Оптимальне за витратами енергії керування за обмеження двох фазових координат

Abstract

У статті визначається закон оптимального керування, який мінімізує енерговитрати в позиційному електроприводі постійного струму з урахуванням обмежень на струм анкера та швидкість його наростання. Зазначено, що позиційний електропривод, який працює в режимах частих пусків-зупинок-реверсів, характеризується істотними витратами енергії. Під час пошуку оптимального керувального впливу враховано обмеження, що накладаються на реальну систему: за напругою, за струмом і швидкістю наростання струму. У результаті визначено закони оптимального керування, що враховують обмеження на струм анкера під час розгону і гальмування; проаналізовано зниження енерговитрат, забезпечене застосуванням таких керувань.

Modern technological processes consist of many operations, among which the positioning operation is one of the most common. Among the numerous positioning systems, electromechanical systems based on various types of electric drives are widely used. These systems are used in industrial robots, manipulators, conveyors, and other technological equipment. Today, the most common type of control systems for position electric drives is systems built on the principle of subordinate regulation of parameters. These systems assume the description of the controlled object in the form of a system of linear differential equations. However, often the largest part of the resulting moment of resistance to movement is the moment created by friction forces, the mathematical description of which cannot be linearized at low speeds of the executive mechanism, which occurs during medium and small displacements. In an electric drive, optimal control usually refers to the selection of control parameters that would provide the best performance in terms of a given criterion for the process of electromechanical energy conversion, or, in other words, the best behavior of the system, its movement toward the goal along the optimal trajectory. The purpose of this article is to determine the law of optimal control that minimizes energy consumption in a DC positional electric drive, considering the constraints on armature current and its rate of change. It is noted that a positional electric drive operating in modes with frequent starts, stops, and reversals is characterized by significant energy losses. In the process of searching for the optimal control impact, the constraints imposed on the real system, including voltage, current, and the rate of current change, were taken into account. As a result, optimal control laws were determined, considering armature current limitations during acceleration and braking. The reduction in energy consumption achieved by applying such control strategies has been analyzed.