Analysis of stability and Hopf bifurcation of delayed feedback spin stabilization of a rigid spacecraft. (English) Zbl 1279.70008
Summary: 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.
MSC:
| 70K50 | Bifurcations and instability for nonlinear problems in mechanics |
| 93B52 | Feedback control |
| 70E15 | Free motion of a rigid body |
| 70E50 | Stability problems in rigid body dynamics |
Keywords:
time delay; spacecraft; delayed feedback control; spin stabilization; stability analysis; bifurcation; multiple scales; normal formReferences:
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