Abstract
This paper is focused on an investigation into the control dynamics of a boom crane through a study of guided payload pendulum motion with a non-uniformly rotating boom-driven pivot center and variable cable length. A time-optimal control problem was formulated and numerically solved with constraints on the allowable payload swaying value using JModelica.org freeware with Optimica extension. Solutions of the optimum speed problem for the dynamic model describing the movement of the payload from the initial position to the final position are found, taking into account the nonlinearities associated with the Coriolis force, and the change in cable length during the motion. Two cases are considered: with and without taking into account the constricts on the swaying value. It was found that taking into account the constricts on the swaying value leads to an overshoot of the phase variable length. The obtained results can be used for cargo transportation by crane in various fields: industry, construction, etc. The resulting control will allow a reduction in cargo transfer time, which will lead to an increase in labor productivity. It will also reduce the amount of payload swaying, which will reduce the likelihood of injury during loading and unloading operations. The model is nonlinear, and the Coriolis force and other nonlinearities are taken into account. The model is electromechanical; the characteristics of the electric motors of the tower and the winch are taken into account. A comparative analysis of the problem of optimal control with and without allowance for restrictions on the cargo swaying value is provided and differences in the control functions for each of these cases are defined. The optimal control, taking into account the change in rope length, allows the solution of practical tasks in moving the cargo, taking into account the presence of obstacles that arise on the way of the cargo.
Highlights
This approximation and linearization of phase variables resulted in the fact that the derived optimal control solution of this problem was valid only for small oscillations of the dynamic system [17]
The aim of our numerical simulation was to identify the effect of the permissible value of payload swing on the optimal performance problem solution
At the sixth step we address concepts of the dynamic similarity theory
Summary
The development trends of modern controlled crane dynamics include: complication of mathematical models of the system by increasing the number of degrees of freedom (DoFs), application of more sophisticated control methods, accounting for external nondeterministic disturbances such as a constant or random wind load [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22]. The important phase variables like the angle between the cable and the vertical as well as the additional angle introduced by the linkage joint between the two parts of crane boom, were linearized and approximated as negligible infinitesimal quantities [17] This approximation and linearization of phase variables resulted in the fact that the derived optimal control solution of this problem was valid only for small oscillations of the dynamic system [17]. The disadvantage of such control is the possibility of significant swaying during the transfer of the load from one position to another, which is unsafe [17]. It should be noted that the modeling and experimentation results turned out to be very similar, which implies that the approach proposed by the authors is really workable [22]
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