Dynamic Behavior Analysis and Stability Control of Tethered Satellite Formation Deployment

In recent years, Tethered Space Systems (TSSs) have received significant attention in aerospace research as a result of their significant advantages: dexterousness, long life cycles and fuel-less engines. However, configurational conversion processes of tethered satellite formation systems in a complex space environment are essentially unstable. Due to their structural peculiarities and the special environment in outer space, TSS vibrations are easily produced. These types of vibrations are extremely harmful to spacecraft. Hence, the nonlinear dynamic behavior of systems based on a simplified rigid-rod tether model is analyzed in this paper. Two stability control laws for tether release rate and tether tension are proposed in order to control tether length variation. In addition, periodic stability of time-varying control systems after deployment is analyzed by using Floquet theory, and small parameter domains of systems in asymptotically stable states are obtained. Numerical simulations show that proposed tether tension controls can suppress in-plane and out-of-plane librations of rigid tethered satellites, while spacecraft and tether stability control goals can be achieved. Most importantly, this paper provides tether release rate and tether tension control laws for suppressing wide-ranging TSS vibrations that are valuable for improving TSS attitude control accuracy and performance, specifically for TSSs that are operating in low-eccentricity orbits.

Dynamic Behavior Analysis of Tethered Satellite System Based on Floquet Theory

In this paper, an n-star general dynamic model of tethered satellite system with closed-loop configuration is provided. An analytical method for periodic solution stability of the general dynamic model is proposed based on Floquet theory, which proved that the periodic solution stability of the system depends on the maximum modulus for the eigenvalue of a matrix related to the Jacobian matrix. The periodic solution stability of a 3-star system with equilateral triangle as the initial configuration is analyzed as an example based upon the analytical method. The critical stable spin angular velocity of the 3-star system is analyzed when the system spins clockwise, and its numerical simulation is carried out to verify the results. The results show that the analytical method of periodic solution stability can solve the critical stable spin angular velocity accurately of the tethered satellite system, and the 3-star system can guarantee stable spin when the spin angular velocity is about 2.1 times of its revolution angular velocity, otherwise the disturbed system will not be able to re-converge to the initial configuration in finite time.

Deployment of Hub-Spoke Tethered Satellite Formation with Adaptive Sliding Mode Tension Control

This paper studies the deployment control of a spinning hub-spoke tethered satellite formation, which is a challenging issue due to the strong nonlinear coupling between the hub and sub-satellites, and the underactuated nature of the system if no thrust is used for control. The mathematical model of the formation system is established based on the assumption of rigid body of the hub, inextensible tether, and lumped masses of the sub-satellites. Two novel formation deployment controllers are proposed based on tension control and hybrid tension-thrust control strategies, where underactuated sliding mode control and nonsingular terminal sliding mode control method are used, respectively. The adaptive control theory is adopted to estimate the unknown upper bound of the gravitational perturbation caused by the rotation of the system around the hub. It can be proven by the Lyapunov theory that the close-loop systems have bounded and asymptotic stability under these two deployment controllers, respectively. Finally, numerical simulations are conducted to validate the effectiveness and robustness of the proposed controllers.