SIX DEGREE-OF-FREEDOM MODELING OF AN UNINHABITED AERIAL VEHICLE. A thesis presented to. the faculty of

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1 SIX DEGREE-OF-FREEDOM MODELING OF AN UNINHABITED AERIAL VEHICLE A thesis presented to the faculty of the Russ College of Engineering and Technology of Ohio University In partial fulfillment of the requirement for the degree Master of Science Sean M. Calhoun June 2006

2 This thesis entitled SIX DEGREE-OF-FREEDOM MODELING OF AN UNINHABITED AERIAL VEHICLE by SEAN M. CALHOUN has been approved for the School of Electrical Engineering and Computer Science and the Russ College of Engineering and Technology by Douglas A. Lawrence Associate Professor of Electrical Engineering and Computer Science Dennis Irwin Dean, Russ College of Engineering and Technology

3 Abstract CALHOUN, SEAN M., M.S., June 2006, Electrical Engineering SIX DEGREE-OF-FREEDOM MODELING OF AN UNINHABITED AERIAL VEHICLE (137 pp.) Director of Thesis: Douglas A. Lawrence Developing a six degree-of-freedom (6-DOF) aircraft model has many practical purposes, especially in these times of rapidly growing Uninhabited Air Vehicle (UAV) technologies. This thesis covers some of the various topics involved in the development of such a model. The research performed was conducted at the Avionics Engineering Center, utilizing the Brumby R/C aircraft. Topics include a brief overview of the instrumentation system, techniques for inertia estimation, and system identification using the Ordinary Least Squares (OLS) method. Finally, the design and development of a Matlab/SIMULINK model will be covered, which will illustrate the accuracy and validity of the 6-DOF model. Approved: Douglas A. Lawrence Associate Professor of Electrical Engineering and Computer Science

4 Acknowledgements I would like to thank all the people who helped contribute to this effort, both students and faculty. I would also like to thank my family, friends and work associates that helped me keep the momentum throughout this entire process. Many thanks to my M.S. committee, Dr. Douglas Lawrence, Dr. Frank Van Graas, Dr. David Diggle, and Dr. Bob Williams, for all of the their time, effort and help with my thesis. Particular thanks to Dr. Van Graas for funding this work and his efforts in the development of the Brumby and to Dr. Lawrence, serving as my advisor, for the countless meetings and priceless guidance he provided throughout all my years at Ohio University. Thanks to Jacob Campbell and Jared Kresge for all of their hard work in development and testing of the instrumentation system. Thanks to Jamie Edwards for serving as pilot and the rest of the Avionics Engineering Center for all the support and encouragement throughout the years. Finally, thanks to my parents for all of their support and sacrifices that have allowed me to achieve all that I have, and to my lovely wife Megan for helping me better understand the English language, but mostly for being the best thing in my life.

5 Glossary of Variables α b B β c x c C D Angle-of-attack Wing span Inertial to body frame rotation matrix Side-slip angle Moment of inertia constants Wing mean geometric chord Dimensionless aerodynamic drag coefficient C Aerodynamic drag coefficients / rotary derivatives D X C l Dimensionless aerodynamic roll coefficient C l X Aerodynamic roll coefficients / rotary derivatives C L Dimensionless aerodynamic lift coefficient C Aerodynamic lift coefficients / rotary derivatives L X C m Dimensionless aerodynamic pitch coefficient C Aerodynamic pitch coefficients / rotary derivatives m X C n Dimensionless aerodynamic yaw coefficient C Aerodynamic yaw coefficients / rotary derivatives n X C Y Dimensionless aerodynamic side force coefficient C Aerodynamic side force coefficients / rotary derivatives Y X D Drag Force δ ail Aileron control surface deflection

6 δ elv Elevator control surface deflection δ rud Rudder control surface deflection F B F X,F Y,F Z F XT,F YT,F ZT g Body forces acting on the aircraft Aerodynamic forces Thrust forces Gravity vector g Local level gravity vector g 0 Local level gravity constant H B H & B I L L M m N ω B Angular momentum vector Angular momentum rate vector Moment of inertia Lift force Roll moment Pitch moment Mass Yaw moment Aircraft body rotation rate ω E p p& ϕ ψ Earth rotation rate Angular roll rate Angular roll acceleration Roll angle Yaw angle

