Iowa State University Capstones, Theses and Graduate Theses and Dissertations Dissertations 2010 Dynamic modeling and ascent flight control of Ares-I Crew Launch Vehicle Wei Du Iowa State University Follow this and additional works at:https://lib.dr.iastate.edu/etd Part of theAerospace Engineering Commons Recommended Citation Du, Wei, "Dynamic modeling and ascent flight control of Ares-I Crew Launch Vehicle" (2010).Graduate Theses and Dissertations. 11540. https://lib.dr.iastate.edu/etd/11540 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please [email protected]. Dynamic modeling and ascent flight control of Ares-I Crew Launch Vehicle by Wei Du A dissertation submitted to the graduate faculty in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Major: Aerospace Engineering Program of Study Committee: Bong Wie, Major Professor Ping Lu Thomas J. Rudolphi Zhijian Wang John Basart Iowa State University Ames, Iowa 2010 Copyright (cid:13)c Wei Du, 2010. All rights reserved. ii TABLE OF CONTENTS LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi CHAPTER 1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Ares-I Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Ares-I Mission Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Interaction Between Structures and Flight Control System . . . . . . . . . . . . 5 1.5 Underactuated Control Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 6 CHAPTER 2. 6-DEGREE-OF-FEEDOM DYNAMIC MODELING . . . . . 7 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Reference Frames and Rotational Kinematics . . . . . . . . . . . . . . . . . . . 8 2.2.1 Earth-Centered Inertial Reference Frame . . . . . . . . . . . . . . . . . 8 2.2.2 Earth-Fixed Equatorial Reference Frame . . . . . . . . . . . . . . . . . . 9 2.2.3 Body-Fixed Reference Frame . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.4 Structural Reference Frame . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.5 Earth-Fixed Launch Pad Reference Frame . . . . . . . . . . . . . . . . . 11 2.2.6 Euler Angles and Quaternions . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.7 Initial Position of Ares-I CLV on the Launch Pad . . . . . . . . . . . . . 13 iii 2.3 The 6-DOF Equations of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3.1 Aerodynamic Forces and Moments . . . . . . . . . . . . . . . . . . . . . 15 2.3.2 Gravity Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3.3 Rocket Propulsion Model . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.3.4 Guidance and Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3.5 Flexible-Body Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.4 Simulation Results of the Rigid Body Ares-I Crew Launch Vehicle . . . . . . . 21 CHAPTER 3. ANALYSIS AND DESIGN OF ASCENT FLIGHT CON- TROL SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2 Pitch Control Analysis of Rigid Launch Vehicles . . . . . . . . . . . . . . . . . 34 3.3 Pitch Control of a Rigid-Body Model of the Ares-I CLV . . . . . . . . . . . . . 39 3.4 Flexible-Body Control of an Ares-I Reference Model . . . . . . . . . . . . . . . 41 3.5 NMP Structural Filter Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.6 Robust Analysis for Structural Filters Design . . . . . . . . . . . . . . . . . . . 49 3.6.1 Uncertainty Description of Rigid-Body Model . . . . . . . . . . . . . . . 49 3.6.2 Uncertainty Description of Flexible-Body Model . . . . . . . . . . . . . 51 3.6.3 Robust Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 54 CHAPTER 4. UNCONTROLLED ROLL DRIFT . . . . . . . . . . . . . . . . 58 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.2 Pitch/Yaw Closed-Loop Instability Caused by Uncontrolled Roll Drift . . . . . 59 4.3 Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.3.1 Simplified Nonlinear Closed-Loop Pitch/Yaw Dynamics . . . . . . . . . 62 4.3.2 Linear Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.3.3 Nonlinear Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.4 New Pitch/Yaw Control Logic with Modified Commanded Quaternions . . . . 79 4.5 Simple Adjustment of Control Gains . . . . . . . . . . . . . . . . . . . . . . . . 85 4.5.1 Rigid Body 6-DOF Nonlinear Simulation Results . . . . . . . . . . . . . 86 iv CHAPTER 5. UNDERACTUATED CONTROL PROBLEM OF AN AX- ISYMMETRIC RIGID BODY . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.2 Steady-State Oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.3 Modified Attitude Quaternion Feedback Control Law . . . . . . . . . . . . . . . 