Tethered-satellite systems have great potential in completing various space missions. However, existing researches mainly focus on the deployment of satellites in a circular orbit, whereas deployment in an elliptical orbit, especially with disturbances, is rarely studied. This study develops a new control strategy to deploy tethered satellites in a low-eccentricity elliptical orbit that also considers system uncertainties and external disturbances. First, the periodical solution of the librational motion of a tethered-satellite system in an elliptic orbit is calculated. Because there is no fixed equilibrium point for deployment in elliptical orbits, the periodical solution is set as the end condition for deployment. After that, the controllability of the system is verified and an open-loop tension-control law is optimized by particle swarm optimization (PSO) and the Nelder-Mead method. To eliminate effects from uncertainties in initial states and errors from the deployment mechanism, an adaptive sliding mode controller is designed to achieve high-precision trajectory tracking. The performance of the proposed controller is compared quantitatively with a proportion-derivative (PD) controller and normal sliding mode controller. Furthermore, Monte Carlo simulations are conducted to demonstrate the effectiveness and robustness of the proposed controller when subjected to uncertain initial states. The simulation results indicate that the proposed control strategy enables the stable deployment of tethered-satellite systems despite the uncertainties and perturbations.

This paper mainly studies the spin-up control of a spinning electrodynamic tether formation (SEDTF) consisting of three linearly distributed nano-satellites 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 nano-satellites 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 nano-satellites. A sliding mode control strategy is then proposed for the spin-up process: 1) 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 electrical current; 2) 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 a SEDTF. Under the regulation of the proposed control strategy, tether deformations are reduced to an insignificant level, and attitude motions of nano-satellites are stabilized around designated orientations.

Two attitude coordination controllers that make the system converge to the equilibrium point in finite time are designed for spacecraft formation flying with actuator saturation constraints. The first finite-time attitude coordination controller is suitable for the situation that all states of the closed-loop system are available. To deal with the problem of failing to measure angular velocity, a novel filter is presented in the second finite-time attitude coordination controller. Because the model of spacecraft formation flying is established based on the rotation matrix, the closed-loop system does not have the drawback of unwinding. The theoretical analysis and simulation results are given to prove the validity of the proposed controllers.

This paper investigates two robust finite-time controllers for the attitude control of the spacecraft by using a modified terminal sliding mode surface. With the use of terminal sliding mode control and adaptive control, the controllers under input saturation can compensate both external disturbances and the uncertainty of the model parameters. By using the first and the second controller, the closed-loop system is finite-time stability and practical finite-time stability, respectively. As the system model is based on the rotation matrix, both controllers are without unwinding. Numerical simulations are given to demonstrate the effectiveness of the finite-time controllers.