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

Atef Ata*, Salwa Elkhoga, Mohamed Shalaby, Shihab Asfour

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)381-389
Number of pages9
Issue number4
StatePublished - 1996
Externally publishedYes


  • Flexible robot
  • Inverse dynamics
  • Liapunov
  • Stability

ASJC Scopus subject areas

  • Software
  • Mechanical Engineering
  • Control and Optimization
  • Artificial Intelligence
  • General Mathematics
  • Rehabilitation
  • Control and Systems Engineering
  • Computer Vision and Pattern Recognition
  • Computer Science Applications
  • Computational Mechanics
  • Modeling and Simulation


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