98 5.4 Nonlinear Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 5.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.6 A Special Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 CHAPTER 6. CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 110 APPENDIX A. A SUMMARY OF THE 6-DOF EQUATIONS OF MOTION 112 APPENDIX B. ADDITIONAL FIGURES FROM 6-DOF SIMULATION . 114 B.1 Atmospheric Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 B.2 Aerodynamic Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 APPENDIX C. LINEARIZATION RESULTS . . . . . . . . . . . . . . . . . . 122 C.1 Nonlinear 6-DOF Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 C.2 Linear Rigid-Body Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 C.3 Linear State-Space Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 C.4 Linear Flexible-Body Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 APPENDIX D. ATTITUDE ERROR QUATERNION KINEMATIC DIF- FERENTIAL EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 APPENDIX E. LINEAR MODEL OF UNCONTROLLED ROLL DRIFT WITH AERODYNAMIC DISTURBANCE . . . . . . . . . . . . . . . . . . 131 APPENDIX F. DERIVATION OF A STEADY-STATE OSCILLATION . . 133 F.1 A Steady-State Oscillation of the Autonomous System . . . . . . . . . . . . . . 133 F.2 Solution of the Quadratic Matrix Equation . . . . . . . . . . . . . . . . . . . . 135 F.3 State Equations of the Steady-State Oscillation . . . . . . . . . . . . . . . . . . 137 v APPENDIX G. DERIVATION OF THE DERIVATIVE OF A LYAPUNOV FUNCTION CANDIDATE. . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 vi LIST OF TABLES Table 2.1 Initial conditions at liftoff . . . . . . . . . . . . . . . . . . . . . . . . . 22 Table 3.1 Ares-I reference parameters at t = 60 sec . . . . . . . . . . . . . . . . . 39 Table 3.2 Ares-I structural bending modes for the pitch axis . . . . . . . . . . . . 41 Table 3.3 Ares-I structural bending modes for the yaw axis . . . . . . . . . . . . 41 Table 3.4 Ares-I rigid-body parametric uncertainty . . . . . . . . . . . . . . . . . 50 Table 4.1 Reference Ares-I CLV parameters at t = 60 sec. . . . . . . . . . . . . . 62 Table 4.2 Routh arrays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 Table 4.3 Three cases for root locus stability analysis. . . . . . . . . . . . . . . . 65 Table 4.4 Three simulation cases for nonlinear stability analysis. . . . . . . . . . 70 Table 5.1 Ares-I reference parameters at t = 60 sec . . . . . . . . . . . . . . . . . 92 Table 5.2 Parameters of steady-state oscillation M . . . . . . . . . . . . . . . . . 93 2 Table 5.3 Simulation cases with p = 0.005 rad/sec . . . . . . . . . . . . . . . . . 99 vii LIST OF FIGURES Figure 1.1 Comparison of Space Shuttle, Ares-I, Ares-V, and Saturn V launch vehicles [1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Figure 1.2 Ares-I CLV configuration [2]. . . . . . . . . . . . . . . . . . . . . . . . 2 Figure 1.3 Flexible mode shapes and sensor locations of the Ares-I Crew Launch Vehicle [1]. Currently, rate-gyro blending is not considered for the Ares-I. 3 Figure 1.4 Ares-I CLV mission profile [2]. . . . . . . . . . . . . . . . . . . . . . . 4 Figure 1.5 Interactionbetweentheascentflightcontrolandthestructuralbending mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Figure 2.1 Ares-I CLV 6-DOF simulation block diagram. . . . . . . . . . . . . . . 7 Figure 2.2 Illustration of Earth-centered inertial reference frame {I~,J~,K~}, Earth- fixedreferenceframe{I~ ,J~ ,K~ }, structuralreferenceframe{~i ,~j ,~k }, e e e s s s and body-fixed reference frame {~i,~j,~k}. . . . . . . . . . . . . . . . . . 8 Figure 2.3 Launch Complex 39B at Kennedy Space Center . . . . . . . . . . . . . 9 Figure 2.4 Earth-fixed launch pad reference frame with a local tangent plan at Launch Complex 39B at Kennedy Space Center. . . . . . . . . . . . . 11 Figure 2.5 IllustrationoftheEarth-centeredinertialreferenceframewith{I~,J~,K~}, the Earth-fixed launch pad (up, east, north) reference frame, and the Ares-I orientation with {~i,~j,~k} on Launch Complex 39B. . . . . . . . . 13 Figure 2.6 A nominal ascent trajectory of Ares-I in the Earth-fixed launch pad reference frame. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Figure 2.7 A nominal ascent trajectory of Ares-I in the pitch plane. . . . . . . . . 