Control of nonlinear spacecraft attitude motion via state augmentation, Lyapunov-Floquet transformation and normal forms

Peter M.B. Waswa, Sangram Redkar

Research output: Contribution to journalArticle

Abstract

This article analyzes and controls the quasi-periodic attitude motion of a gravity-gradient stabilized spacecraft in eccentric orbit by way of system states augmentation, Lyapunov-Floquet transformation and normal forms simplification. Perturbing torques in the ambient space environment can be shown to engender spacecraft attitude motion represented by nonlinear dynamics coupled in the roll-yaw axes; and, uncoupled planar dynamics in the pitch axis. The non-planar dynamics equations are homogeneous and analytically solvable. However, the pitch attitude motion is nonlinear, possesses parameter-varying coefficients and is subjected to external periodic excitations. Consequently, we transform the unwieldy attitude dynamics into relatively more amenable schemes for analysis and control law synthesis. Subsequently, we demonstrate the implementation of linear and nonlinear control laws (i.e. bifurcation and sliding mode control laws) on the relatively acquiescent transformed attitude dynamics. By employing a two-pronged approach, the quasi-periodic planar motion is independently shown to be stabilizable via the nonlinear control approaches.

Original languageEnglish (US)
JournalAdvances in Space Research
DOIs
StatePublished - Jan 1 2019
Externally publishedYes

Fingerprint

Spacecraft
spacecraft
augmentation
bifurcation
torque
sliding
transform
gravity
approach control
yaw
eccentric orbits
aerospace environments
Sliding mode control
simplification
Gravitation
Orbits
Torque
gravitation
gradients
coefficients

Keywords

  • Gravity gradient
  • Hopf bifurcation
  • Lyapunov-Floquet transformation
  • Nonlinear dynamics
  • Normal forms
  • Periodic dynamics control
  • Sliding mode
  • Spacecraft attitude
  • State augmentation

ASJC Scopus subject areas

  • Aerospace Engineering
  • Astronomy and Astrophysics
  • Geophysics
  • Atmospheric Science
  • Space and Planetary Science
  • Earth and Planetary Sciences(all)

Cite this

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title = "Control of nonlinear spacecraft attitude motion via state augmentation, Lyapunov-Floquet transformation and normal forms",
abstract = "This article analyzes and controls the quasi-periodic attitude motion of a gravity-gradient stabilized spacecraft in eccentric orbit by way of system states augmentation, Lyapunov-Floquet transformation and normal forms simplification. Perturbing torques in the ambient space environment can be shown to engender spacecraft attitude motion represented by nonlinear dynamics coupled in the roll-yaw axes; and, uncoupled planar dynamics in the pitch axis. The non-planar dynamics equations are homogeneous and analytically solvable. However, the pitch attitude motion is nonlinear, possesses parameter-varying coefficients and is subjected to external periodic excitations. Consequently, we transform the unwieldy attitude dynamics into relatively more amenable schemes for analysis and control law synthesis. Subsequently, we demonstrate the implementation of linear and nonlinear control laws (i.e. bifurcation and sliding mode control laws) on the relatively acquiescent transformed attitude dynamics. By employing a two-pronged approach, the quasi-periodic planar motion is independently shown to be stabilizable via the nonlinear control approaches.",
keywords = "Gravity gradient, Hopf bifurcation, Lyapunov-Floquet transformation, Nonlinear dynamics, Normal forms, Periodic dynamics control, Sliding mode, Spacecraft attitude, State augmentation",
author = "Waswa, {Peter M.B.} and Sangram Redkar",
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T1 - Control of nonlinear spacecraft attitude motion via state augmentation, Lyapunov-Floquet transformation and normal forms

AU - Waswa, Peter M.B.

AU - Redkar, Sangram

PY - 2019/1/1

Y1 - 2019/1/1

N2 - This article analyzes and controls the quasi-periodic attitude motion of a gravity-gradient stabilized spacecraft in eccentric orbit by way of system states augmentation, Lyapunov-Floquet transformation and normal forms simplification. Perturbing torques in the ambient space environment can be shown to engender spacecraft attitude motion represented by nonlinear dynamics coupled in the roll-yaw axes; and, uncoupled planar dynamics in the pitch axis. The non-planar dynamics equations are homogeneous and analytically solvable. However, the pitch attitude motion is nonlinear, possesses parameter-varying coefficients and is subjected to external periodic excitations. Consequently, we transform the unwieldy attitude dynamics into relatively more amenable schemes for analysis and control law synthesis. Subsequently, we demonstrate the implementation of linear and nonlinear control laws (i.e. bifurcation and sliding mode control laws) on the relatively acquiescent transformed attitude dynamics. By employing a two-pronged approach, the quasi-periodic planar motion is independently shown to be stabilizable via the nonlinear control approaches.

AB - This article analyzes and controls the quasi-periodic attitude motion of a gravity-gradient stabilized spacecraft in eccentric orbit by way of system states augmentation, Lyapunov-Floquet transformation and normal forms simplification. Perturbing torques in the ambient space environment can be shown to engender spacecraft attitude motion represented by nonlinear dynamics coupled in the roll-yaw axes; and, uncoupled planar dynamics in the pitch axis. The non-planar dynamics equations are homogeneous and analytically solvable. However, the pitch attitude motion is nonlinear, possesses parameter-varying coefficients and is subjected to external periodic excitations. Consequently, we transform the unwieldy attitude dynamics into relatively more amenable schemes for analysis and control law synthesis. Subsequently, we demonstrate the implementation of linear and nonlinear control laws (i.e. bifurcation and sliding mode control laws) on the relatively acquiescent transformed attitude dynamics. By employing a two-pronged approach, the quasi-periodic planar motion is independently shown to be stabilizable via the nonlinear control approaches.

KW - Gravity gradient

KW - Hopf bifurcation

KW - Lyapunov-Floquet transformation

KW - Nonlinear dynamics

KW - Normal forms

KW - Periodic dynamics control

KW - Sliding mode

KW - Spacecraft attitude

KW - State augmentation

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