Stationkeeping of an L₂ Libration Point Satellite with θ-D Technique

Ming Xin; S. N. Balakrishnan; Henry J. Pernicka; Michael W. Dancer

Stationkeeping of an L₂ Libration Point Satellite with θ-D Technique

Ming Xin
, S. N. Balakrishnan
, Henry J. Pernicka
, Michael W. Dancer

Research output: Contribution to journal › Article › peer-review

Abstract

A new method for L ₂ libration-point orbit stationkeeping is proposed in this paper using continuous thrust. The circular restricted three-body problem with Sun and Earth as the two primaries is considered. The unstable orbit about the L ₂ libration-point requires stationkeeping maneuvers to maintain the nominal path. In this study, an approach, called the "θ-D technique," based on optimal control theory gives a closed-form suboptimal feedback solution to solve this nonlinear control problem. In this approach the Hamiltonian-Jacobi-Bellman (HJB) equation is solved approximately by adding some perturbations to the cost function. The controller is designed such that the actual trajectory tracks a predetermined reference orbit with good accuracy. Numerical results employing this method demonstrate the potential of this method.

Original language	American English
Journal	Proceedings of the 2004 American Control Conference
State	Published - Jan 1 2004

Keywords

Jacobian Matrices
Aerospace Control
Approximation Theory
Artificial Satellites
Control System Synthesis
Feedback
Nonlinear Control Systems
Nonlinear Equations
Perturbation Techniques
Suboptimal Control

Disciplines

Aerospace Engineering
Mechanical Engineering

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Stationkeeping of an L Libration Point Satellite with -D TechniFinal published version, 441 KBLicense: CC BY

Cite this

@article{f0d7033a0d0a4af1bfae2ce0296b4c6f,

title = "Stationkeeping of an L₂ Libration Point Satellite with θ-D Technique",

abstract = " A new method for L 2 libration-point orbit stationkeeping is proposed in this paper using continuous thrust. The circular restricted three-body problem with Sun and Earth as the two primaries is considered. The unstable orbit about the L 2 libration-point requires stationkeeping maneuvers to maintain the nominal path. In this study, an approach, called the {"}θ-D technique,{"} based on optimal control theory gives a closed-form suboptimal feedback solution to solve this nonlinear control problem. In this approach the Hamiltonian-Jacobi-Bellman (HJB) equation is solved approximately by adding some perturbations to the cost function. The controller is designed such that the actual trajectory tracks a predetermined reference orbit with good accuracy. Numerical results employing this method demonstrate the potential of this method.",

keywords = "Jacobian Matrices, Aerospace Control, Approximation Theory, Artificial Satellites, Control System Synthesis, Feedback, Nonlinear Control Systems, Nonlinear Equations, Perturbation Techniques, Suboptimal Control",

author = "Ming Xin and Balakrishnan, \{S. N.\} and Pernicka, \{Henry J.\} and Dancer, \{Michael W.\}",

year = "2004",

month = jan,

day = "1",

language = "American English",

journal = "Proceedings of the 2004 American Control Conference",

}

TY - JOUR

T1 - Stationkeeping of an L₂ Libration Point Satellite with θ-D Technique

AU - Xin, Ming

AU - Balakrishnan, S. N.

AU - Pernicka, Henry J.

AU - Dancer, Michael W.

PY - 2004/1/1

Y1 - 2004/1/1

N2 - A new method for L 2 libration-point orbit stationkeeping is proposed in this paper using continuous thrust. The circular restricted three-body problem with Sun and Earth as the two primaries is considered. The unstable orbit about the L 2 libration-point requires stationkeeping maneuvers to maintain the nominal path. In this study, an approach, called the "θ-D technique," based on optimal control theory gives a closed-form suboptimal feedback solution to solve this nonlinear control problem. In this approach the Hamiltonian-Jacobi-Bellman (HJB) equation is solved approximately by adding some perturbations to the cost function. The controller is designed such that the actual trajectory tracks a predetermined reference orbit with good accuracy. Numerical results employing this method demonstrate the potential of this method.

AB - A new method for L 2 libration-point orbit stationkeeping is proposed in this paper using continuous thrust. The circular restricted three-body problem with Sun and Earth as the two primaries is considered. The unstable orbit about the L 2 libration-point requires stationkeeping maneuvers to maintain the nominal path. In this study, an approach, called the "θ-D technique," based on optimal control theory gives a closed-form suboptimal feedback solution to solve this nonlinear control problem. In this approach the Hamiltonian-Jacobi-Bellman (HJB) equation is solved approximately by adding some perturbations to the cost function. The controller is designed such that the actual trajectory tracks a predetermined reference orbit with good accuracy. Numerical results employing this method demonstrate the potential of this method.

KW - Jacobian Matrices

KW - Aerospace Control

KW - Approximation Theory

KW - Artificial Satellites

KW - Control System Synthesis

KW - Feedback

KW - Nonlinear Control Systems

KW - Nonlinear Equations

KW - Perturbation Techniques

KW - Suboptimal Control

UR - https://scholarsmine.mst.edu/mec_aereng_facwork/3478

M3 - Article

JO - Proceedings of the 2004 American Control Conference

JF - Proceedings of the 2004 American Control Conference

ER -

Stationkeeping of an L₂ Libration Point Satellite with θ-D Technique

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