Agenda

1. Solar Sail Attitude Control using a Combination of a Feedforward and a Feedback ControllerD. Romagnoli, T. Oehlschlägel

2. Agenda 1 Introduction 2 Controller Structure 3 Simulations Results 4 Conclusions

3. 1 Introduction

4. Problem Statement • Solar sail coupling between trajectory • and attitude is crucial for performance • analysis • High performance reorientation • maneuvers may be important for • demanding missions (like those with • close fly-by of the Sun or planetary ones) • The control authority is a critical issue in • selecting/designing the control system

5. Objectives • Develop a controller that is able to • perform attitude maneuvers around the • three body axes of the sail • Select and model a controller actuator • which satisfies the requirements of high • control authority and technological • feasibility • Study the performances during attitude • maneuvers given the sail‘s parameters • and the selected actuator • Understand the reorientation capabilieties • of a solar sail, independently from • trajectory constraints

6. The CM-CP Control Technique Counter-Clockwise Control Torque Clockwise Control Torque No Control Torque

7. 2 Controller Structure

8. Equations of Motion for the Control Design Control Torques External Torques [Ref. Wie B. and Murphy D. „Solar-Sail Attitude Control Design for a Solar Flight Validation Mission“, Journal of Spacecraft and Rockets, Vol. 144, No. 4, July-August 2007]

9. Equations of Motion for the Control Design +Z CP +Y The contribution coming from the offset of the center of pressure is the most significant source of disturbance It MUST be included in the controller design to improve the performances!!

10. Non-Diagonal Inertia Off - Set External Torque Total Control Torque Settings Maneuver Parameters FF Control Torque Control Torque To Ballasts‘ Position Attitude Dynamics & Kinematics Feed-Forward Controller Maneuver Time FF Predicted States FB Control Torque Errors Feed-Back Controller Measured/Simulated States The Basic Loop Structure Feedforward‘s Fast Response + Feedback‘s Ability of Coping with Unpredicted Disturbances

11. The Feedforward: basics Initial Quaternion Final Quaternion Polynomial of 9th degree with boundary conditions on its derivatives up to the third order

12. The Feedforward: basics • Assumptions for the feedforward design: • The effect of the offset is included • The inertia matrix is constant • The mass distribution leads to a diagonal inertia matrix

13. The Feedforward: an Example Euler Axis = 38° +Z +Z Yaw (+Z) = 35° +Y +Y Pitch (+Y) = 15°

14. The Feedforward: an Example 38°

15. The Feedforward Controller Once the polynomial has been computed: • All the (predicted) states of the system are known at each time-step • All the (predicted) inputs to the system are known at each time-step But: • A detailed description of the system‘s dynamic is required • The predicted/desired states and inputs do not • consider disturbing effects coming from • not included sources

16. The Feedback Controller Error Dynamics The system can be linearized about the zero-point…

17. The Feedback Controller …and controlled using a simple LQR approach! Weighting matrices are: Gain Matrix Diagonal submatrices

18. 3 Simulations Reults

19. Simulations Results: Sail Parameters [Ref. Wie B. and Murphy D. „Solar-Sail Attitude Control Design for a Solar Flight Validation Mission“, Journal of Spacecraft and Rockets, Vol. 144, No. 4, July-August 2007]

20. +Z Yaw (+Z) = 35° +Y Simulations Results: Single Axis Maneuver Desired maneuver: Roll: 0°  0° Pitch: 0°  0° Yaw: 0°  35° Under the effects of: • no offset • no external torque • a diagonal inertia matrix

21. +Z Yaw (+Z) = 35° +Y Simulations Results: Single Axis Maneuver

22. Simulations Results: Single Axis Maneuver Maneuver Time: 3370 sec or about 57 min

23. Simulations Results: Single Axis Maneuver Maneuver Time: 3370 sec or about 57 min

24. Simulations Results: Single Axis Maneuver VIDEO

25. +Z Yaw (+Z) = 35° +Y Pitch (+Y) = 45° Simulations Results: Two Axes Maneuver Desired maneuver: Roll: 0°  0° Pitch: 0°  45° Yaw: 0°  35° Under the effects of: • an offset of 0.1 m in both directions • an external torque around the +Z axis • a non-diagonal inertia matrix

26. Simulations Results: Two Axes Maneuver Maneuver Time: 7270 sec or about 122 min

27. Simulations Results: Two Axes Maneuver Maneuver Time: 7270 sec or about 122 min

28. Simulations Results: Two Axes Maneuver VIDEO

29. 4 Conclusions

30. Conclusions • The problem of attitude control for solar sails has been introduced • A control strategy which uses both a feedforward and a • feedback controller has been described • Some example maneuvers have been presented to describe • the performances of the proposed controller

31. Open Points Controller Improvement: - use of H-Infinity controller instead of LQR - include better time optimization routines - develop a complete 6 DoF simulation, including coupled orbit and attitude dynamics Model Improvement: - include sailcraft (booms and membrane) flexibility in the model - investigation of coupling effects between attitude and structure dynamics - current approach involves cosimulation with structural analysis in ANSYS and dynamic simulation and control in MATLAB/SIMULINK - any suggestions or comments on this topic are welcome!

32. THANK YOU!!!! Daniele Romagnoli DLR Institute of Space Systems GNC Department Phone: (+49) 421 24420135 Mail: daniele.romagnoli@dlr.de