Port-Hamiltonian Based Control of the Sun-Earth 3D Circular Restricted Three-Body Problem: Stabilization of the L1 Lagrange Point
Open Access
- 1 January 2020
- journal article
- research article
- Published by Scientific Research Publishing, Inc. in Modern Mechanical Engineering
- Vol. 10 (03), 39-49
- https://doi.org/10.4236/mme.2020.103005
Abstract
In this paper, we use Port-Hamiltonian framework to stabilize the Lagrange points in the Sun-Earth three-dimensional Circular Restricted Three-Body Problem (CRTBP). Through rewriting the CRTBP into Port-Hamiltonian framework, we are allowed to design the feedback controller through energy-shaping and dissipation injection. The closed-loop Hamiltonian is a candidate of the Lyapunov function to establish nonlinear stability of the designed equilibrium, which enlarges the application region of feedback controller compared with that based on linearized dynamics. Results show that the Port-Hamiltonian approach allows us to successfully stabilize the Lagrange points, where the Linear Quadratic Regulator (LQR) may fail. The feedback system based on Port-Hamiltonian approach is also robust against white noise in the inputs.Keywords
This publication has 22 references indexed in Scilit:
- HerschelSpace ObservatoryAstronomy & Astrophysics, 2010
- Trajectory and Correction Maneuver During the Transfer from Earth to Halo OrbitChinese Journal of Aeronautics, 2008
- The James Webb Space TelescopeSpace Science Reviews, 2006
- Transit-Orbit Search for Planar Restricted Three-Body Problems with PerturbationsJournal of Guidance, Control, and Dynamics, 2004
- Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systemsAutomatica, 2002
- Putting energy back in controlIEEE Control Systems, 2001
- New approach to halo orbit determination and controlJournal of Guidance, Control, and Dynamics, 1996
- The general problem of the stability of motionInternational Journal of Control, 1992
- The stability of the Lagrange triangular point and a theorem of ArnoldJournal of Differential Equations, 1986
- Halo Orbit Formulation for the ISEE-3 MissionJournal of Guidance and Control, 1980