### Abstract

A spacecraft with electrodynamic tether orbiting the Earth will be subject to a periodic forcing term induced by the variation of the magnetic field along the orbit. The periodic forcing term leads to a family of unstable periodic solutions for a tether carrying a constant current. This paper presents a control design for stabilizing these periodic solutions. The design consists of a control law for stabilizing the open-loop equilibrium and a bias term which forces the system trajectory away from the equilibrium. The tether needs to be positioned away from open-loop equilibrium for the tether to affect the orbit parameters. An approximation of the periodic solutions of the closed loop system is found as a series expansion in the parameter plane spanned by the controller gain and the bias term. The stability of the solutions is investigated using linear Floquet analysis of the variational equation and the region of stable periodic solutions in the parameter plane is found.

Original language | English |
---|---|

Title of host publication | Proceedings of the European Control Conference 2009 |

Publisher | IEEE |

Publication date | 2009 |

Pages | 2169-2174 |

ISBN (Print) | 9783952417393 |

Publication status | Published - 2009 |

Event | European Control Conference 2009 - Budapest, Hungary Duration: 23 Aug 2009 → 26 Aug 2009 http://www.conferences.hu/ecc09/ |

### Conference

Conference | European Control Conference 2009 |
---|---|

Country | Hungary |

City | Budapest |

Period | 23/08/2009 → 26/08/2009 |

Internet address |

### Keywords

- Control and Systems Engineering
- Closed loop systems
- Orbits
- Space flight
- Damping injection
- Electro-dynamic tether
- Periodic forcing
- Periodic solution
- Series expansion
- System trajectory
- Tethered satellite systems
- Variational equations
- Tetherlines

## Cite this

Larsen, M. B., & Blanke, M. (2009). Stabilization of periodic solutions in a tethered satellite system by damping injection. In

*Proceedings of the European Control Conference 2009*(pp. 2169-2174). IEEE.