Lyapunov-Floquet control of satellite relative motion in elliptic orbits

Sherrill, Ryan E.; Sinclair, Andrew J.; Sinha, Subhash C.; Lovell, T. Alan

doi:10.1109/taes.2015.140281

Cited by 16 publications

(10 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Consequently, we intend to exploit this propitious attribute in our investigation. Applications of L-F transformations in spacecraft dynamics have been previously investigated by authors such as [8,26]. The former demonstrates how L-F theory enhances the representation of relative spacecraft dynamics in elliptical orbits, while the latter further proposes an orbit control law based on L-F theory.…”

Section: • Normal Form (Nf) Theorymentioning

confidence: 94%

“…The approximation of LFT matrix via Chebyshev polynomials contains elements Q ij t ðÞwith truncated Fourier representations as shown in Eq. (8). Q À1 ij t ðÞhas similar Fourier representation:…”

Section: Attitude Motion Analysismentioning

confidence: 99%

“…Inopportunely, dynamics of space systems tend to be commonly represented by coupled analytical models that possess complex structures encompassing nonlinearity, parameter-variant coefficients, and periodic external excitation terms [4][5][6][7][8][9]. The requisite analysis essential to fathom such motion is not a trivial undertaking-except for few special cases, the general solution for such dynamical systems cannot be found.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Analysis and Control of Nonlinear Attitude Motion of Gravity-Gradient Stabilized Spacecraft via Lyapunov-Floquet Transformation and Normal Forms

Waswa¹,

Redkar²

2020

Advances in Spacecraft Attitude Control

View full text Add to dashboard Cite

This chapter demonstrates analysis and control of the attitude motion of a gravity-gradient stabilized spacecraft in eccentric orbit. The attitude motion is modeled by nonlinear planar pitch dynamics with periodic coefficients and additionally subjected to external periodic excitation. Consequently, using system state augmentation, Lyapunov-Floquet (L-F) transformation, and normal form simplification, we convert the unwieldy attitude dynamics into relatively more amenable schemes for motion analysis and control law development. We analyze the dynamical system's periodicity, stability, resonance, and chaos via numerous nonlinear dynamic theory techniques facilitated by intuitive system state augmentation and Lyapunov-Floquet transformation. Versal deformation of the normal forms is constructed to investigate the bifurcation behavior of the dynamical system. Outcome from the analysis indicates that the motion is quasi-periodic, chaotic, librational, and undergoing a Hopf bifurcation in the small neighborhood of the critical point-engendering locally stable limit cycles. Consequently, 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 quasiperiodic planar motion is independently shown to be stabilizable via the nonlinear control approaches.

show abstract

Section: • Normal Form (Nf) Theorymentioning

confidence: 94%

Section: Attitude Motion Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Analysis and Control of Nonlinear Attitude Motion of Gravity-Gradient Stabilized Spacecraft via Lyapunov-Floquet Transformation and Normal Forms

Waswa¹,

Redkar²

2020

Advances in Spacecraft Attitude Control

View full text Add to dashboard Cite

show abstract

“…Since the dynamic matrixĀ(ν) is periodic of period 2π, the next step consists in the application of Floquet-Lyapunov theory, as in [7] and [22], and to look for a periodic similarity transformation matrix S(ν), transforming the original LTV dynamical system into an equivalent LTI dynamical system, namely:…”

Section: A Floquet-lyapunov Similarity Transformationmentioning

confidence: 99%

“…Equation (22) represents a matrix differential equation whose solution is given in equation (23) and comes from Floquet Theory [4]. Therefore,…”

Section: A Floquet-lyapunov Similarity Transformationmentioning

confidence: 99%

A Hybrid Control Framework for Impulsive Control of Satellite Rendezvous

Brentari

Urbina

Arzelier

et al. 2019

IEEE Trans. Contr. Syst. Technol.

View full text Add to dashboard Cite

We focus on the problem of satellite rendezvous between two spacecraft in elliptic orbits. Using a linearized model of the relative dynamics, we first propose a periodic similarity transformation based on Floquet-Lyapunov theory, leading to a set of coordinates under which the free motion is linear timeinvariant. Then we address the problem of impulsive control of satellite rendezvous as a hybrid dynamical system, and we show that the arising elegant representation enables designing impulsive control laws with different trade-offs between computational complexity and fuel consumption. The adopted hybrid formalism allows us to prove suitable stability properties induced by the proposed controllers. The results are comparatively illustrated on simulation examples.

show abstract

A direct analysis and control of nonlinear time-variant spacecraft dynamics in the vicinity of small irregularly shaped bodies

Waswa

Redkar

2022

Nonlinear Dyn

View full text Add to dashboard Cite

Lyapunov-Floquet control of satellite relative motion in elliptic orbits

Cited by 16 publications

References 27 publications

Analysis and Control of Nonlinear Attitude Motion of Gravity-Gradient Stabilized Spacecraft via Lyapunov-Floquet Transformation and Normal Forms

Analysis and Control of Nonlinear Attitude Motion of Gravity-Gradient Stabilized Spacecraft via Lyapunov-Floquet Transformation and Normal Forms

A Hybrid Control Framework for Impulsive Control of Satellite Rendezvous

A direct analysis and control of nonlinear time-variant spacecraft dynamics in the vicinity of small irregularly shaped bodies

Contact Info

Product

Resources

About