Dynamics and control of tethered satellite systems

Abstract

The purpose of this research is to investigate the dynamics of a tethered satellite system in which the flexibility of the tether is considered and to design control laws for the deployment and retrieval of the tethered subsatellite using a method based on the Lyapunov stability theory. The dynamics of the system considered is modelled with as little simplifications and assumptions as possible to keep the problem tractable and at the same time physically realistic. Effects of geometric nonlinearity is taken into account. The hybrid governing equations are discretized by using the Galerkin's method. The flexible tether is also modelled as a series of beads which are connected in series by massless springs. Several tension and reel rate feedback control laws for deployment and retrieval are designed using Lyapunov's method when flexibility of the tether is neglected. It was found that the tension control laws designed for the simplified system can have a stabilizing effect on the vibrations of the tether. The performance of the full dynamic system with the designed control laws is investigated via simulations using both the Galerkin and bead model. At the same time, observations regarding the dynamics of the system and the validity of using the Galerkin's discretization procedure for a variable length tether are investigated. It is shown that the effects of geometric nonlinearity is significant during retrieval and that when geometric nonlinearity is included, an artificial instability is introduced into the Galerkin model causing sudden divergence of the system response during retrieval. This behavior is reproduced even for a simplified two dimensional example problem. It was found that the bead model produces a response that is physically realistic. Simulation studies using the bead model show that when reel rate control laws are used, vibrations grow to the point where the system becomes unstable. However, the tension control laws successfully retrieve the tethered subsatellite and were found to be effective in damping the elastic longitudinal vibrations in the early stages of retrieval. A nonrecursive order-N method for efficiently simulating the bead model is also introduced. The feasibility of implementing the order-N method for parallel computation is investigated using two parallel computer architectures. It was found that, due mostly to communication time, the use of the parallel computers do not offer any improvement in overall computation time.