NASA Contractor Report 4268 Design of Integrated Pitch Axis for Autopilot/Autothrottle and Integrated Lateral Axis for Autopilot/Yaw Damper for NASA TSRV Airplane Using Integral LQG Methodology Isaac Kaminer, Russell A. Bensnn, Edward E. Coleman, and Yaghoob S. Ebrahimi CONTRACT NAS1-18027 JAiVUARY 1990 NASA Contractor Report 4268 Design of Integrated Pitch Axis for Autopilot/Autothrottle and Integrated Lateral Axis for Autopilot/Yaw Damper for NASA TSRV Airplane Using Integral LQG Methodology Isaac Kaminer, Russell A. Benson, Edward E. Coleman, and Yaghoob S. Ebrahimi Boeing Commercial Airplane Company Seattle, Washington Prepared for Langley Research Center under Contract NAS1-18027 I\]S:GGA Aeicnauiics arid Space Administration Office of Management Scientific and Technical Information Division 1990 TABLE OF CONTENTS 1.0 SUMMARY ................................................................ 1 2.0 INTRODUCTION ........................................................... 2 3.0 SYMBOLS AND ABBREVIATIONS .......................................... 3 3.1 Symbols ............................................................ 3 3.2 Abbreviations ...................................................... 5 4.0 SETTING UP FLIGHT CONDITIONS AND AERO MODELS .................... 6 4.1 Cruise .............................................................. 9 4.2 Cruise Transition .................................................... 9 4.3 Landing ............................................................ 10 4.4 Generation of the Open-Loop Airplane Models ......................... 10 5.0 CONTROL DESIGN METHODOLOGY ....................................... 15 5.1 Specify Design Objectives ............................................ 15 5.2 Formulate Design Requirements ....................................... 16 5.3 OpenLoop Analysis ................................................. 17 5.3.1 Eigenstructure Decomposition ................................ 17 5.3.2 Controllability Analysis .................................... 17 5.3.3 Observability Analysis ..................................... 18 5.3.4 FrequencyResponse .......................................... 18 . 5.3.5 Time Domain Simulation .................................... 19 5.4 Controller Structure .................................................. 19 5.5 Synthesis Model Definition ........................................... 21 5.5.1 Independent Inputs ........................................... 21 5.5.2 Regulated Variables ......................................... 21 5.5.3 Criteria Outputs ............................................ 21 5.6 Cost Function Weighting. Controller Gains. and Gain Scheduling ......... 22 5.6.1 Cost Function Weightings .................................... 22 5.6.2 Controller Gains and Gain Scheduling ......................... 23 5.7 Sensor Selections and Output Filtering ................................. 24 5.8 Closed Loop Analysis ................................................ 24 5.8.1 Eigenvalues ................................................ 25 5.8.2 Broken Loop Frequency Responses ............................. 25 5.8.3 Singular Value Analysis ..................................... 25 5.8.4 Covariance Response ........................................ 25 5.8.5 Command Frequency Responses ............................... 26 5.8.6 Time Domain Simulation .................................... 26 5.9 Iteration to Satisfy Design Requirements ............................... 26 5.10 Summary of Design Methodology ...................................... 27 6.0 DESIGN REQUIREMEN73 .................................................. 28 6.1 Longitudinal Axis Design Requirements ................................ 28 6.2 Lateral Axis Design- Requirements ..................................... 29 7.0 LONGITUDINAL AXIS DESIGN ............................................ 32 7.1 Feedforward Modes .................................................. 32 7.1.1 Altitude Hold Mode ........................................ 32 iii PRECEDWG PAGE BUNK NOT FILMU) TABLE OF CONTENTS (Continued) 7.1.2 Glideslope Capture and Hold ................................ 35 7.1.3 Flare Mode .................................................. 37 7.1.4 Go-AroundMode ............................................ 37 7.1.5 Flight Path Angle Mode ..................................... 39 7.1.6 Speed Hold Mode ............................................ 39 7.2 Feedback Regulator Design ........................................... 41 7.2.1 Cruise Regulator Design ..................................... 41 7.2.1.1 Open Loop Analysis ................................ 42 7.2.1.2 Output Criteria Creation ........................... 42 7.2.1.3 Gain Scheduling ................................... 