Analysis of stability and Hopf bifurcation of delayed feedback spin stabilization of a rigid spacecraft

Morad Nazari; Eric A. Butcher

doi:10.1007/s11071-013-1006-5

Analysis of stability and Hopf bifurcation of delayed feedback spin stabilization of a rigid spacecraft

Morad Nazari, Eric A. Butcher

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

10 Scopus citations

Abstract

The stability and bifurcation of delayed feedback spin stabilization of a rigid spacecraft is investigated in this paper. The spin is stabilized about the principal axis of the intermediate moment of inertia using a simple delayed feedback control law. In particular, linear stability is analyzed via the exponential-polynomial characteristic equations and then the method of multiple scales is used to obtain the normal form of the Hopf bifurcation. Bifurcation diagrams and the dynamics of the delayed closed-loop system are verified using continuation software and with numerical simulations.

Original language	English (US)
Pages (from-to)	801-817
Number of pages	17
Journal	Nonlinear Dynamics
Volume	74
Issue number	3
DOIs	https://doi.org/10.1007/s11071-013-1006-5
State	Published - Nov 2013
Externally published	Yes

Keywords

Bifurcation
Delayed feedback control
Multiple scales
Normal form
Spacecraft
Spin stabilization
Stability analysis
Time delay

ASJC Scopus subject areas

Control and Systems Engineering
Aerospace Engineering
Ocean Engineering
Mechanical Engineering
Applied Mathematics
Electrical and Electronic Engineering

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title = "Analysis of stability and Hopf bifurcation of delayed feedback spin stabilization of a rigid spacecraft",

abstract = "The stability and bifurcation of delayed feedback spin stabilization of a rigid spacecraft is investigated in this paper. The spin is stabilized about the principal axis of the intermediate moment of inertia using a simple delayed feedback control law. In particular, linear stability is analyzed via the exponential-polynomial characteristic equations and then the method of multiple scales is used to obtain the normal form of the Hopf bifurcation. Bifurcation diagrams and the dynamics of the delayed closed-loop system are verified using continuation software and with numerical simulations.",

keywords = "Bifurcation, Delayed feedback control, Multiple scales, Normal form, Spacecraft, Spin stabilization, Stability analysis, Time delay",

author = "Morad Nazari and Butcher, {Eric A.}",

note = "Funding Information: Acknowledgement Financial support of from the National Science Foundation under Grant No. CMMI-1131646 is gratefully acknowledged. The authors would also like to thank Dr. Young S. Lee for his valuable help and support.",

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AU - Nazari, Morad

AU - Butcher, Eric A.

N1 - Funding Information: Acknowledgement Financial support of from the National Science Foundation under Grant No. CMMI-1131646 is gratefully acknowledged. The authors would also like to thank Dr. Young S. Lee for his valuable help and support.

PY - 2013/11

Y1 - 2013/11

N2 - The stability and bifurcation of delayed feedback spin stabilization of a rigid spacecraft is investigated in this paper. The spin is stabilized about the principal axis of the intermediate moment of inertia using a simple delayed feedback control law. In particular, linear stability is analyzed via the exponential-polynomial characteristic equations and then the method of multiple scales is used to obtain the normal form of the Hopf bifurcation. Bifurcation diagrams and the dynamics of the delayed closed-loop system are verified using continuation software and with numerical simulations.

AB - The stability and bifurcation of delayed feedback spin stabilization of a rigid spacecraft is investigated in this paper. The spin is stabilized about the principal axis of the intermediate moment of inertia using a simple delayed feedback control law. In particular, linear stability is analyzed via the exponential-polynomial characteristic equations and then the method of multiple scales is used to obtain the normal form of the Hopf bifurcation. Bifurcation diagrams and the dynamics of the delayed closed-loop system are verified using continuation software and with numerical simulations.

KW - Bifurcation

KW - Delayed feedback control

KW - Multiple scales

KW - Normal form

KW - Spacecraft

KW - Spin stabilization

KW - Stability analysis

KW - Time delay

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Analysis of stability and Hopf bifurcation of delayed feedback spin stabilization of a rigid spacecraft

Abstract

Keywords

ASJC Scopus subject areas

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