In this thesis, dynamics and control of multi-body tethered satellite systems are investigated. First a dynamical model is developed that takes into account the three dimensional librational motion of the system as well as the nonlinear vibrations of the tethers, both in longitudinal and transverse directions. The assumed modes method is used to discretize the continuous tethers. Using Lagrange's equations, splitting the vector of generalized coordinates to a set of subvectors, where each subvector corresponds to a specific tether, a set of nonlinear ordinary differential equations governing the motion of the system is obtained in the explicit analytical form. A fourth order strain energy expression is used in the formulation to allow the possibility of moderately large deformation of the tethers. The equations are applicable whether the length of the tethers are constant (station-keeping phase) or changing with time (deployment and retrieval phases). They are transformed into vector form for simulation purposes. / Among the external forces, the aerodynamic forces and their effects on the dynamics and stability of the system are given more attention. The free molecular flow model is used to calculate the aerodynamic forces resulting from the material damping of the tethers are considered in this investigation. These forces, which are very difficult to model accurately, are modelled using a viscous damping model. / Equilibrium configurations of the system, as special solutions of the equations of motion, in the absence or presence of the aerodynamic forces, are studied in more detail. A closed form solution to the static equilibrium equations is obtained when there is no external force acting on the system other than the gravitational force. The set of nonlinear equations of motion is then linearized analytically about a particular equilibrium configuration for stability and eigenvalue analysis. The natural frequencies of some single-tether as well as multi-tether systems are calculated using these linearized equations. / Stability of a single-tether system in low orbit missions is investigated, ignoring the aerodynamic forces on the main-satellite as well as on the tether. Assuming a particular geometrical configuration for the subsatellite and using the linearized equations, the effect of the aerodynamic forces, particularly aerodynamic lift, on the stability of the system as well as the equilibrium configuration of the system is examined through the eigenvalue analysis. This analysis is then extended to multi-body systems. / Finally the problem of controlling the nonlinear system through the application of Lyapunov's stability theory is examined for multi-body tethered systems, ignoring the transverse oscillations of the tethers. Initially, based on the Hamiltonian of the system, a Lyapunov function is introduced for a system with massless and rigid tethers. It leads to a linear tension control law. When the mass of the tethers is taken into account the Lyapunov function is modified and a new tension control law is developed which is no longer linear. With the assumption that the longitudinal oscillations of the tethers are small compared to the length of the tethers, a Lyapunov functions is constructed for systems with elastic tethers. At the end, a hybrid control law is examined to improve the performance of the controlled system.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.28796 |
| Date | January 1995 |
| Creators | Keshmiri, Mehdi |
| Contributors | Misra, Arun K. (advisor) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy (Department of Mechanical Engineering.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001459948, proquestno: NN05731, Theses scanned by UMI/ProQuest. |
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