Statistical Investigation about the SDRE Optimality for Satellites with Nonlinearities

Abstract

The Attitude Control System (ACS) of a Satellite can be designed with success by linear control theory if the satellite has slow angular motions. However, for fast maneuvers, the linearized models are not able to represent the effects of the nonlinear terms. One candidate technique to design the ACS of the satellite under fast maneuvers is the State-Dependent Riccati Equation (SDRE), which provides an effective algorithm for synthesizing nonlinear feedback control taking into account the nonlinearities. Nonetheless, much criticism has been leveled against the SDRE method since it does not assure global asymptotic stability (GAS), because there are situations in which global asymptotic stability cannot be achieved (e.g., systems with multiple equilibrium points). One way to study the GAS is by estimating the region of attraction (ROA) which in turn is fundamental to investigate the performance of the controller designed by the SDRE method The Brazilian National Institute for Space Research (INPE) is responsible to build a Remote-Sensing Satellites, called Amazonia-1. The ACS of the Amazonia-1 satellite must be stabilized in three axes so that the optical payload can point to the desired target. In this paper, one investigates the performance of the Amazonia-1 ACS using a statistical test (unpaired t-test) that compares the optimality inside the ROA controlled by LQR and SDRE. By several simulations running a full Monte Carlo perturbation satellite model one observes a significant difference between the optimality of the two controllers in favor of SDRE when nonlinearities are accounted for.