Observer-Based Adaptive Backstepping Sliding-Mode Control of the Satellite Attitude with a Partially Filled Spherical Fuel Tank

Modeling and controlling the fuel slosh phenomenon in a satellite is a vital problem in the field of satellite attitude control. In this paper, a satellite with a partially filled spherical fuel tank that uses diaphragm as a propellant management device (PMD), has been considered. The fuel slosh dynamics is modeled by a spherical pendulum with two degrees of freedom (DOF) and a rigid arm, which represents the first mode of sloshing. The effects of the diaphragm that surround the fuel surface, are considered as torsional spring-damper attached to the satellite body. The coupled equations of satellite motion and fuel are derived using the Lagrange method. The nonlinear control method based on the backstepping method (backstepping method, backstepping sliding mode, adaptive backstepping sliding mode) is used for the control of the satellite attitude. The stability of the controllers has been proved using Lyapunov functions. Since fuel state variables cannot be measured as system output, a nonlinear observer based on the Thau method is provided to estimate the fuel state variables. Finally, the performance of the proposed controllers and observer is evaluated using the numerical simulations.