizing the Transition Trajectory with Direct Method
5.2.6 Steps for Solving the Optimal Transition Trajectory
5.2.7 Transitional Trajectory Obtained by Indirect Method
5.3 The Maximum Range Gliding Trajectory of the Hypersonic Aircraft
5.3.1 Guess Initial Values for Optimal Control Problem by Direct Method
5.3.2 Indirect Method for Solving Optimal Control Problems
5.3.3 The Maximum Range Gliding Trajectory of the Hypersonic Aircraft
References
6 Direct Method for Gliding Trajectory Optimization Problem
6.1 Direct Method for Solving Optimal Control Problems
6.2 Direct Shooting Method
6.2.1 Direct Multiple Shooting Method
6.2.2 Direct Method of Discrete Control
6.2.3 Gradual Subdividing Optimization Strategy
6.3 Direct Collocation Method
6.3.1 General Form of Direct Collocation Method
6.3.2 Direct Transcription
6.3.3 Implicit Integral Method
6.3.4 Solving Optimal Trajectory Problems with NLP
6.4 Direct Collocating Method for Trajectory with Maximum Gliding Cross Range of Hypersonic Aircraft
6.4.1 Mathematical Model
6.4.2 Re-entry Flight Control Law with Given Angle of Attack Profile
6.4.3 Solution of Maximum Cross Range Problem by Direct Collocation Method
6.4.4 Optimization Example
6.4.5 Summary
6.5 Pseudo-spectral Method for the Optimal Trajectory of the Hypersonic Vehicle with the Longest Cross-Range
6.5.1 Introduction of Pseudo-spectral Method
6.5.2 Optimization Examples and Results
7 Concept of Steady Glide Reentry Trajectory and Stability of Its Regular Perturbation Solutions
7.1 Introduction
7.2 Kinetic Equations
7.3 Definition of the Steady Glide Trajectory
7.4 Effects of Control Variable on SGT
7.5 Effects of Initial Value on SGT
7.6 Analytical Solution of SGT
7.6.1 Altitude Dynamic Differential Equation
7.6.2 Analytical Steady Glide Altitude
7.6.3 Second-Order Item
7.6.4 Analytical Solutions of Flight Path Angle and Vertical Acceleration
7.7 Dynamic Characteristics of SGT
7.7.1 Stability Analysis
7.7.2 Natural Frequency and Damping
7.8 Feedback Control of SGT
7.8.1 Feedback Design
7.8.2 Fixed-Damping Differential Feedback Method
7.9 Conclusions
References
8 Analytical Solutions of Steady Glide Reentry Trajectory in Three Dimensions and Their Application to Trajectory Planning
8.1 Introduction
8.2 Mathematical Model
8.2.1 Definition of Coordinate Frame
8.2.2 Kinematic Equations
8.2.3 Decoupling of Equations
8.3 Analytical Solution of Glide Trajectory
8.3.1 Analytical Solution of Altitude
8.3.2 Analytical Solution of Range
8.3.3 Analytical Solution of Heading Angle
8.3.4 Analytical Solution of Longitude and Latitude
8.3.5 Analytical Solution of Velocity
8.3.6 Optimal Initial Glide Angle
8.4 Simulation
8.4.1 Comparison Between Analytical Solution and Numerical Integral
8.4.2 Comparison with Bell Analytical Solution
8.4.3 Application of Analytic Solutions in Trajectory Planning
8.5 Summary
References
9 Trajectory Damping Control Technique for Hypersonic Glide Reentry
9.1 Introduction
9.2 Guidance Scheme
9.2.1 Mathematical Proof
9.2.2 Command Flight-Path Angle for L/Dmax
9.2.3 Guidance Scheme for Range Maximization and Trajectory Damping Control
9.2.4 Extended Guidance Scheme for Glide Range Control
9.3 Hypersonic Vehicle Model
9.4 Results and Discussion
9.4.1 Performance of Guidance Scheme
9.4.2 Application of the Extended Guidance Scheme
9.5 Conclusions
References
10 Steady Glide Dynamic Modeling and Trajectory Optimization for High Lift-To-Drag Ratio Reentry Vehicle
10.1 Introduction
10.2 Dynamics and Vehicle Description
10.2.1 Entry Dynamics
10.2.2 Entry Trajectory Constraints
10.2.3 Vehicle Description and Model Assumption
10.3 Trajectory-Oscillation Suppressing Scheme
10.3.1 Generic Theory for the Oscillation Suppressing Scheme
10.3.2 Performance of the Trajectory-Oscillation Suppressing Scheme
10.4 Steady Glide Dynamic Modeling and Trajectory Optimization
10.4.1 Steady Glide Dynamic Modeling
10.4.2 Hp-Adaptive Gaussian Quadrature Collocation Method
10.4.3 Numerical Example of Trajectory Optimization Without Bank Reversal
10.4.4 Numerical Example of Trajectory Optimization with Bank Reversal
10.4.5 Verification of Feasibility for the Pseudospectral Solution
10.5 Conclusion
References
11 Singular Perturbation Guidance of Hypersonic Glide Reentry
11.1 Singular Perturbation Guidance for Range Maximization of a Hypersonic Glider
