Automatic correction of orbital elements using continuous thrust controlled in closed loop

This work aims to study and simulate the control of a spacecraft trajectory in order to correct automatically and simultaneously the orbital elements that define the orbit: semi-major axis, eccentricity, periapse argument, inclination and right ascension of the ascending node. Thus, to perform the control of the trajectory was used a propulsion system able to apply thrust with adjustable magnitude and direction of application. In this study it was considered that the propulsion system is controlled in closed loop, so the adjustments of the magnitude and direction of thrust depends on the error generated by comparing a reference state (position and velocity) and a current state. The reference state is determined according to the final orbital parameters. The current state is estimated at each step of the simulation, therefore, the reference and current states must be determined and compared at each step in order to generate the error signal that is inserted into the trajectory control system. However, the control of the orbital parameters simultaneously can be characterized as a multi-objective problem with conflicting goals. The correction of the semi-major axis causes an eccentricity modification and vice-versa. One possibility to deal with this problem is to define when and where to make adjustments for each of the parameters. Thus, the automatic control seeks the best way to correct each parameter, adjusting each one sequentially. At the end of the process all orbital parameters are automatically adjusted and maintained due to the use of the closed loop control system.