Vibration Analysis and Motion Control Method for an Under-Actuated Tower Crane
Roberto P. L. Caporali
Roberto P. L. Caporali, Department of Mathematics for Applied Physics of Roberto Caporali, Imola, BO, Italy.
Manuscript received on 17 December 2023 | Revised Manuscript received on 23 December 2023 | Manuscript Accepted on 15 January 2023 | Manuscript published on 30 January 2024 | PP: 1-11 | Volume-11 Issue-1, January 2024 | Retrieval Number: 100.1/ijies.A108811010124 | DOI: 10.35940/ijies.A1088.11010124
Open Access | Editorial and Publishing Policies | Cite | Zenodo | OJS | Indexing and Abstracting
© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: In this paper, we develop a solution for controlling a tower crane, which is considered a non-rigid system, and therefore able to deform and experience vibrations during motion. Notably, large tower cranes show high structural dynamics. Under external excitations, the payload tends to sway around its vertical position, and this motion is coupled to the resulting dynamic vibration of the crane structure. These induced vibrations may cause instability and severe damage to the crane system. Furthermore, the energy stored in the flexible structure of a tower crane causes vibrations in the structure during the acceleration and deceleration of slewing movements. A crane operator perceives these vibrations as an unstable speed of the boom. Such behaviour involves controlling the crane, exact positioning and manual control of the crane’s movement at low pivoting speeds. We define an Elastic model of the Slewing crane and analyse the bending and Torsional elasticity of the Tower, as well as the Jib Elasticity. With an approximated method, we calculate the natural wavelengths of the crane structure in the slewing direction. We consider the tower crane as a nonlinear under-actuated system. The motion equations are obtained considering both the normal vibration modes of the tower crane and the sway of the payload. An elastic model of the Slewing crane is achieved, modelling the crane jib as an Euler-Bernoulli beam. Even the payload dynamics are considered when developing an Anti-sway solution based on the movement equation. We define an iterative calculation of the sway angles and obtain the corresponding velocity profiles, implementing two types of solutions: an input-shaping control in open-loop, to be used with automatic positioning, and a “command smoothing” method in open-loop, used for reducing the sway of the payload with operator control. These solutions result in a reduction of the vibrations in the crane structure. As a consequence, the tower crane is not subject to the strong horizontal and vertical oscillations during the motion of the elastic structure.
Keywords: Slewing Control, Tower Crane, Vibrational Analysis, Finite Element Method, Anti-Sway.
Scope of the Article: Applied Mathematics and Mechanics