Vibration Analysis and Motion Control Method for an Under-Actuated Tower Crane
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In this paper, we developed a solution for controlling a tower crane thought as a no-rigid system, and therefore able to have deformation and, during the motion, vibrations. Particularly, 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 serious 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 behavior involves the control of the crane, particularly precise positioning and manual control of the crane movement at low pivoting speed. We define an Elastic model of the Slewing crane and analyze the bending and Torsional elasticity of the Tower, and 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, modeling the crane jib as an Euler-Bernoulli beam. Even the payload dynamic is considered, developing an Anti-sway solution by the equation of the movement. We define an iterative calculation of the sway angles and obtain the corresponding velocity profiles, implementing two kinds of solution: 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 the operator control. These solutions lead to a reduction of the vibrations of 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.
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