This study focuses on stabilizing the libration dynamics of an electrodynamic tether system (EDTS) using generalized torques induced by the Lorentz force. In contrast to existing numerical optimization methods, a novel analytical feedback control law is developed to stabilize the in-plane and out-of-plane motions of a tether by modulating the electric current only. The saturation constraint on the current is accounted for by adding an auxiliary dynamic system to the EDTS. To enhance the robustness of the proposed controller, multiple perturbations of the orbital dynamics, modeling uncertainties, and external disturbances are approximated using a neural network in which the weighting matrix and approximation error are estimated simultaneously, such that these perturbations are well compensated for during the control design of the EDTS. Furthermore, a dynamically scaled generalized inverse is utilized to address the singular matrix in the control law. The closed-loop system is proven to be ultimately bounded based on Lyapunov stability theory. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed analytical control law.

The paper presents a high-efficient finite difference method for solving the PDE model of the single-link flexible manipulator system with boundary feedback control. Firstly, an abstract state-space model of the manipulator is derived from the original PDE model and the associated boundary conditions of the manipulator by using the velocity and bending curvature of the flexible link as the state variables. Then, the second-order implicit Crank-Nicolson scheme is adopted to discretize the state-space equation, and the second-order one-sided approximation is used to discretize the boundary conditions with excitations and feedback control. At last, the state-space equation combined with the boundary conditions of the flexible manipulator is transformed to a system of linear algebraic equations, from which the response of the flexible manipulator can be easily solved. Numerical simulations are carried out to simulate the manipulator under various excitations and boundary feedback control. The results are compared with ANSYS to demonstrate the accuracy and high efficiency of the presented method.

Space debris, especially the space debris cloud, has threatened severely the safety of future space missions. In the framework of multibody system dynamics, a computational approach is proposed in this study to investigate the dynamics of net deployment and capture of space debris cloud using this net subject to large overall motions and large deformations. To obtain high simulation fidelity of capturing space debris cloud, the gradient deficient beam element of the absolute nodal coordinate formulation (ANCF) is employed to discretize threads which are woven into the net. The normal contact force between the net and the debris cloud and among debris particles is computed by using the penalty method. Some deployment examples are presented to investigate the influences of shooting velocity of bullets and microgravity as well as the angle between the traveling direction of the net and the microgravity direction on the deployment characteristics of the tethered net. Other capturing examples are given to clarify the effect of the deployment area of the net at the moment it starts to contact with the debris cloud on the capture rate and to demonstrate the effectiveness of the proposed approach for capturing space debris cloud using the net in microgravity conditions.