Station keeping and momentum management of low-thrust satellites using MPC

Abstract This work proposes a Model Predictive Control (MPC) policy for simultaneous station keeping and momentum management of a low-thrust nadir-pointing satellite in geostationary orbit around the Earth. The satellite is equipped with six electrically powered thrusters and three axisymmetric reaction wheels, which must be coordinated to control the satellite's orbital position and, concurrently, unload the wheels' stored angular momentum. The MPC policy enforces constraints that maintain the satellite in a tight latitude and longitude window and in a tight nadir-pointing attitude configuration, while minimizing the delta-v provided by the thrusters. The MPC policy exploits a prediction model of the environmental disturbance forces in order to significantly reduce the delta-v required for station keeping, and enforces constraints determined by the thruster configuration to select control forces and torques that can be generated by the propulsion system. Numerical simulations of the control policy in closed-loop with the satellite nonlinear dynamics under high-precision orbit propagation provided by Systems Tool Kit (STK) that validate the performance of the proposed design in terms of thruster usage and constraint enforcement are presented.

[1]  K. T. Tan,et al.  Linear systems with state and control constraints: the theory and application of maximal output admissible sets , 1991 .

[2]  T. Edelbaum.  Optimum low-thrust rendezvous and station keeping , 1963 .

[3]  Alexander Domahidi,et al.  Embedded optimization methods for industrial automatic control , 2017 .

[4]  Chun C. Chao,et al.  On the propagation and control of geosynchronous orbits , 1983 .

[5]  W. H. Clohessy,et al.  Terminal Guidance System for Satellite Rendezvous , 2012 .

[6]  Alberto Bemporad,et al.  Model Predictive Control Tuning by Controller Matching , 2010, IEEE Transactions on Automatic Control.

[7]  E. Gilbert,et al.  Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: Stability and moving-horizon approximations , 1988 .

[8]  P. Hughes.  Spacecraft Attitude Dynamics , 1986 .

[9]  I. Kolmanovsky,et al.  AAS 15-307 STATION-KEEPING AND MOMENTUM-MANAGEMENT ON HALO ORBITS AROUND L 2 : LINEAR-QUADRATIC FEEDBACK AND MODEL PREDICTIVE CONTROL APPROACHES , 2022 .

[10]  J. T. Hoeksema,et al.  Earth-Affecting Solar Causes Observatory (EASCO): A potential International Living with a Star Mission from Sun-Earth L5 , 2011 .

[11]  Alan D. Reth,et al.  GOES-R STATIONKEEPING AND MOMENTUM MANAGEMENT , 2006 .

[12]  Shashi Kant Shrivastava,et al.  Orbital perturbations and stationkeeping of communication satellites , 1978 .

[13]  Dennis S. Bernstein,et al.  Inertia-Free Spacecraft Attitude Control Using Reaction Wheels , 2013 .

[14]  Stephen P. Boyd,et al.  Metric Selection in Douglas-Rachford Splitting and ADMM , 2014 .

[15]  Djamel Benatia,et al.  High Thrust Station Keeping Maneuvers for Geostationary Satellites , 2015 .

[16]  Andrea Garulli,et al.  All-Electric Spacecraft Precision Pointing Using Model Predictive Control , 2015 .

[17]  I. Katz,et al.  Fundamentals of Electric Propulsion: Ion and Hall Thrusters , 2008 .

[18]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[19]  Dimitri P. Bertsekas,et al.  Dynamic Programming and Optimal Control, Two Volume Set , 1995 .

[20]  Stefano Di Cairano,et al.  Opportunities and potential of model predictive control for low-thrust spacecraft station-keeping and momentum-management , 2015, 2015 European Control Conference (ECC).

[21]  A. Raghunathan,et al.  ADMM for Convex Quadratic Programs: Linear Convergence and Infeasibility Detection , 2014, 1411.7288.

[22]  Joseph M. Davila,et al.  Earth-Affecting Solar Causes Observatory (EASCO): a mission at the Sun-Earth L5 , 2011, Optical Engineering + Applications.

[23]  E. M. Soop.  Handbook of Geostationary Orbits , 2010 .

[24]  Euhanna Ghadimi,et al.  Optimal Parameter Selection for the Alternating Direction Method of Multipliers (ADMM): Quadratic Problems , 2013, IEEE Transactions on Automatic Control.

[25]  R. Fletcher,et al.  Practical Methods of Optimization: Fletcher/Practical Methods of Optimization , 2000 .

[26]  Alberto Bemporad,et al.  An Accelerated Dual Gradient-Projection Algorithm for Embedded Linear Model Predictive Control , 2014, IEEE Transactions on Automatic Control.

[27]  Bong Wie,et al.  Space Vehicle Dynamics and Control, Second Edition , 2008 .

[28]  Rolf Findeisen,et al.  A fast gradient method for embedded linear predictive control , 2011 .

[29]  James B. Rawlings,et al.  Postface to “ Model Predictive Control : Theory and Design ” , 2012 .

[30]  James R. Wertz,et al.  Space Mission Analysis and Design , 1992 .

[31]  Ilya Kolmanovsky,et al.  Nonlinear model predictive control strategy for low thrust spacecraft missions , 2014 .

[32]  R. Drai,et al.  Electric Station Keeping of Geostationary Satellites: a Differential Inclusion Approach , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[33]  Edgar Y. Choueiri,et al.  ELECTRIC PROPULSION. , 1888, Science.

[34]  Stefano Di Cairano,et al.  Model Predictive Control for simultaneous station keeping and momentum management of low-thrust satellites , 2015, 2015 American Control Conference (ACC).

[35]  Christopher J. Damaren,et al.  Spacecraft Dynamics and Control: An Introduction , 2013 .

[36]  Agnes Fienga,et al.  Use of MESSENGER radioscience data to improve planetary ephemeris and to test general relativity , 2013, 1306.5569.

[37]  Stefano Di Cairano,et al.  Projection-free parallel quadratic programming for linear model predictive control , 2013, Int. J. Control.

[38]  Stefano Di Cairano,et al.  Alternating direction method of multipliers for strictly convex quadratic programs: Optimal parameter selection , 2014, 2014 American Control Conference.

[39]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[40]  D. D. Mueller,et al.  Fundamentals of Astrodynamics , 1971 .

[41]  Antonio F. B. A. Prado,et al.  On one approach to the optimization of low-thrust station keeping manoeuvres , 2012 .

[42]  M. Martinez-Sanchez,et al.  Spacecraft Electric Propulsion—An Overview , 1998 .

[43]  Yurii Nesterov,et al.  Introductory Lectures on Convex Optimization - A Basic Course , 2014, Applied Optimization.

[44]  D. Limón,et al.  Input-to-State Stability: A Unifying Framework for Robust Model Predictive Control , 2009 .

[45]  Vivian Martins Gomes,et al.  Low-Thrust Out-of-Plane Orbital Station-Keeping Maneuvers for Satellites , 2012 .

[46]  Alberto Bemporad,et al.  Model Predictive Idle Speed Control: Design, Analysis, and Experimental Evaluation , 2012, IEEE Transactions on Control Systems Technology.

[47]  Kenn E. Clark.  Survey of Electric Propulsion Capability , 1975 .

[48]  Bong Wie,et al.  Space Vehicle Dynamics and Control , 1998 .

[49]  Manfred Morari,et al.  Computational Complexity Certification for Real-Time MPC With Input Constraints Based on the Fast Gradient Method , 2012, IEEE Transactions on Automatic Control.