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

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel Agenda Introduction Simulations Results Controller Structure 4 Conclusions

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel Introduction 1

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel 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

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel 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 sails parameters and the selected actuator Understand the reorientation capabilieties of a solar sail, independently from trajectory constraints

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel The CM-CP Control Technique No Control Torque Clockwise Control Torque Counter-Clockwise Control Torque

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel Controller Structure 2

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel [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] Control Torques External Torques Equations of Motion for the Control Design

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel Equations of Motion for the Control Design +Y +Z CPCP 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!!

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel The Basic Loop Structure Maneuver Parameters Feed-Forward Controller Attitude Dynamics & Kinematics Settings Maneuver Time Control Torque To Ballasts Position Feed-Back Controller Measured/Simulated States FF Control Torque FF Predicted States Errors FB Control Torque Total Control Torque Off - Set Non-Diagonal Inertia External Torque Feedforwards Fast Response + Feedbacks Ability of Coping with Unpredicted Disturbances

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel The Feedforward: basics Initial Quaternion Final Quaternion Polynomial of 9 th degree with boundary conditions on its derivatives up to the third order

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel The Feedforward: basics Assumptions for the feedforward design: 1.The effect of the offset is included 2.The inertia matrix is constant 3.The mass distribution leads to a diagonal inertia matrix

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel The Feedforward: an Example +Y +Z Pitch (+Y) = 15° Yaw (+Z) = 35° +Y +Z Euler Axis = 38°

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel 38° The Feedforward: an Example

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel 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 systems dynamic is required The predicted/desired states and inputs do not consider disturbing effects coming from not included sources

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel The Feedback Controller Error Dynamics The system can be linearized about the zero-point…

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel The Feedback Controller …and controlled using a simple LQR approach! Weighting matrices are: Gain Matrix Diagonal submatrices

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel Simulations Reults 3

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel Simulations Results: Sail Parameters Geometry Size Boom length Sail area mmm2mmm2 Masses Sails Booms Ballasts (each) Bus Other Total kg Inertia Ix (roll) Iy (pitch) Iz (yaw) kg m 2 [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]

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel Simulations Results: Single Axis Maneuver Roll: 0° 0° Pitch: 0° 0° Yaw:0° 35° Under the effects of: no offset no external torque a diagonal inertia matrix +Y +Z Yaw (+Z) = 35° Desired maneuver:

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel Simulations Results: Single Axis Maneuver +Y +Z Yaw (+Z) = 35°

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel Simulations Results: Single Axis Maneuver Maneuver Time: 3370 sec or about 57 min

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel Simulations Results: Single Axis Maneuver Maneuver Time: 3370 sec or about 57 min

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel Simulations Results: Single Axis Maneuver VIDEO

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel Simulations Results: Two Axes Maneuver +Y +Z Pitch (+Y) = 45° Yaw (+Z) = 35° 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 Desired maneuver:

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel Simulations Results: Two Axes Maneuver Maneuver Time: 7270 sec or about 122 min

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel Simulations Results: Two Axes Maneuver Maneuver Time: 7270 sec or about 122 min

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel Simulations Results: Two Axes Maneuver VIDEO

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel Conclusions 4

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel Conclusions 1.The problem of attitude control for solar sails has been introduced 2.A control strategy which uses both a feedforward and a feedback controller has been described 3.Some example maneuvers have been presented to describe the performances of the proposed controller

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel 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! 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

2 nd International Symposium on Solar Sailing D. Romagnoli & T. Oehlschlägel THANK YOU!!!! Daniele Romagnoli DLR Institute of Space Systems GNC Department Phone: (+49) Mail: