Thrust-vector control of a three-axis stabilized upper-stage rocket with fuel slosh dynamics

• Equations of motion for a three-axis stabilized spacecraft with fuel slosh are obtained.
• Thrust-vector control problem for an upper-stage rocket is formulated.
• A Lyapunov-based nonlinear feedback control law is designed.
• Simulation results are included to illustrate the effectiveness of the controller.

This paper studies the thrust vector control problem for an upper-stage rocket with fuel slosh dynamics. The dynamics of a three-axis stabilized spacecraft with a single partially-filled fuel tank are formulated and the sloshing propellant is modeled as a multi-mass–spring system, where the oscillation frequencies of the mass–spring elements represent the prominent sloshing modes. The equations of motion are expressed in terms of the three-dimensional spacecraft translational velocity vector, the attitude, the angular velocity, and the internal coordinates representing the slosh modes. A Lyapunov-based nonlinear feedback control law is proposed to control the translational velocity vector and the attitude of the spacecraft, while attenuating the sloshing modes characterizing the internal dynamics. A simulation example is included to illustrate the effectiveness of the control law.