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  • Nonlinear Fault-Tolerant Guidance and Control forDamaged Aircraft

    by

    Gong Xin Xu

    A thesis submitted in conformity with the requirementsfor the degree of Master of Applied Science

    Graduate Department of Aerospace Science and EngineeringUniversity of Toronto

    Copyright c 2011 by Gong Xin Xu

  • Abstract

    Nonlinear Fault-Tolerant Guidance and Control for Damaged Aircraft

    Gong Xin Xu

    g.xu@utoronto.ca

    Master of Applied Science

    Graduate Department of Aerospace Science and Engineering

    University of Toronto

    2011

    This research work presents a fault-tolerant flight guidance and control framework to

    deal with damaged aircraft. Damaged scenarios include the loss of thrust, actuator mal-

    function and airframe damage. The developed framework objective is to ensure that

    damaged aircraft can be stabilized and controlled at all times. The guidance system

    is responsible for providing the airspeed, vertical and horizontal flight path angle com-

    mands while considering aircraft dynamics. The control system, designed by the non-

    linear state-dependent Riccati equation (SDRE) control method, is used to track the

    guidance commands and to stabilize the damaged aircraft. The versatility of SDRE al-

    lows it to passively adapt to the aircraft parameter variations due to damage. A novel

    nonlinear adaptive control law is proposed to improve the controller performance. The

    new control law demonstrated improved tracking ability. The framework is implemented

    on the nonlinear Boeing 747 and NASA Generic Transport Model (GTM) to investigate

    the simulation results.

    ii

  • Acknowledgements

    I would like to express my deepest gratitude to my thesis supervisor Professor Hugh Liu

    for giving me the opportunity to work on the fault-tolerant flight control topic, and for

    his continuous guidance and support throughout the research. His encouragement and

    advice led me to the right path and are greatly appreciated.

    I would also like to thank the other members of my research committee, Professor

    Peter Grant and Professor Christopher Dameren for their valuable feedback and com-

    ments.

    My heartfelt appreciation also goes to the friends and colleagues at the Flight Systems

    and Control (FSC) group at UTIAS, Chen, Connie, Difu, Everett, Jason, Keith, Sohrab

    and others. They made my life at FSC an enjoyable and memorable experience.

    I would also like to extend my deepest gratitude to my family for their unconditional

    love and support.

    iii

  • Contents

    1 Introduction 1

    1.1 Aircraft Flight Control System Design . . . . . . . . . . . . . . . . . . . 1

    1.2 Research Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

    1.3 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

    1.4 Research Objectives & Contribution . . . . . . . . . . . . . . . . . . . . 7

    1.5 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

    2 Aircraft Dynamics 9

    2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

    2.2 Aircraft Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

    2.2.1 Nonlinear Equations of Motion . . . . . . . . . . . . . . . . . . . . 11

    2.3 Nonlinear Aerodynamic Coefficients . . . . . . . . . . . . . . . . . . . . . 14

    2.3.1 Boeing 747-100/200 . . . . . . . . . . . . . . . . . . . . . . . . . . 14

    2.3.2 NASA GTM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

    2.4 Damaged Aircraft Modeling . . . . . . . . . . . . . . . . . . . . . . . . . 17

    2.5 Trim Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

    2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

    3 Fault-tolerant Flight Guidance and Control Problem 25

    3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

    3.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

    3.3 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

    iv

  • 3.4 Aircraft Guidance Law Design . . . . . . . . . . . . . . . . . . . . . . . . 28

