Slosh-free feedback stabilization of liquid-propellant satellites with robustness to fuel density

Fuel sloshing plays a direct and pivotal role in the tracking control tasks of liquid-propellant satellites. To address this problem, existing works have considered some simplifying assumptions on fuel motion, such as fuel rigidity and potential ideal fluid. On the other hand, most studies have used discretized model-based control schemes to stabilize the infinite-dimensional satellite-fuel system, which can cause spillover instability and lead to a significant loss of accuracy. This paper solves the boundary feedback stabilization problem for the satellite-diaphragm tank system. This study presents two significant contributions to the field. First, it derives nonlinear parabolic partial ordinary differential equations that govern the attitude-trajectory dynamics of a satellite containing viscous fuel, utilizing Hamilton's principle. Second, it constructs innovative boundary feedback laws that provide stability in the attitude/trajectory control in the presence of fuel sloshing as well as robustness to variations in fuel density, employing the control Lyapunov functional methodology. These advancements provide a deeper understanding of satellite dynamics and enhance the effectiveness of control strategies in the presence of viscous fuel. The primary challenge resides in the fact that no sensor can be deployed within the fuel domain. Thus, the proposed boundary feedback control scheme does not require exact knowledge of fuel density and simply requires measurements of (i) rigid satellite data, and (ii) fuel boundary parameters. Additional controller features are highlighted by simulation results, including its transient response benefits in contrast to existing results and also the controller/viscosity contributions in fuel stabilization. In summary, the analysis reveals an average reduction in root mean square error for the attitude by 20 %. Furthermore, the convergence to the desired attitude is observed to be 42 % faster when compared to existing methods.