7 q q& q r r& ρ S T B θ U V V abs V B V & B V W W Y Angular pitch rate Angular pitch acceleration Free-stream dynamic pressure Angular yaw rate Angular yaw acceleration Air density Wing reference area Net torque Pitch angle True airspeed, forward direction True airspeed, starboard direction Absolute velocity Velocity of the aircraft with respect to the air Acceleration of the aircraft with respect to the air Velocity of air with respect to inertial space True airspeed, down direction Side-force

8 Table of Contents viii Abstract...iii Acknowledgements... iv Glossary of Variables... v List of Tables... x List of Figures... xi Chapter 1: Introduction Approximate Equations Output Error Filter Methods Input-Output Models Equation-Error Method Thesis Overview Equations of Motion Aircraft Mass Properties System Identification Data Collection DOF Modeling Chapter 2: Equations of Motion Translational Motion Rotational Motion Aerodynamic Coefficients Chapter 3: Inertia Estimation Fuselage Wings X - Axis Y - Axis Z Axis Rudder X Axis Y Axis Z Axis Wing Pipe Pitot Tube Landing Gear Front Landing Gear Rear Landing Gear Engine and Instrumentation Brumby Mass Property Results Chapter 4: System Identification Ordinary Least Squares Chapter 5: Instrumentation System Objective Sensors Air Data Boom... 49

9 119 Figure C-23: Maneuver 12 - Rudder Doublet (1/2) Figure C-24: Maneuver 12 - Rudder Doublet (2/2)

10 120 Figure C-25: Maneuver 13 - Rudder Doublet (1/2) Figure C-26: Maneuver 13 - Rudder Doublet (2/2)

11 121 Figure C-27: Maneuver 14 - Rudder Doublet (1/2) Figure C-28: Maneuver 14 - Rudder Doublet (2/2)

12 122 Figure C-29: Maneuver 15 - Rudder Doublet (1/2) Figure C-30: Maneuver 15 - Rudder Doublet (2/2)

13 123 Figure C-31: Maneuver 16 - Rudder Doublet (1/2) Figure C-32: Maneuver 16 - Rudder Doublet (2/2)

14 124 Figure C-33: Maneuver 17 - Rudder Doublet (1/2) Figure C-34: Maneuver 17 - Rudder Doublet (2/2)

15 Appendix D: Brumby Specifications 125 BACKGROUND The Avionics Engineering Center at Ohio University has over 40 years of experience in aircraft navigation, communication, and surveillance systems. This experience, combined with the acquisition of the Brumby UAV, will be used to enter into the UAV research area. The Brumby UAV was built in Australia by Sydney University. This research platform can handle up to an 8 kg payload that fits into an area with easy access. These features allow for navigation and application sensor payloads. To date several avionics payload configurations have been flown to perform research missions such as: short baseline GPS attitude research, wireless LAN repeater research, and in-flight aircraft aerodynamics system ID research. With the system ID of the aircraft, future work includes the development of aircraft control laws which will allow for the achievement of different levels of autonomous flight. SPECIFICATIONS Physical: Delta Wing Aircraft Wingspan 2.52m (8.27 ft) Fuselage Length 1.97m (6.46 ft) Engine Power 5.2 kw (7.2 hp) Max. Endurance minutes Payload Weight <= 8 kg (without filing for an FAA permit) Fiberglass Composite Fuselage Enables Interior Antenna Placement 10 Channel Radio Control Receiver Current Research Payload: PC/ MHz Geoid Processor 100MB Solid State Disk On Chip Canadian Marconi ALLSTAR GPS Receiver Airdata Boom with Total and Static Pressure Ports as well as Angle of Attack and Side Slip Vanes MEMS IMU (Crossbow & AGNC) Electronic Compass Control Surface Position Monitors 900MHz Spread Spectrum Transceiver CONTACT: Dr. Frank van Graas, 345 Stocker, Ohio University, Athens, OH Phone: (740) Fax: (740)

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