Suboptimal Control on Nonlinear Satellite Simulations using SDRE and H-infinity

Resumo

The control 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 all the perturbations
due to the effects of the nonlinear terms present in the dynamics which compromises the system’s performance.

Therefore, a nonlinear control technique yields better performance. Nonetheless, these nonlinear control tech-
niques can be more sensitive to uncertainties. One candidate technique for the design of the satellite's control law

under a fast maneuver is the State-Dependent Riccati Equation (SDRE). SDRE provides an effective algorithm for
synthesizing nonlinear feedback control by allowing nonlinearities in the system states. The Brazilian National

Institute for Space Research (INPE, in Portuguese) was demanded by the Brazilian government to build remote-
sensing satellites, such as the Amazonia-1 mission. In such missions, the satellite must be stabilized in three-axes

so that the optical payload can point to the desired target. Although elsewhere the application of the SDRE tech-
nique has shown to yield better performance for the missions developed by INPE, a subsequent important question

is whether such better performance is robust to uncertainties. In this paper, we investigate whether the application
of the SDRE technique in the AOCS is robust stable to uncertainties in the missions developed by INPE. Moreover,
in order to handle such uncertainty appropriately, we propose a combination of SDRE with H-infinity based on a
left coprime factorization. In such a way that the attention is moved to the size of error signals and away from the
size and bandwidth of selected closed-loop transfer function. The initial results showed that SDRE controller is
robust to 5%, at least, variations in the inertia tensor of the satellite.