|Vibration Control of a Timoshenko Cantilever Beam with Varying Length
Phuong-Tung Pham, Gyoung-Hahn Kim, and Keum-Shik Hong*
International Journal of Control, Automation, and Systems, vol. 20, no. 1, pp.175-183, 2022
Abstract : This paper addresses the vibration control of a Cartesian palletizer consisting of a trolley and a robotic arm, wherein the robotic arm is modeled as a thick cantilever beam of varying length. The Timoshenko beam theory, which describes the behavior of thick beams, is used to model the robotic arm’s dynamics. A mathematical model describing the trolley’s motion and the robotic arm’s vibration is established based on the extended Hamilton principle. According to this dynamic model, a boundary control law is proposed to suppress the undesired transverse vibration of the robotic arm. The uniform stability of the closed-loop system is proven via the Lyapunov method. The simulation results show that the proposed control law can simultaneously control the trolley’s position and the robotic arm’s vibration.
Axially moving system, boundary control, Lyapunov method, Timoshenko beam, vibration control.
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