45 7.2.1.4 Speed on Elevator (WE) Configuration ............... 47 7.2.2 Landing Regulator Design .................................... 47 7.2.2.1 Gain Scheudling ................................... 50 7.2.2.2 Airspeed Complementary Filter ..................... 50 7.3 Digital Implementation .............................................. 54 7.4 Results ............................................................. 56 7.4.1 Linear Analysis ............................................ 56 7.4.2 Nonlinear Testing .......................................... 59 8.0 LATERAL AXIS DESIGN .................................................... 61 8.1 Heading Controller Design ............................................ 61 8.1.1 Regulated Variables ........................................ 61 8.1.2 Criterion Outputs and Weighting Matrices .................... 63 8.1.3 Gains and Gain Schedules ................................... 65 8.1.4 Beta Complementary Filter .................................. 65 8.1.5 Closed Loop Heading Controller .............................. 67 8.2 Heading Controller Results ........................................... 67 8.2.1 Eigenvalues ............................................... 67 8.2.2 Gain and Phase Margins ....................................... 67 8.2.3 Covariance Responses ....................................... 67 8.2.4 Frequency Responses ........................................ 70 8.2.5 Time Domain Simulation .................................... 70 8.3 Localizer Controller Design ........................................... 70 8.3.1 Controller Structure and Gains ............................... 70 8.3.2 Localizer Capture Logic ...................................... 70 8.4 Localizer Controller Results ........................................... 73 8.4.1 Eigenvalues ................................................ 73 8.4.2 Gain and Phase Margins ..................................... 73 8.4.3 Covariance Responses ........................................ 73 8.5 Nonlinear Simulation of Localizer Capture and Track .................... 73 8.6 Summary of Lateral Axis Design ....................................... 77 9.0 CONCLUSIONS ........................................................... 78 APPENDIX A: Longitudinal Axis Results ............................................ 79 APPENDIX B: Lateral Axis Results .................................................. 103 REFERENCES ..................................................................... 144 iV I- ' ** 6 LIST OF FIGURES Figure 1 . Two-Degrees-of-Freedom Design ............................................... 1 2 . Stall Speeds .................................................................. 7 3 . Operational Limits and Placards ............................................... 8 4 . Two-Degrees-of-Freedom Controller Structure .............................. 20 5 . Controller Structure ........................................................... 33 6 . Altitude Hold Mode .......................................................... 33 7a . Glideslope Capture and Hold Mode ............................................ 35 7b . Glideslope Geometry .......................................................... 35 7c . Altitude Integrator Command Computation ...................................... 36 8 . Flare Mode ................................................................. 38 9 . Go-Around Mode .............................................................. 38 10. Flight Path Angle Mode ...................................................... 40 11 . Speed Hold (Mach or CAS) Mode ............................................... 40 12. Cruise Controller Synthesis Model .............................................. 43 13. General Structure of Cruise Feedback Controller .................................. 48 14 . Landing Controller .Synthesis Model ........................................... 49 15 . Landing Controller .Thrust Gains Schedule ...................................... 52 16. Landing Controller .Elevator Gains Schedule .................................... 52 17. Complementary Filter ......................................................... 53 18 . Digital Implementation .Delta Coordinates .................................... 55 19 . Throttle Limiting .Controller Switching ........................................ 57 20 . Closed Loop Block Diagram of Integral Model Following Structure .................. 62 21 . Feedforward Controller Showing Regualted Variables and Ideal Models ........... 64 22 . LQG Synthesis Model Showing Criteria Outputs and Weighting Matrices .......... 64 23. Design Aileron Feedback Gains ................................................. 66 24 . Feedback Gain Schedules ...................................................... 66 25. Detailed Closed Loop