Simulations of LQR Control on Linear Spacecraft Dynamics about Asteroid Equilibrium Points

Future exploratory missions to asteroids may require a spacecraft to perform attitude and position change maneuvers within small perturbations of the equilibrium point to conduct measurements and make observations based on mission requirements. The non-linear dynamics of the spacecraft can be approximated to be linear given that the system operates about an equilibrium point and the signals are small. Based on this, the linearized system is equivalent to the non-linear system within a limited operating range. This project follows this precedent and applies a closed loop LQR controller to perturbations of 1%, 2% and 5% from asteroid 101955 Bennu’s equilibrium points. The LQR controller methodology requires that weighting matrices Q and R which penalize the states and the controls respectively to be iterated for – depending on the application requirements. The iteration procedure is the primary objective of this project and is conducted for six different spacecraft orientations about eight different equilibrium points. The procedure examines the settling times and response plots to critique the performance of the controller. This paper presents the underlying control theory, the modelling scenario, the simulation procedure, results and some patterns discovered in the results. This project was conducted in conjunction with [3] and presents the results of simulations based on linearized spacecraft dynamics. The results of the non-linear spacecraft dynamics simulations can be found in [3].