Some results on feedback stabilization of a one-link flexible arm

Abstract

: The aim of this report is to exhibit a class of stabilizing feedback laws for a structurally undamped one--link flexible arm with control applied at one extremity. A finite-- dimensional model of the arm, corresponding to a discretization in space, is first considered. The arm is then modeled by a classical partial differential equation, no finite dimensional approximation being made in the control analysis. In both cases, stability of the closed--loop system is proven, using a Lyapunov method and applying Lasalle's principle. The practical significance of the proposed results is commented upon and illustrated by simulation experiments. Key words: modeling and control of flexible structures, partial differential equations, feedback stabilization. R'esum'e : On 'etudie dans ce rapport une classe de feedbacks stabilisants pour un bras robot flexible sans amortissement structurel command'e `a l'une de ses extr'emit'es. On consid`ere tout d'abord un mod`ele de dimension finie du bras, ...