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

Abstract

SUMMARYThe 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.