Sliding Mode Control Strategy of Spinning Electrodynamic Tether Formation during Its Spin-Up Process

This article mainly studies the spin-up control of a spinning electrodynamic tether formation (SEDTF) consisting of three linearly distributed nanosatellites connected by two tethers. The main challenge of the spin-up process is that due to the coupling effect of two tethers, more significant tether deformation and attitude disturbance on tethered nanosatellites emerge than that of a single-tether system. To deal with this problem, the dynamic model is first established for analyzing flexible tether motions and attitude motions of three nanosatellites. A sliding mode control strategy is then proposed for the spin-up process. First, considering the underactuation problem of the tether system, a sliding mode controller with an adaptive law is proposed to track spinning motion and stabilize tether deformation by adjusting only the electrical current. Second, considering the disturbance of constantly oscillating tension force, a sliding mode controller with a fixed-time prescribed performance is proposed to ensure a fast stabilization of attitude motions. Numerical results validate a synchronized spin-up of an SEDTF. Under the regulation of the proposed control strategy, tether deformations are reduced to an insignificant level, and attitude motions of nanosatellites are stabilized around designated orientations.