11.1.1 Problem Formulation (Dimensionless Model)
11.1.2 Reduced-Order System Solutions
11.1.3 Slow-Boundary Layer Solutions
11.1.4 Fast-Boundary Layer Solutions
11.1.5 Simulation Results
11.1.6 Comparison and Analysis
11.2 Improved Singular Perturbation Guidance for Maximum Glide Range
11.2.1 Dynamic Model and Solutions to the Reduced-Order System
11.2.2 Boundary Layer Correction
11.2.3 Slow Boundary-Layer Correction
11.2.4 Fast Boundary-Layer Correction
11.2.5 Guidance Law Derivation
11.2.6 Simulation Results and Analyses
11.3 Summary
References
12 3-D Reentry Guidance with Real-Time Planning of Reference using New Analytical Solutions Based on Spectral Decomposition Method
12.1 Introduction
12.2 Equations of Motion
12.3 Entry Trajectory Constraints
12.3.1 Path Constraints
12.3.2 Terminal Conditions
12.4 Analytical Solutions to Hypersonic Gliding Problem
12.4.1 Auxiliary Geocentric Inertial (AGI) Frame
12.4.2 Linearization of the Equations of Motion
12.4.3 Analytical Solutions
12.4.4 Example for Accuracy Verification
12.5 Entry Guidance
12.5.1 Descent Phase
12.5.2 Quasi-Equilibrium Glide Phase
12.5.3 Altitude Adjustment Phase
12.5.4 Results and Discussion
12.5.5 Nominal Cases
12.6 Conclusions
Appendix
References
13 Omnidirectional Autonomous Reentry Guidance Based on 3-D Analytical Glide Formulae Considering Influence of Earth’s Rotation
13.1 Introduction
13.2 Entry Guidance Problem
13.2.1 Equations of Motion
13.2.2 Path Constraints
13.2.3 Terminal Conditions
13.3 Omnidirectional Autonomous Entry Guidance
13.3.1 Overview
13.3.2 Descent Phase
13.3.3 Steady Glide Phase
13.4 Altitude Adjustment Phase
13.4.1 Correction of Baseline AOA Profile and Second Bank Reversal
13.4.2 Baseline Bank Angle in AAP
13.4.3 AOA and Bank Angle Commands in AAP
13.5 Results and Discussion
13.5.1 Nominal Cases
13.5.2 Monte Carlo Simulations
13.6 Conclusions
Appendix 1: Generalized States of Motion
Appendix 2: Generalized Aerodynamic Forces
References
14 Analytical Steady-Gliding Guidance Employing Pseudo-Aerodynamic Profiles
14.1 Introduction
14.2 Entry Guidance Problem
14.2.1 Equations of Motion
14.2.2 Path Constraints
14.2.3 Terminal Conditions
14.3 Analytical Entry Guidance Design
14.3.1 Descent Phase
14.3.2 Steady Glide Phase
14.3.3 Altitude Adjustment Phase
14.4 Results and Discussion
14.4.1 Nominal Cases
14.4.2 Monte Carlo Simulations
14.5 Conclusions
References
15 Linear Pseudospectral Guidance Method for Eliminating General Nominal Effort Miss Distance
15.1 Introduction
15.2 Generic Theory of LGPMPC
15.2.1 Linearization of Nonlinear Dynamic System and Formulation of Linear Optimal Control Problem
15.2.2 Linear Gauss Pseudospectral Method
15.2.3 Singularity of Differential Approximation Matrices for Different Pseudospctral Methods
15.2.4 Boundary Control of Linear Gauss Pseudospctral Method
15.2.5 Implementation of LGPMPC
15.3 Application to Terminal Guidance
15.3.1 Terminal Guidance Problem and Three-Dimensional Mode
15.3.2 Initial Guess and Target Model
15.3.3 Cases for Target with Straight-Line Movements
15.3.4 Comparison with Adaptive Terminal Guidance
15.4 Conclusion
Appendix
References
16 Linear Pseudospectral Reentry Guidance with Adaptive Flight Phase Segmentation and Eliminating General Nominal Effort Miss Distance
16.1 Introduction
16.2 Entry Dynamics, Entry Trajectory Constraints and Vehicle Description
16.2.1 Entry Dynamics
16.2.2 Entry Trajectory Constraints
16.2.3 Vehicle Description and Model Assumption
16.2.4 Auxiliary Geocentric Inertial Frame and Emotion Dynamics
16.3 Linear Pseudospectral Model Predictive Entry Guidance
16.3.1 Descent Phase Guidance
16.3.2 Glide Phase Entry Guidance
16.3.3 Terminal Adjustment Phase
16.3.4 Implementation of the Proposed Method
16.4 Numeric Results and Discussion
16.4.1 Normal Cases for Various Destinations
16.4.2 Monte Carlo Simulations
16.5 Conclusion
References
17 Trajectory-shaping Guidance with Final Speed and Load Factor Constraints
17.1 Introduction
17.2 Equations of Motion
17.3 Guidance Law Overview
17.4 Trajectory Shaping Guidance
17.4.1 Guidance Form
17.4.2 Generalized Closed Form Solutions for TSG
17.4.3 Stability Domain of Guidance Coefficients
17.5 Final Speed Control Scheme
17.6 Model of CAV-H
17.7 Results and Discussion
17.8 Conclusions
References