Sloshing disturbance rejection control design for liquid-filled spacecrafts

This paper studies the sloshing disturbance rejection control (SDRC) problem for liquid-filled spacecrafts, in which the motion of the spacecraft is described by ordinary differential equations (ODEs) and the fluid dynamics is described by the Burgers' equation with the acceleration due to the inertial force of liquid. The sloshing force is that the fluid, via pressure and viscous effects, exerts on the spacecraft, containing the sloshing disturbance and the inertial force of liquid. The modal decomposition technique is initially applied to the Burgers' equation to derive an infinite dimensional ODE system of coupled slow and fast dynamics, and thus, the sloshing disturbance is divided into two parts: slow and fast. Based on the slow subsystem of the Burgers' equation, an observer is constructed to estimate the slow sloshing disturbance, which is called the slow sloshing disturbance observer (SSDO). Then, a low dimensional SSDO-based H_∞ SDRC design is developed in terms of linear matrix inequalities (LMIs), where the slow sloshing disturbance is compensated by the SSDO, and the fast one is attenuated by H_∞ control. The resulting controller can ensure that the ODE system of the spacecraft is exponentially stable in the presence of the slow sloshing disturbance and satisfies a prescribed attenuation level in the presence of the fast sloshing disturbance. Finally, the proposed method is applied to the control of a unilateral movement liquid-filled spacecraft to illustrate its effectiveness.