Stabilization of a Class of Flexible Structures Tipped with Dynamic Actuators

Abstract

In this paper, the feedback stabilization problems are investigated for a class of mechanically flexible cantilevered beams tipped with dynamic actuators on the free end. First, the mathematical models of the whole structure including the dynamic actuator are given by a couple of equations described by secondorder partial and ordinary differential equations. Secondly, based on such hybrid system model the feedback stabilization problem of the total system is investigated. To do this, a Lyapunov function is found from the total energy point-of-view, related to the actuator and the flexible structure parts. The conditions are derived for the feedback gains used in the dynamic actuator. Furthermore, some simulation results are presented. Finally, as the extension, the feedback stabilization problem is considered for the system which is subject to random disturbance.