Attitude Control and Stability Analysis of Electric Sail

This article investigates the attitude control and stability analysis of an electric solar wind sail (E-sail) by considering elastic deflection of tethers while assuming main spacecraft and remote units as point masses. The attitude and orbital motion of the E-sail is analyzed by a high-order high-fidelity E-sail model derived from the nodal position finite-element method, where the attitude angles are implicitly described via the nodal coordinates. To overcome the difficulty in handling the stability analysis of high-order model under the Lyapunov framework, the E-sail's attitude dynamics is approximated explicitly by a reduced order analytical model with only three attitude angles. A sliding mode control law is proposed for the E-sail attitude control based on the reduced order analytical E-sail model and its stability is proved by the Lyapunov theory. Finally, two schemes are derived to map the control torque to either the control thrust at remote units or the voltages of main tethers respectively, which are applied to the high-fidelity E-sail model for attitude control. Numerical simulation demonstrates that the proposed control law performs similarly with the high-fidelity and reduced order analytical E-sail models if proper control gains are selected. It shows that the control law developed from the reduced order analytical E-sail model can stably control the attitude of a real E-sail. The investigation also indicates that the high-order flexible E-sail model provides an effective virtual testbed to evaluate the E-sail attitude control strategy derived from the reduced order attitude dynamics.