Optimal turning maneuvers for six-degree-of-freedom high angle-of-attack aircraft models

168 Pages·2016·2.98 MB·English

Iowa State University Capstones, Theses and
Retrospective Theses and Dissertations
Dissertations
1995
Optimal turning maneuvers for six-degree-of-
freedom high angle-of-attack aircraft models
Jen-nai Chou
Iowa State University
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Recommended Citation
Chou, Jen-nai, "Optimal turning maneuvers for six-degree-of-freedom high angle-of-attack aircraft models " (1995).Retrospective
Theses and Dissertations. 10891.
https://lib.dr.iastate.edu/rtd/10891
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Optimal turning maneuvers for six-degree-of-freedom
high angle-of-attack aircraft models
by
Jen-nai Chou
A Dissertation Submitted to the
Graduate Faculty in Partial Fulfillment of the
Requirements for the Degree of
DOCTOR OF PHILOSOPHY
Department: Aerospace Engineering and Engineering Mechanics
Major: Aerospace Engineering
ApMoved: Members of the Committee:
Signature was redacted for privacy. Signature was redacted for privacy.
Signature was redacted for privacy.
Signature was redacted for privacy.
Signature was redacted for privacy.
For the Major Department
Signature was redacted for privacy.
Signature was redacted for privacy.
For the Graduate College
Iowa State University
Ames, Iowa
1995
Copyright © Jen-nai Chou, 1995. All rights reserved.
OMI Number: 9531727
DMI Hicrofoim 9531727
Copyright 1995, by UHl Compcuiy. All rights reserved.
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ii
TABLE OF CONTENTS
NOMENCLATURE xii
ABSTRACT xv
1. INTRODUCTION 1
2. DYNAMICS 5
2.1 Aircraft Models 5
2.2 Degrees of Freedom 6
2.3 Assumptions 7
2.4 Coordinate Systems 8
2.5 Euler Angles LI
2.5.1 Limitations of Euler Angles 12
2.6 Quaternions 12
2.6.1 System Transformation 15
2.6.2 Differential Equations 15
2.6.3 Euler Angle to Quaternion Transformation 16
2.7 Equations of Motion 16
3. METHODS AND NUMERICAL TECHNIQUES 22
3.1 Parameter Optimization 23
iii
3.1.1 Control Pajameterization 25
3.1.2 State Parameterization 27
3.2 Inverse Dynamics Approach 28
3.3 Control-Integration Approach 29
3.4 Nonlinear Programming Methods 32
3.4.1 Sequential Quadratic Programming 34
3.4.2 Nelder-Mead Simplex Method 35
3.5 Constraints 37
3.5.1 Control Constraints 38
3.5.2 Path Constraints 39
3.6 Interpolation Methods 41
3.7 Integration Schemes 43
3.8 Non-dimensionalization and Scaling 44
3.9 Singular Arc Problems 45
3.10 Homotopy Approach 47
4. PRELIMINARY INVESTIGATION 49
4.1 Van der Pol Problem 49
4.1.1 Original Van der Pol Problem 50
4.1.2 Constrained Van der Pol Problem 54
4.2 Soliman's Problem (Singular Arc Problem) 57
4.2.1 Original Soliman's Problem 57
4.2.2 Modified Soliman's Problem 60
4.3 Risk-Avoidance Trajectories 65
iv
5. MINIMUM-TIME TURNING MANEUVERS: PROBLEMS AND
RESULTS 75
5.1 Introduction 75
5.2 2-D Maximum-Flight-Path-Angle Problem 77
5.2.1 2-D Minimum-Time-to-Half-Loop Problem 79
5.2.2 3-D Minimum-Time-to-Half-Loop Problems 81
5.2.3 3-D Minimum-Time-to-Turn Problem 83
6. GLOBAL OPTIMIZATION 90
6.1 Introduction 90
6.2 Genetic Algorithm 91
6.3 Simulated Annealing 94
6.3.1 Adaptive Simulated Annealing 95
6.4 Hybrid Optimization 97
6.5 Results and Discussion 98
7. CONCLUSION 103
7.1 Work Performed 103
7.2 Main Contributions 105
7.3 Future Research 107
REFERENCES 109
ACKNOWLEDGMENTS 119
APPENDIX A. RISK-AVOIDANCE PROBLEM STATEMENTS . 120
APPENDIX B. OPTIMAL TRAJECTORIES 125
V
APPENDIX C. GLOBAL OPTIMAL MINIMUM-TIME-TO-HALF-
LOOP TRAJECTORIES 142
vi
LIST OF TABLES
Table 2.1: The Flat-Earth, Body Axes 6-DOF Equations for the F-16
Model 17
Table 4.1: Results of Van der Pol problem by different approaches ... 52
Table 5.1: 2-D High Alpha F-16 Half-Loop Maneuver Results 85
Table 5.2: 3-D High Alpha F-16 Minimum-Time-To-Half-Loop Maneu­
ver Results 86
Table 5.3: 3-D High Alpha F-16 Minimum-Time-Turn Maneuver Results 88
Table 6.1: Results of 3-D High Alpha F-16 Minimum-Time-to-HaJf-Loop
Maneuver by GA, ASA, and Hybrid Methods 101