    3.5 Guidance Law Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

    3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

    4 State-Dependent Riccati Equation Control Method 33

    4.1 SDRE Control Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

    4.2 Stability and Optimality Analysis . . . . . . . . . . . . . . . . . . . . . . 38

    4.2.1 Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

    4.2.2 Optimality Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 39

    4.3 The Art and Capabilities of SDRE . . . . . . . . . . . . . . . . . . . . . 40

    4.4 Simulation Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

    4.4.1 Loss-of-thrust example - UAV example . . . . . . . . . . . . . . . 46

    4.4.2 Damaged Aircraft - B747 . . . . . . . . . . . . . . . . . . . . . . . 53

    4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

    5 Adaptive State-Dependent Riccati Equation Control Method 62

    5.1 Adaptive Control Method . . . . . . . . . . . . . . . . . . . . . . . . . . 65

    5.2 Stability Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

    5.2.1 Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

    5.3 Simulation Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

    5.3.1 Baseline Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

    5.3.2 Adaptive Law Design . . . . . . . . . . . . . . . . . . . . . . . . . 73

    5.3.3 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

    5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

    6 Conclusions and Future Work 78

    A Derivations 80

    B State-dependent coefficients 83

    v

  • Bibliography 87

    List of Tables

    2.1 Failure Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

    2.2 Trimmed States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

    2.3 Trimmed Controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

    4.1 Straight and Level Flight Trim Results . . . . . . . . . . . . . . . . . . . 46

    4.2 Design Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

    5.1 GTM Trim Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

    List of Figures

    1.1 Military and Civil Aircraft . . . . . . . . . . . . . . . . . . . . . . . . . . 2

    1.2 Mechanical and FBW Systems . . . . . . . . . . . . . . . . . . . . . . . . 2

    2.1 Aircraft Reference Frames . . . . . . . . . . . . . . . . . . . . . . . . . . 10

    2.2 Boeing 747 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

    2.3 NASA GTM Simulink Environment . . . . . . . . . . . . . . . . . . . . . 17

    2.4 GTM Damage Case Example . . . . . . . . . . . . . . . . . . . . . . . . 19

    2.5 Trim Routine Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

    2.6 B747 Trimmed Airspeed . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

    2.7 B747 Trimmed Roll Angle . . . . . . . . . . . . . . . . . . . . . . . . . . 22

    2.8 B747 Trimmed Angle of Attack . . . . . . . . . . . . . . . . . . . . . . . 23

    2.9 B747 Trimmed Pitch Angle . . . . . . . . . . . . . . . . . . . . . . . . . 23

    vi

  • 2.10 B747 Trimmed Sideslip Angle . . . . . . . . . . . . . . . . . . . . . . . . 23

    2.11 B747 Trimmed Yaw Angle . . . . . . . . . . . . . . . . . . . . . . . . . . 23

    2.12 B747 Trimmed Roll Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

    2.13 B747 Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

    2.14 B747 Trimmed Pitch Rate . . . . . . . . . . . . . . . . . . . . . . . . . . 23

    2.15 B747 Lateral Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

    2.16 B747 Trimmed Yaw Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

    2.17 B747 Altitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

    3.1 Proposed Guidance and Control Framework . . . . . . . . . . . . . . . . 27

    3.2 Guidance Law Illustration . . . . . . . . . . . . . . . . . . . . . . . . . . 29

    4.1 SDRE Design Flowchart . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

    4.2 Undamaged UAV: Airspeed Time History . . . . . . . . . . . . . . . . . 49

    4.3 Undamaged UAV: Flight Path Angle Time History . . . . . . . . . . . . 49

    4.4 Undamaged UAV: Angle of Attack Time History . . . . . . . . . . . . . . 49

    4.5 Undamaged UAV: Pitch Rate Time History . . . . . . . . . . . . . . . . 49

    4.6 Undamaged UAV: Throttle Control Time History . . . . . . . . . . . . . 49

    4.7 Undamaged UAV: Elevator Time History . . . . . . . . . . . . . . . . . . 49

    4.8 Undamaged UAV: Tracking Distance Error Time History . . . . . . . . . 50

    4.9 Undamaged UAV: Altitude Time History . . . . . . . . . . . . . . . . . . 50

    4.10 Damaged UAV: Airspeed Time History . . . . . . . . . . . . . . . . . . . 51

    4.11 Damaged UAV: Flight Path Angle Time History . . . . . . . . . . . . . . 51

    4.12 Damaged UAV: Angle of Attack Time History . . . . . . . . . . . . . . . 51

    4.13 Damaged UAV: Pitch Rate Time History . . . . .