Development and testing of algorithms for optimal thruster command distribution during MTG orbital manoeuvres

An accurate satellite attitude and orbit control is a key factor for a successful mission. It guarantees for example sun acquisition on solar panels, fine pointing for optimal telescope usage or satellite lifting to reach higher orbits, when required. Furthermore attitude and orbit control is applied to compensate any occurring disturbances within the space environment. The problem tackled in the present thesis is the optimization of thruster commanding to perform spacecraft orbital manoeuvres. The main objective is to develop different algorithms that are suitable for on-board implementation and to compare their performance. For an optimal thruster command distribution the algorithms shall solve linear programming (or optimization) problems, more exact they shall compute thruster on-times to generate desired torques and/or forces, which are requested by the on-board software. In total three different algorithms are developed of which the first one is based on the pseudoinverse of a matrix, the second one is a variation of the Simplex method and the third one is based on Karmarkar’s algorithm, which belongs to the interior-point methods. The last two methods are well known procedures to solve linear programming problems and in theory they have been analyzed before. However this paper proves their practical application and industrial feasibility for orbital manoeuvres of the weather satellites of ESA’s MTG project and their scalability to any number of thrusters on a generic satellite for 6 degrees of freedom manoeuvres. There are 6 MTG satellites and each has 16 one-sided reaction control thrusters, placed at specific positions and pointed towards defined directions. Physical mechanisms limit the thrusters output to minimum on- and off-times. The focus of this thesis will be on the orbital transfer mode, due to the high disturbances that arise during four motor firing sessions at the apogee, executed to reach higher orbits and finally GEO. The firing sessions are performed by a liquid apogee engine and while this engine is in boost mode, the thrusters shall be used for attitude control only. The technique (nominal case) developed by OHB for this maneuver and currently operational uses 4 thrusters only, which are all pointing in the engine’s direction. They are also used to settle the fuel before the engine is turned on. For control the Pseudoinverse method is applied. If one of the 4 thrusters fails, the backup scenario takes place, which includes using 4 totally different thrusters and no fuel settling, due to their unfavorable position with respect to the engine. The initial idea of this work was to develop a controller for 6 thrusters, using only 2 of the 4 nominal case thrusters, to have a better control performance in the backup case. The Pseudoinverse method was developed by OHB before, thus only small changes needed to be applied to work with 6 thrusters. The two other algorithms, based on the Simplex and Karmarkar method, were completely developed from scratch. To analyze their performance several tests were executed. This includes unit tests on a simple computer hardware with different input, Monte Carlo simulations on a cluster to test if the algorithms are suitable for MTG orbital manoeuvres and the application to 12 thrusters, mounted on a generic satellite to generate torques and forces at the same time for 6 degrees of freedom manoeuvres. For each thruster configuration the worst case outputs are shown in so called minimum control authority plots. The performance analysis consists of the maximum and average deviation between requested and generated torque/force, the average computed thruster on-times, the algorithms computation(running) time and iteration steps. For MTG the test results clearly confirm that the usage of 6 thrusters leads to more accurate generated torques and better control authority, than using only 4 thrusters. The Simplex method stands out here in particular, showing excellence performance regarding torque precision. Nevertheless the accuracy goes at the expense of computation effort. While the Pseudoinverse method is very fast and needs only one iteration step, the Simplex is half a magnitude, the Karmarkar one magnitude slower. But the latter lead to lower thruster on-times in terms of firing duration and thus fuel consumption is reduced. Also it is shown that Simplex and Karmarkar can control 12 thrusters at the same time to generate torques and forces, which proves their scalability to any thruster distribution. In the end it comes to the question whether generating a more accurate torque/force or the computational effort, which is strongly hardware dependent, is more important. A decision which depends on the mission’s objective. This paper shows that all three implemented algorithms are able to handle attitude control in the MTG backup scenario and beyond