Structure-Preserving Stabilization for Hamiltonian System and its Applications in Solar Sail

Xu, Ming; Xu, Shijie

doi:10.2514/1.34757

Cited by 38 publications

(28 citation statements)

References 9 publications

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“…Along with new forms of motion, a solar sail offers the possibility to maintain a spacecraft in the vicinity of an equilibrium point or more generically, a reference orbit, by controlling the attitude configuration and, therefore, without the direct utilization of chemical propulsion. Several wellknown approaches such as, linearized optimal control [65,66], Hamiltonian structure-preserving stabilization [67], or look-ahead strategies [68,69] are generally applicable to the stationkeeping problem for a solar sail. The control input is typically determined by the orientation of a solar sail, which is defined in terms of some angles, or as a pointing vector.…”

Section: Opportunities To Exploit Coupled Orbit-attitude Dynamics In mentioning

confidence: 99%

Attitude dynamics in the circular restricted three-body problem

Guzzetti

Howell

2018

Astrodyn

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This document reflects the effort of constructing a basis for understanding attitude motion within a multi-body problem with application to spacecraft flight dynamics. The circular restricted three-body problem (CR3BP) is employed as a model for the orbital motion.Then, attitude dynamics is discussed within the CR3BP. Conditions for bounded attitude librations and techniques for the identification of such behavior are presented: initially for a spacecraft fixed at an orbital equilibrium point, and later for a vehicle that moves on non-linear periodic orbit. While previous works focus on specific challenges, this analysis serves to create a more general framework for attitude dynamics within the CR3BP. A larger framework enables additional observations. For example, a linkage is noted between regions of bounded motion that may appear on an attitude grid search map and families of periodic attitude solutions. Finally, coupling effects between attitude and orbit dynamics within the CR3BP, ones that enable new options for trajectory design, are considered an important opportunity, and should be included in a general framework. As a proof of that concept, sailcraft trajectories are generated within a coupled orbit-attitude model only using a sequence of constant commands for the attitude actuators.

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Section: Opportunities To Exploit Coupled Orbit-attitude Dynamics In mentioning

confidence: 99%

Attitude dynamics in the circular restricted three-body problem

Guzzetti

Howell

2018

Astrodyn

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“…For a Hamiltonian system, there exist hyperbolic equilibria that have stable, unstable and centre manifolds, with the unstable manifold generating the instability. However, a control law can be applied which will establish Lyapunov stability of the relative motion about the equilibrium point and stabilize an unstable configuration [35,36]. Assuming active control is actuated by the spring coupling parameters (equivalent to modulating their natural length), the dynamics of the controlled system can be written as ⎡ ⎢ ⎢ ⎢ ⎣q …”

Section: Structure-preserving Stabilization Controlmentioning

confidence: 99%

“…A detailed development and proof of the control law can be found elsewhere [35]. This control strategy can work effectively through estimating the relative motion and maintaining the Hamiltonian the structure of the problem.…”

Section: Structure-preserving Stabilization Controlmentioning

confidence: 99%

Reconfiguration of a smart surface using heteroclinic connections

Zhang

McInnes

2017

Proc. R. Soc. A.

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A reconfigurable smart surface with multiple equilibria is presented, modelled using discrete point masses and linear springs with geometric nonlinearity. An energy-efficient reconfiguration scheme is then investigated to connect equal-energy unstable (but actively controlled) equilibria. In principle, zero net energy input is required to transition the surface between these unstable states, compared to transitions between stable equilibria across a potential barrier. These transitions between equal-energy unstable states, therefore, form heteroclinic connections in the phase space of the problem. Moreover, the smart surface model developed can be considered as a unit module for a range of applications, including modules which can aggregate together to form larger distributed smart surface systems.

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“…Here we apply the control of preserving Hamiltonian structure developed to stabilize the motions near the hyperbolic equilibrium to generate a stable Lissajous orbit [10], which is impossible for the controller with the dissipative structure [11].…”

Section: Stabilization Of Hyperbolic or Degenerated Equilibriummentioning

confidence: 99%

“…A solar sail is an ideal application object of the aforementioned controller for no consumption of fuel [10]. Now we investigate the dynamics of controlled sails and modify the pseudo-potential function from Eq.…”

Section: Application To Solar Sailsmentioning

confidence: 99%

Displaced orbits generated by solar sails for the hyperbolic and degenerated cases

2011

Acta Mech Sin

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Displaced non-Keplerian orbits above planetary bodies can be achieved by orientating the solar sail normal to the sun line. The dynamical systems techniques are employed to analyze the nonlinear dynamics of a displaced orbit and different topologies of equilibria are yielded from the basic configurations of Hill's region, which have a saddlenode bifurcation point at the degenerated case. The solar sail near hyperbolic or degenerated equilibrium is quite unstable. Therefore, a controller preserving Hamiltonian structure is presented to stabilize the solar sail near hyperbolic or degenerated equilibrium, and to generate the stable Lissajous orbits that stay stable inside the stabilizing region of the controller. The main contribution of this paper is that the controller preserving Hamiltonian structure not only changes the instability of the equilibrium, but also makes the modified elliptic equilibrium become unique for the controlled system. The allocation law of the controller on the sail's attitude and lightness number is obtained, which verifies that the controller is realizable.

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Structure-Preserving Stabilization for Hamiltonian System and its Applications in Solar Sail

Cited by 38 publications

References 9 publications

Attitude dynamics in the circular restricted three-body problem

Attitude dynamics in the circular restricted three-body problem

Reconfiguration of a smart surface using heteroclinic connections

Displaced orbits generated by solar sails for the hyperbolic and degenerated cases

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