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Causal inverse dynamics of a flexible hub-arm system through Liapunov's second method

Published online by Cambridge University Press:  09 March 2009

Atef Ata ,
Salwa Elkhoga ,
Mohamed Shalaby  and
Shihab Asfour
Atef Ata
Affiliation:
Department of Industrial Engineering University of Miami. Coral Gables. Fl. 33124 (USA).
Salwa Elkhoga
Affiliation:
Department of Engineering Mathematics. Faculty of Engineering, Alexandria University (Egypt).
Mohamed Shalaby
Affiliation:
Department of Engineering Mathematics. Faculty of Engineering, Alexandria University (Egypt).
Shihab Asfour
Affiliation:
Department of Industrial Engineering University of Miami. Coral Gables. Fl. 33124 (USA).
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Summary

The main objective of this work is to study the performance of a flexible single hub-arm system. The equations of motion are derived using the extended Hamilton principle. The Liapunov functional is used as a condition for the stability analysis. The Liapunov functional is considered as the sum of the internal energy of the flexible beam. The required drive torque was obtained directly through the solution of the inverse dynamic problem. Although the flexible link is nonminimum phase in nature, the use of Liapunov and the PD controller guarantee the causality for the stable case. The effects of tip mass as well as its inertia in the case of stable and asymptotic stable systems were investigated to ensure the validity of this procedure.

Keywords

Inverse dynamicsFlexible robotStabilityLiapunov.
Type
Article
Information
Robotica , Volume 14 , Issue 4 , July 1996 , pp. 381 - 389
Copyright
Copyright © Cambridge University Press 1996

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