24 viii Figure 2.8 Time histories of conventional roll, pitch, and yaw angles, (φ,θ,ψ), of the Ares-I CLV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Figure 2.9 Trajectory in ECI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Figure 2.10 Center of pressure and center of gravity. . . . . . . . . . . . . . . . . . 26 Figure 2.11 Center of gravity offset.. . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Figure 2.12 Relative velocity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Figure 2.13 Altitude. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Figure 2.14 Mach number. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Figure 2.15 Dynamic pressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Figure 2.16 Angle of attack and angle of sideslip. . . . . . . . . . . . . . . . . . . . 29 Figure 2.17 Bending load Qα . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 total Figure 2.18 RCS torque. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Figure 2.19 Angular velocity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Figure 2.20 Euler angles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Figure 2.21 Attitude quaternion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Figure 2.22 Attitude-error quaternion. . . . . . . . . . . . . . . . . . . . . . . . . . 32 Figure 2.23 Gimbal angles.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Figure 3.1 Reference trajectory and an operation point of Ares-I CLV in the pitch plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Figure 3.2 A simplified dynamic model of a launch vehicle for preliminary pitch control design. All angles are assumed to be small. . . . . . . . . . . . 35 Figure 3.3 Poles and zeros of Ares-I CLV rigid-body model transfer function. . . . 40 Figure 3.4 Root locus vs overall loop gain K of the pitch control system of a rigid Ares-I model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Figure 3.5 Block diagram of attitude control loop with flexible-body dynamics. . . 42 Figure 3.6 Flexible structure in the pitch plane. . . . . . . . . . . . . . . . . . . . 43 Figure 3.7 Block diagram of the flexible-body part of the pitch transfer function. 44 Figure 3.8 Pitch transfer function model of a reference model of the Ares-I CLV. . 44 ix Figure 3.9 Root locus of the pitch control system without structural filters. . . . . 45 Figure 3.10 Root locus of the pitch control system with two NMP structural filters. 47 Figure 3.11 Impulse responses for the pitch attitude θ (in degrees) of the flexible Ares-I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Figure 3.12 Impulseresponsesforthepitchgimbalangleδ(indegrees)oftheflexible Ares-I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Figure 3.13 General control configuration. . . . . . . . . . . . . . . . . . . . . . . . 50 Figure 3.14 M-∆ structure for robust stability analysis. . . . . . . . . . . . . . . . 51 Figure 3.15 Plant with multiplcative uncertainty. . . . . . . . . . . . . . . . . . . . 51 Figure 3.16 Bode plot of parameter uncertainty plant and perturbed plant samples. 52 Figure 3.17 Bode plot magnitude. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Figure 3.18 Block diagram of perturbed transfer function G (s). . . . . . . . . . . 54 pi Figure 3.19 Bode plot samples of G (s) with frequencies uncertainty and the flex boundary of perturbed models P3 G (s). . . . . . . . . . . . . . . . 55 i=1 pi Figure 3.20 Block diagram of perturbed attitude control system. . . . . . . . . . . 56 Figure 3.21 µ-plot for RS of structural filters design. . . . . . . . . . . . . . . . . . 57 Figure 4.1 Attitude quaternion for an unstable closed-loop system caused by un- controlled roll drift. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Figure 4.2 Euler angles for an unstable closed-loop system caused by uncontrolled roll drift. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Figure 4.3 Gimbal angles for an unstable closed-loop system caused by uncon- trolled roll drift. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Figure 4.4 A simplified block diagram representation of the quaternion based as- cent flight control system of Ares-I CLV. . . . . . . . . . . . . . . . . . 62 1−q2 Figure 4.5 Plot of the function B = 4e. . . . . . . . . . . . . . . . . . . . . . . 65 q4e Figure 4.6 Root locus plot for Case 1. . . . . . . . . . . . . . . . . . . . . . . . . . 66 Figure 4.7 Root locus plot for Case 2. . . . . . . . . . . . . . . . . . . . . . . . . . 67