Model Predictive Control of a Parafoil and Payload System

1. Model Predictive Control of a Parafoil and Payload System By: Nathan Slegers Department of Mechanical Engineering Oregon State University Corvallis, Oregon 97331

2. Topics Covered • Dynamic Modeling of the Parafoil and Payload System • N. Slegers, M. Costello, “Aspects of Control for a Parafoil and Payload System,” Journal of Guidance, Control, and Dynamics, Vol 26, No 6, 2003. • N. Slegers, M. Costello, “On the Use of Rigging Angle and Canopy Tilt for Control of a Parafoil and Payload System,” AIAA Atmospheric Flight Mechanics Conference and Exhibit, Austin, Texas, August 2003, AIAA Paper 2003-5609. • N. Slegers, M. Costello, “Comparison of Measured and Simulated Motion of a Controllable Parafoil and Payload System,” AIAA Atmospheric Flight Mechanics Conference and Exhibit, Austin, Texas, August 2003, AIAA Paper 2003-5611. • Model Predictive Control • N. Slegers, M. Costello, “Model Predictive Control Of A Parafoil And Payload System ,” AIAA Atmospheric Flight Mechanics Conference and Exhibit, Providence, RH, August 2004, AIAA Paper 2004-XXXX.

3. Deploy System Motivation Download Objective To Payload Through IR Port

4. Dynamic Modeling • Three Models Have Been Created • 9 DOF With Canopy Modeled As Panels • Components of the Position Vector of the Pivot Point in the Inertial Frame • Euler Roll, Pitch and Yaw Angles of the Payload • Euler Roll, Pitch and Yaw Angles of the Parafoil • 6 DOF With Canopy and Payload Having Combined Aerodynamic Coefficients • Reduced Order Linear Model Required For Model Predictive Control

5. 9DOF Equations of Motion Translation and Rotation Dynamics Equations Kinematic Equations

6. 6 DOF Equations of Motion Translation and Rotation Dynamics Equations Kinematic Equations

7. Advantage Of Modeling Canopy With Panels • Control Authority Reverses and Two Modes of Control are Demonstrated • Roll Steering: Lift Dominated and Rolls Parafoil • Skid Steering: Drag/Side Force Dominates Yaws Parafoil Turn Rate vs. Curvature (10 deg Right Brake) Turn Rate vs. Brake Deflection

8. Alternative Lateral Control Methods • Conventionally Lateral Control Is Achieved By Deflecting Parafoil Brakes Asymmetrically • Alters Lift and Drag Magnitudes • Control Reversal May Be Present At Small Brake Deflections • Alternatively Canopy Tilting Can Achieve Lateral Control • Alters Lift and Drag Direction Not Magnitudes • Control Reversal Does Not Exist Canopy Tilt

9. Coupling Determines Direction of Control Response Coupling of 1.4 Degrees of Canopy Tilt From 1 Inch of Brake Results in Positive Turn Rates 1.0 Deg/in Results in Nearly No Response 0.5 Deg/in Results in Negative Turn Rates Parafoil Canopies Are Highly Flexible Membranes, Deflection of Parafoil Brakes Also Tilts the Canopy on That Side. Canopy Tilt and Brake Coupling Brake Deflection and Canopy Tilt Coupling (Deg/in)

10. Model Predicted Turn Rates With Canopy Tilt Correction Panel Deflection and Canopy Tilting Control Methods Can Be Combined Into the Model Two Controls Methods Nearly Cancel Resulting in Correct Direction and Magnitude of Response

11. Model Predictive Control • Model Predictive Control Uses A Model To Predict The Future Dynamics of A System And Produces An Optimal Control Sequence For The Desired Dynamics • Consider A Linear Discrete Time System Described As: • A Cost Function Weighting Tracking Error And Control Input Is Formed

12. Model Predictive Control • Estimated States Are Found To Be: • Cost Function Can Be Rewritten As:

13. Model Predictive Control • The Optimal Control Sequence Is Found By Minimizing The Cost Function With Respect To The Control Sequence Resulting In: • Notice That K Is Constant And Is Calculated Ahead Of Time. The Sequence Only Requires A Desired State And The Current State. • Only The Next Control Is Found By Using Only The First Row Of K.

14. Parafoil Linear Model • MPC Requires A Linear Model • A Full State Linear Model Can Only Be Produced For A Small Range Of Yaw/Heading Angle • A Reduced State Linear Model Was Created From The Nonlinear 6DOF Model • It Turns Out That Yaw Angle Is The State With The Most Significant Control Authority

15. Acquiring Desired States • Optimal Control Sequence Requires Current States And Desired Output As A Linear Combination Of The States. • The Desired Path In The X-Y Plane Was Mapped Into A Desired Heading Angle Assuming A Constant Velocity And No Side Slip • Intersect Distance • Used To Define How Quickly To Get On Desired Path • Small Value Used If Important To Be On Path From Pt 1 To Pt 2 • Large Value Used If More Concerned With Only Points • Look Ahead Distance • Defines When To Increment Desired Path Points

16. Full State Measurement • Model Predictive Control Requires Roll and Yaw Angles and Rates Along With Latitude and Longitude • WAAS Enabled GPS Receiver Acquires 3 Inertial Positions • Attitude Is Acquired Through A Three Axis Magnetometer, 3 Axis Accelerometer And 3 Axis Gyroscope 4 PWM Output Channels Kalman Select Channels 4 PWM Input Channels Control Select Channel Attitude Sensor Wireless Transeiver

17. Parafoil And Payload Test System

18. Estimation Of Reduced State Aerodynamic Coefficients • Constant Linear Model Aerodynamic Coefficients Are Estimated Through A Recursive Weighted Least Squares Estimator (Kalman Filter Estimating Constants) • Requires Rate Of Change Of the Roll and Yaw Rate

19. Implementation Of Estimation • A Control Sequence Is Initiated And Continuously Cycled • The Control Sequence Creates A Sinusoidal Roll And Yaw Rate So The Numerically Estimated Derivatives Are Well Behaved KALMANMODE ON KALMAN MODE OFF

20. Estimation Flight Data Angular Accelerations Control Sequence

21. Comparison Of Model Vs Flight Data Roll Angle Roll Rate Yaw Rate Yaw Angle

22. Tracking A Box With Model Predictive Control

23. PT 5 PT 3 PT 1 PT 4 PT 2 Tracking Zigzag With Model Predictive Control

24. Summary Of Model Predictive Control • A Reduced State Linear Model Was Developed For Use In MPC • A Mapping From A Desired X-Y Path To A Desired Yaw Angle Was Established • Model Parameters Were Estimated Effectively Performance And Steady State Error Is Directly Related To Errors In Measured Yaw Angle • Through An Intersect Distance And Look Ahead Distance MPC Can Be Tuned For Different Objectives • MPC is a natural and effective way to autonomously control the trajectory of a parafoil and payload system

25. Dynamic Modeling, Control Aspects and Model Predictive Control of a Parafoil and Payload System By: Mark Costello, Associate Professor Nathan Slegers, Ph.D. Student Department of Mechanical Engineering Oregon State University Corvallis, Oregon 97331

26. Model Predictive Control of a Parafoil and Payload System By: Nathan Slegers Department of Mechanical Engineering Oregon State University Corvallis, Oregon 97331