Global asymptotic stabilization of a spinning top with torque actuators using stereographic projection

Author

Wan, C.J. ; Tsiotras, Panagiotis ; Coppola, V.T. ; Bernstein, D.S.

Author_Institution

Dept. of Aerosp. Eng., Michigan Univ., Ann Arbor, MI, USA

Volume

1

fYear

1994

fDate

29 June-1 July 1994

Firstpage

536

Abstract

The dynamical equations for a spinning top are derived in which the orientation is specified by a complex variable using stereographic projection of Poisson´s equations. Necessary and sufficient conditions for Lyapunov stability of the uncontrolled motion of a spinning top are given using the Energy-Casimir method. Control laws that globally asymptotically stabilize the spinning top to the sleeping motion using two torque actuators are then synthesized by employing techniques from the theory of systems in cascade form and generalized using Hamilton-Jacobi-Bellmann theory with zero dynamics.

Keywords

Lyapunov methods; asymptotic stability; motion control; Energy-Casimir method; Hamilton-Jacobi-Bellmann theory; Lyapunov stability; Poisson´s equations; dynamical equations; global asymptotic stabilization; necessary and sufficient conditions; sleeping motion; spinning top; stereographic projection; torque actuators; uncontrolled motion; Actuators; Eigenvalues and eigenfunctions; Equations; Space vehicles; Spinning; Stability; Torque;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, 1994

Print_ISBN

0-7803-1783-1

Type

conf

DOI

10.1109/ACC.1994.751795

Filename

751795