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.
Keywords: Floquet theory; control; dynamic behavior; stable deployment; tethered satellite formation.