Agenda
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Transcript of Agenda
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Solar Sail Attitude Control using a Combination of a
Feedforward and a Feedback Controller
D. Romagnoli, T. Oehlschlägel
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2nd International Symposium on Solar SailingD. Romagnoli & T. Oehlschlägel
Agenda
1
2
3
Introduction
Simulations Results
Controller Structure
4 Conclusions
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2nd International Symposium on Solar SailingD. Romagnoli & T. Oehlschlägel
Introduction
1
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2nd International Symposium on Solar SailingD. 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
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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
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2nd International Symposium on Solar SailingD. Romagnoli & T. Oehlschlägel
The CM-CP Control Technique
No Control TorqueClockwise Control TorqueCounter-Clockwise Control Torque
PM CC PC
MCMC
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Controller Structure
2
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2nd International Symposium on Solar SailingD. 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]
zextxSr
yxyxzz
xSr
zxxzyy
zyzyxx
TyFmM
mJJJ
TzFmM
mJJJ
TJJJ
,,
yext,,
xext,
Control Torques
External Torques
Equations of Motion for the Control Design
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2nd International Symposium on Solar SailingD. Romagnoli & T. Oehlschlägel
Equations of Motion for the Control Design
zoffset,,,
yoffset,yext,,
xext,
TTyFmM
mJJJ
TTzFmM
mJJJ
TJJJ
zextxSr
yxyxzz
xSr
zxxzyy
zyzyxx
+Y
+Z
CP
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!!
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The Basic Loop Structure
Maneuver Parameters
Feed-ForwardController
Attitude Dynamics & Kinematics
Settings
Maneuver TimeControl Torque To Ballasts‘ Position
Feed-BackController
Measured/Simulated States
FF Control Torque
FF Predicted States Errors
FB Control Torque
Total Control Torque
Off - SetNon-Diagonal
InertiaExternal Torque
Feedforward‘s Fast Response + Feedback‘s Ability of Coping with Unpredicted Disturbances
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2nd International Symposium on Solar SailingD. Romagnoli & T. Oehlschlägel
The Feedforward: basics
Initial Quaternion
Final Quaternion
ftft ,, 0
Polynomial of 9th degree with boundary conditions on its derivatives up to the third order
43223495 12642054031570 ttttttp f
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2nd International Symposium on Solar SailingD. 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
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The Feedforward: an Example
+Y
+Z
Pitch (+Y) = 15°
Yaw (+Z) = 35°
+Y
+ZEuler Axis = 38°
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38°
The Feedforward: an Example
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2nd International Symposium on Solar SailingD. 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 system‘s dynamic is required
• The predicted/desired states and inputs do not consider disturbing effects coming from not included sources
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The Feedback Controller
Error Dynamics
dtq
e
q
realdesired
realdesired
ωωωX
qe
II
ωωTω tot
1
2
1
The system can be linearized about the zero-point…
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The Feedback Controller
…and controlled using a simple LQR approach!
101010555100100100diagQ
Weighting matrices are:
101010diagR
IDP KKKK
Gain Matrix
Diagonal submatrices
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Simulations Reults
3
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Simulations Results: Sail Parameters
Geometry
SizeBoom lengthSail area
4028
1200
mmm2
Masses
SailsBoomsBallasts (each)BusOther
Total
671
15020
185
kgkgkgkgkgkg
Inertia
Ix (roll)Iy (pitch)Iz (yaw)
434021712171
kg m2
kg m2
kg m2
[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]
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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
+ZYaw (+Z) = 35°
Desired maneuver:
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Simulations Results: Single Axis Maneuver
+Y
+ZYaw (+Z) = 35°
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Simulations Results: Single Axis Maneuver
Maneuver Time: 3370 sec or about 57 min
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2nd International Symposium on Solar SailingD. Romagnoli & T. Oehlschlägel
Simulations Results: Single Axis Maneuver
Maneuver Time: 3370 sec or about 57 min
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2nd International Symposium on Solar SailingD. Romagnoli & T. Oehlschlägel
Simulations Results: Single Axis Maneuver
VIDEO
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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:
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Simulations Results: Two Axes Maneuver
Maneuver Time: 7270 sec or about 122 min
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2nd International Symposium on Solar SailingD. Romagnoli & T. Oehlschlägel
Simulations Results: Two Axes Maneuver
Maneuver Time: 7270 sec or about 122 min
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2nd International Symposium on Solar SailingD. Romagnoli & T. Oehlschlägel
Simulations Results: Two Axes Maneuver
VIDEO
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2nd International Symposium on Solar SailingD. Romagnoli & T. Oehlschlägel
Conclusions
4
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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
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2nd International Symposium on Solar SailingD. 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
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2nd International Symposium on Solar SailingD. Romagnoli & T. Oehlschlägel
THANK YOU!!!!Daniele RomagnoliDLR Institute of Space SystemsGNC DepartmentPhone: (+49) 421 24420135 Mail: [email protected]