Analysis of the optimal speed-based start-up mode of the tower crane swing mechanism under control limitations
DOI:
https://doi.org/10.32347/2410-2547.2026.116.251-262Keywords:
tower crane, load, velocity, slewing mechanism, optimal control constraints, Ring-Rot-PSO methodAbstract
A comparative analysis of the optimal starting mode of the tower crane slewing mechanism in terms of speed under asymmetric (task 1) and symmetric (task 2) constraints on optimal control is presented in a scientific article. A two-mass dynamic model was used for the research, whose motion in time is described by a system of two second-order differential equations. In the course of further research, the system of two second-order differential equations was reduced to a single fourth-order differential equation. After performing the appropriate transformations, the fourth-order differential equation was presented in Cauchy form and the initial and final conditions of motion were given, under which the load oscillations will be eliminated after the turning mechanism reaches a steady speed.The optimisation task itself was reduced to the task of unconditional minimisation of a complex integral-terminal functional, where the terminal component is responsible for the fulfilment of the final boundary conditions, and the integral component is responsible for the speed of the mechanism. A series of 54 experimental studies (27 for each of the tasks under investigation) was planned, in which the independent factors were the length of the flexible suspension (which was 10, 15 and 20 metres), the load projection (which was 5, 15 and 20 m), and the load mass (which was 500, 2000 and 5000 kg).During the theoretical studies, the main assessment was carried out according to the following indicators: the duration of the system acceleration to the steady-state speed value; the maximum deviation of the flexible suspension of the load from the vertical; the maximum and root mean square values of the power in the drive and the acceleration of the load.The results of the analysis showed that when using asymmetric constraints for optimal control (task 1), the acceleration time of the studied system to a steady state speed increases compared to symmetric constraints (task 2) in the range from 1.23 to 15. 28 %, and the maximum values of kinematic characteristics decrease from 5.46 to 42.85 % and energy indicators from 0.48 to 27.83 %.
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