Lagrangian, Hamiltonian, And Energy-Based Control For Space Tethered System

Abstract

A typical and useful way to derive the dynamics equation of the tethered systems is by means of the Lagrange’s equations and various dynamic models of different tethered missions are established by the Lagrangian formulation. The Hamiltonian formulation is also widely used in the mechanical systems for its well-known symplectic structure property. With this in mind, the dynamics equation of the tethered system’s motion are deduced by Hamilton’s equations in this research. The relation between the Lagrangian and Hamiltonian is shown by Legendre transformation. The goodness of the Hamiltonian formulation is intuitive to reveal the Energy balance property that corresponds to the passivity property. Furthermore, the Hamiltonian energy function of tethered system is employed for facilitating the controller design. In order to bring the system into operations, the energy based control is to achieve the tethered system for precise positioning. Simulations are used to demonstrate the effectiveness of the designed controller.