Time-optimal Control of a Simple Pendulum with a Movable Pivot. Part 2
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International Applied Mechanics, Vol. 56, No. 2, March, 2020
TIME-OPTIMAL CONTROL OF A SIMPLE PENDULUM WITH A MOVABLE PIVOT. PART 2* V. S. Loveikin1, Yu. A. Romasevich1*, A. S. Khoroshun2, and A. G. Shevchuk1
We carried out numerical modeling of the dynamics of a pendulum with a movable pivot (a crane with a load on a flexible suspender) during the application of these optimal controls (obtained in Part 1) by means of a frequency-controlled drive. The modeling results demonstrated sufficient (for practical applications) quality of the optimal controls even when external stochastic perturbations (wind gusts) act on the system. A comparative analysis of the modeling results showed that the modified constraints allow us to reduce by several times the dynamic forces in the crane by slightly increasing the duration of motion. The results of experimental studies of control in the laboratory conditions allowed us to identify the causes of the deviation of the actual crane speed from the optimal one and to propose methods to eliminate it. Keywords: modeling, experimental investigation, time-optimal control, load oscillation, dynamic loads, gantry crane Introduction. The problems of the time-optimal control of a simple pendulum with a movable pivot are relevant for the synthesis of control algorithms for load-lifting cranes that transport cargo on a flexible suspension (overhead and gantry cranes). Indeed, the motion of these load-lifting machines is adequately described by the equations of a simple pendulum with a movable pivot and, therefore, in the subsequent presentation, we will study the optimal control of the motion of a simple pendulum with a movable pivot using the example of a load-lifting crane with a load on a flexible suspension. The general approach in the study of the practical implementation of the time-optimal controls of systems consists in computer modeling and analysis of the obtained results [1, 7, 8, 10, 14–16] followed by experiments in a laboratory [7, 9, 12] or in production conditions [2]. The development of microprocessor technology and adjustable drive mechanisms [3] allows us to improve the quality of the control of crane mechanisms and creates the prerequisites for the effective implementation of optimal controls in practice. This work is the second part of the study of the problems of the time-optimization of a simple pendulum with a movable pivot (a crane with a load on a flexible suspension). Here the main emphasis is placed on the possibility of practical implementation of optimal controls for a crane and on determining the advantages and disadvantages of optimal controls with classical and modified control constraints. Both theoretical and experimental methods were used for the research.
1
National University of Life and Environmental Sciences of Ukraine, 12v Geroev Oborony St., Kyiv, Ukraine; e-mail: *[email protected]. 2S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterova St., Kyiv, Ukraine; e-mail: [email protected]. Translated from
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