Modeling and Control of Electrodynamic Tethers - an Energy and Topology Approach

A space tether is a cable used to connect spacecrafts in an orbiting structure. If an electrical current is lead through the tether, it can be utilized to provide propulsion for the spacecraft. In this case the cable is referred to as an electrodynamic tether. The system utilizes the magnetic field of the Earth for creating a Lorentz force along the tether which occur when a current carrying wire operates in a magnetic field. The use of electrodynamic tethers are interesting since they operate solely on electrical energy, which can be provided by solar panels of the spacecrafts. In this way the amount of propellant a spacecraft need to bring from Earth can be reduced. In this thesis the modeling and control of electrodynamic tethers are investigated, both when a single tether is used to connect two spacecrafts, and when the tethers are used i more general formations of spacecrafts. One of the main challenges when using electrodynamic tethers is that the force created along the tether is based on an external uncontrollable condition, namely the magnetic field. Even whit a known model of the magnetic field, limitations to the creation of the Lorentz force still exists, since the force can only be generated perpendicular to the instantaneous magnetic field. Furthermore, the control problem is complicated by the time variations in the magnetic field. This thesis solves these problems by utilizing an energy-based system description and a passivity-based control design. An advantage of the energy-based approach is that the stability of the system can easily be investigated, based on the energy flow in the system. Systems of several spacecrafts connected by tethers has many applications, for example in connection with space telescopes and space stations. Tethered formations are advantageous, compared to formations of free-flying spacecrafts, since a predetermined geometry of spacecrafts is easily maintained. This thesis investigates the use of electrodynamic tethers for such tethered satellite formaii tions with focus on the modeling and control aspects. One can think of many different structures for solving tasks in space, and separate derivations of the dynamical equations can be cumbersome. It can therefore be advantageous to be able to model a formation independent of its topology, i.e. the way tethers and satellites are interconnected. The thesis treats a class of formations in a generic framework, using graph theory to describe the topology of the formations. The framework can be used both to deduce the equations of motion for the attitude motion of the formation and for control design regarding the same motion. The main part of the thesis consists of five scientific papers which have been submitted for international journals and conferences during the PhD project.