Stability and control of tethered satellite with chemical propulsion in orbital plane

The tethered satellite with chemical propulsion has broad application prospects in the disposal of abandoned satellites, the orbital rescue of spacecrafts, and the transportation of space supplies, which is completely different from the traditional applications of tethered satellites. Therefore, new research on its dynamics, stability, and control becomes useful and interesting. In this article, based on a dumbbell model of tethered satellite, the dynamics equations of tethered system in orbital maneuvering are established. Furthermore, according to the definitions of transversal and radial propulsive coefficients, analytical solutions of the equilibrium position for librational angle are derived during maneuvering in orbital plane; meanwhile, the effects of propulsive coefficients on librational stability are analyzed, which provides a basis for a selection of expected attitude trajectory. Then, a method of hierarchical sliding-mode tension control is presented to track the expected in-plane angle. This method can address the underactuated problem of tethered systems without either complex coordinate transformation for the system state model or constraint equation restrictions. During orbital flight, in-plane and out-of-plane angles are decoupled, so the tether tension control cannot be conducted to inhibit the out-of-plane angle. To solve this problem, the binormal component of thrust acceleration normal to the orbital plane is adopted as a control variable, and a feedback linearization-based thrust controller is designed to damp out the out-of-plane angle. Afterwards, orbital transfer cases between two circular orbits are studied to demonstrate the effectiveness of the tethered satellite with chemical propulsion. Numerical simulation results indicate that the stability of librational angles has a close relation to propulsive coefficients, and distributions of stable centers and unstable saddle points are totally different on both sides of bifurcation point. In addition, tracking control requirements for tethered satellite are guaranteed by designed controllers, which ensure flight safety in orbital maneuvering.