Abstract
Transient modes of bridge cranes movement determine their energy, dynamic and electrical performance, as well as productivity and durability of work. An optimal control problem of its movement has been solved while making an analysis of indicators for efficient performance of a bridge crane. Terminal and integral criteria have been selected as optimization criteria. They represent undesirable dynamic properties of the crane. Legendre method has been used to determine the possibility for achieving minimum of the optimization criterion. An analysis of the Euler-Poisson equation, which is a necessary condition for the minimum of the integral criterion, has shown that it is impossible to find a solution for the optimization problem in an analytical form. A method of differential evolution has been used in order to find an approximate solution to the optimization problem. The approximate (suboptimal) solution has been found in the complex domain, which is a limited domain conjunction of dynamic parameters and phase coordinates of the system. Limitation in the domain of the system phase coordinates (a polynomial basis function has been used in the paper) provides the possibility to attain absolute minimums of terminal problem criteria. A simulation of the bridge crane motion has been carried out in order to establish an efficiency for implementation of the suboptimal control. During this process dynamic mechanical characteristics of its electric drive have been taken into account. While carrying out the simulation, a frequency and an amplitude of the electric drive voltage in the crane movement mechanism have been changed (frequency scalar method for speed changing of an asynchronous electric drive has been used). A comparative analysis of the dynamic, kinematic, electrical and energy performance indicators of the bridge crane under suboptimal and S-curved (standard) laws of frequency and voltage variations in the crane electric drive has made it possible to establish an improvement in the efficiency of its operation under suboptimal control.
Highlights
Bridge cranes are used in many processing of the state-of-the-art technology
The compilation of the models allowed find an analytical expressions for dynamical loads calculation
Because of a system processing depends on the external forces and system parameters [28, 29], the solution of optimization problems if crane dynamics has to be found in domains of movement regimes and system parameters
Summary
На основе анализа показателей эффективности работы мостового крана решена задача оптимального управления его передвижением. В качестве критериев оптимизации выбраны терминальные и интегральный критерии, отображающие нежелательные динамические свойства крана. Анализ уравнения Эйлера – Пуассона, которое является необходимым условием минимума интегрального критерия, показал, что аналитическое нахождение решения оптимизационной задачи невозможно. Для нахождения приближенного решения оптимизационной задачи использован метод дифференциальной эволюции. Ограничение области фазовых координат системы (в статье использована полиномиальная базисная функция) дало возможность достичь абсолютных минимумов терминальных критериев задачи. Для установления эффективности реализации субоптимального управления проведено моделирование движения мостового крана с учетом динамической механической характеристики его электропривода. Сравнительный анализ динамических, кинематических, электрических и энергетических показателей работы мостового крана при субоптимальном и S-образном (стандартном) законах изменения частоты и напряжения питания электропривода крана дал возможность установить улучшение эффективности его работы при субоптимальном управлении.
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