Active Vibration Suppression of the Free-Floating In-Orbit Manufacturing System Using Computational Control Framework

This paper presents a nonlinear vibration-control framework for a flexible satellite structure modeled using a Nodal Position Finite Element formulation. The system couples a rigid base with a variable-length flexible beam to represent in-orbit manufacturing or deployable appendages. Dynamic responses are integrated using the Newmark-β method with automatic mesh adaptation. Local element dynamics are expressed in a compact state-space form and controlled via a Sontag-type Control Lyapunov Function approach that generates continuous stabilizing feedback. Separate base and tip controllers provide translational and rotational actuation for attitude stabilization and vibration suppression. Simulation results show that the proposed strategy achieves sufficient damping and stable deformation control under base excitation and structural growth. The method demonstrates the feasibility of combining arbitrary Lagrangian–Eulerian finite element modeling with nonlinear Lyapunov-based control for future large, flexible space systems undergoing on-orbit structural evolution.