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.
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This study was sponsored by the budget program “Support for Priority Areas of Scientific Research” (KPKVK 6541230).
Translated from Prikladnaya Mekhanika, Vol. 56, No. 2, pp. 95–103, March–April 2020.
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Loveikin, V.S., Romasevich, Y.A., Khoroshun, A.S. et al. Time-optimal Control of a Simple Pendulum with a Movable Pivot. Part 2. Int Appl Mech 56, 208–215 (2020). https://doi.org/10.1007/s10778-020-01007-9
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DOI: https://doi.org/10.1007/s10778-020-01007-9