Observer-based boundary feedback control for attitude tracking of rigid bodies with partially liquid-filled cavities

Abstract

In the attitude tracking control tasks of rigid bodies with partially filled cavities, liquid sloshing is a crucial characteristic that hinders effective controller design and accuracy improvement. To overcome this problem, we propose a novel boundary feedback control (BFC) scheme based on the PDE-ODE cascade governing the rigid body attitude and internal liquid dynamics. We further develop an innovative PDE-based observer to cope with requirements on the infinite number of unmeasurable boundary states. Thus, using only attitude data, the discussed boundary controller can stabilize the attitude tracking error and the infinite-dimensional internal dynamics. The asymptotic stability of the closed-loop observer-based controller is established via the Lyapunov direct method. Finally, to show its efficacy, the proposed methodology is applied to the attitude tracking problem of a typical liquid-propellant satellite. In summary, the novelty is twofold: (i) due to dealing with the original involved PDE-ODE cascade, the formulated control strategy is more accurate than the relevant studies that have used liquid rigidity and potential ideal flow assumptions; (ii) the observer design approach is much broader than existing ones for nonlinear parabolic-type PDEs.