1. Regulation of Magnetically Actuated Satellites using Model Predictive Control with Disturbance Modelling
Mark Wood (Ph.D. Student)
Wen-Hua Chen (Senior Lecturer)
Department of Aeronautical and Automotive Engineering
Loughborough University UK

2. Outline of the Presentation
Background of the study
Design specifications
Model Predictive Control (MPC)
Disturbance modelling
Simulation and verification
Conclusions

3. Loughborough University
Loughborough: a small town in Midland of England
First technological university in UK
Ranked in top 15 in last 6 consecutive years
Well known in sport and engineering
Guardian University League Table – top ten universities
1 Oxford
2 Cambridge
Imperial College London
St. Andrews
University College London
London School of Economics
Edinburgh
Warwick
9 Loughborough University
Bath
Times The Good University Guide
12th (2008); 6th (2007)

4. European Space Agency’s GOCE mission
The Gravity Field and Steady-State Ocean Circulation Explorer (GOCE)
Measure high-accuracy gravity gradients and provide global models of the Earth's gravity field and of the geoid.
First mission in the European Space Agency’s living planet programme
Will be launched in 2008

5. Control System Configurations
Low earth orbit drag caused by air
Drag-free systems--Ion thruster Assembly (ITA)
Only X position axis is controlled but Y and Z are not controlled.
Disturbance torques:
Drag: mismatch between CoA and CoM
Propulsion: act line does not necessarily cross the CoM

6. Magnetic attitude control
3 axes attitude control
Combined reaction wheels and magnetotorquers.
The wheels maintain the pointing stability and high bandwidth feedback
the magnetotorquers provide only a low-bandwidth means to dump excess momentum.
Fully magnetic attitude control/active 3-axis stabilization
robustness
Reliability
low power consumption
cost-efficiency
Magnetic actuator/magnetotorquer

7. Control challenges
Limit and variation of the Earth magnetic field with the orbit
No torque/force along the direction of the Earth magnetic field
Inclination of the orbit
Two axes are controllable at any time but all axes are controllable over the orbit M B T

8. Control challenges (cont.)
Unstable dynamics (pitch axis is unstable, roll and yaw axes are neutral stable)
Almost periodic systems
Not come back to the same location after one orbit
Satellite orbit
Earth rotation
Drift in Y and Z axis
Time-varying systems
Sign of the magnetic field components change with the orbit

9. Magnetic field (24 hours)

10. Satellite attitude dynamics
State variables: Roll, pitch, yaw angle and their rates
Magnetotorquer dipole moments
Two Possible approaches for control design: Torque or magnetotorquer moments as input

11. Existing approaches Industrial design
PD controller to generate required torque ; then project it perpendicular to the magnetic field
Real torque is different from the required torque
(almost) Periodic LQ controller design (Psiaki, 2001)
Nonlinear magnetic attitude control (Wisniewski and Blanke, 1999; Lovera and Astolfi, 2004,2005; Silani and Lovera, 2005)

12. Motivation for MPC approaches
Use the information of the orbit and its magnetic field: not only the current location but the future location
Deal with structure constraints– lack of controllability on one axis
Possible for control magnitude constraints

13. MPC with Attitude control
Convert to time-invariant systems
where the control input is the torque
Time varying system is replaced by time-varying constraints on the control input

14. MPC with on-line optimisation
Model prediction ,
Performance index
Constraints
Structure and magnitude constraints on control

15. Air density time history

16. Disturbance Modelling
Constant disturbance
Periodic disturbance
Kalman filtering

17. Control configuration
Predictive Controller
Satellite Dynamics
Star Sensor and Accelerometer
Kalman
Filter
Environmental Torques
Estimated pointing, angular rate and external disturbance
Control Torque
Measured
angle
Aerodynamic, Thruster, Gravity Gradient
Modified MPC algorithms
with disturbance terms

18. GOCE Test Bench Supplied by the European Space Agency
Updated by Loughborough with new control strategies
Consisting of three main parts
Orbit and environment model
Satellite nonlinear dynamics
DFACS (draft free attitude control systems)

19. DFACS Sensors: Star tracker + Acc
Estimator: 3 types of Kalman filtering
Guidance: LvLh Frame
Control: Feed-forward controller + Model predictive controller/PD controller
Actuation: Ion thruster assembly + 3 magnetic torquers
Environment: Dipole models of the Earth magnetic filed or 8th order IGRF2000 model, atmosphere/air density modelled by MSIS90 model
Disturbance: drag, gravity, ion thruster assembly misalignment

20. Performance specifications:

21. Feedforward + MPC performance

22. Comparison between constant and periodic disturbance models

23. Disturbance estimation

24. Conclusions
MPC provides a promising tool for satellite magnetic attitude control
Feedforward further improves its performance
Attempts to increase the complexity of the disturbance model seems to have little effect on the performance of the controller
Real-time implementation will be on the main area for research

25. Acknowledgment Thanks the European Space Agency (ESA) for
Financial support
Provision of the GOCE simulator
Comments from Drs. Denis Fertin and Christian Phillipe