Research On Dynamic And Control Of Electrodynamic Tether

Electrodynamic tether will generate Lorentz force by the interaction between the tether with current and the geomagnetic field in order to realize the orbital maneuver of normal spacecraft and the deorbit of sapce debris.Compare to the chemical thrusters,electrodynamic tether has the advantages of low mass,propellantless,ease of operation,and almost the same thrust force with the electric thrusters.But considering the large space size,limited thrust force,and continute space perturbations,the electrodynamic tether will experience a series of complex nonlinear dynamic behaviors.This dissertation will study the dynamic and control of the electrodynamic tether during deployment,station-keeping,active orbital maneuver and passive deorbit.The major contents of this dissertation consist of the following parts:For the dynamic and control of tethered deployment,under the assumption of the rigid rod,the finite time control method based on the cascaded sliding mode surfaces is designed to deploy the tether stably.Firstly,the dynamic model of tethered deployment is built based on the Lagrange equation,and the generalized forces caused by the Lorentz force are calculated.Then,a PD controller is designed according to the linear state equation near the equilibrium position,and control arguments are determinate by KTC theory.The finite time sliding mode control based on the cascaded sliding mode surfaces is also designed to deploy the tether quickly,and the stability is proved.Finally,the induced current through the bare tether based on OML theory is calculated,then analyze the effect of induced current on the in-plane and out-of-plane during the deployment.In order to suppress the libration of the tether during the deployment,an on/off control strategy is demonstrated.For the tethered dynamic and control of active orbital maneuver,long-term motion is studied by flourier series' s current.Firstly,analytical periodic solutions and numerical periodic solutions are presented by perturbation method and differential-correction numerical algorithm,and the stabilities of the period solutions are verified by the Floquet's theory.Then,considering the Lorentz force as continue small thrust forces,the current through the tether is expressed by the flourier series.Submitted to the orbital perturbation equations,the average orbital motion equations are expressed by only five control arguments,then quasi-linear controller are used to realize orbital maneuver control.Finally,considering the in-plane and out-of-plane motion of the tether,Gauss pseudo-spectral method is used to get the optimal control current under some optimal index.For the dynamic and control during deorbiting based on flexible tether model,lumped-mass model consisting of finite mass points connected by strings and dampers and the outside forces acting on each mass point are derived,then the motion equation of the deorbit is given by the Newton second law.Then,analyze the effects of orbital arguments,tether arguments and the heating on the induced current,Lorentz force and the performance of deorbit.Finally,two stable controllers based on the Hamilton energy and libration angles of visual rigid rod are designed to guarantee the stability of the tether during the deorbit progress.For the state estimation of electrodynamic tether,Unscented Kalman Filter using spherical simplex sigma-point selection and the square root is selected as estimator.First,nonlinear state equations of the rigid insulated electrodynamic tether and the measurement equations given by the output of GPS receivers or three axis tension sensor are built.Then,nonlinear state equations of the lumped-mass electrodynamic tether are given,and the measurement equations containing two and three segments are given by the outputs of two GPS receivers and two three axis tension sensors mounted on the main satellite and subsatellite.Finally,the performances of the filters are verified by numerical simulations.