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 w.chen@lboro.ac.uk

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

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)

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

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

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

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

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

Magnetic field (24 hours)

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

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)

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

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

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

Air density time history

Disturbance Modelling Constant disturbance Periodic disturbance Kalman filtering

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

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)

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

Performance specifications:

Feedforward + MPC performance

Comparison between constant and periodic disturbance models

Disturbance estimation

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

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