Regular Papers

International Journal of Control, Automation and Systems 2022; 20(1): 175-183

Published online January 17, 2022

https://doi.org/10.1007/s12555-021-0490-5

© The International Journal of Control, Automation, and Systems

Vibration Control of a Timoshenko Cantilever Beam with Varying Length

Phuong-Tung Pham, Gyoung-Hahn Kim, and Keum-Shik Hong*

Pusan National University

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.

Keywords Axially moving system, boundary control, Lyapunov method, Timoshenko beam, vibration control.

Article

Regular Papers

International Journal of Control, Automation and Systems 2022; 20(1): 175-183

Published online January 1, 2022 https://doi.org/10.1007/s12555-021-0490-5

Copyright © The International Journal of Control, Automation, and Systems.

Vibration Control of a Timoshenko Cantilever Beam with Varying Length

Phuong-Tung Pham, Gyoung-Hahn Kim, and Keum-Shik Hong*

Pusan National University

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.

Keywords: Axially moving system, boundary control, Lyapunov method, Timoshenko beam, vibration control.

IJCAS
June 2024

Vol. 22, No. 6, pp. 1761~2054

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