Синтез оптимальної за швидкодією системи керування стрілочним електроприводом

Abstract

UA: У статті запропоновано синтез системи керування стрілочним електродвигуном з нульовою швидкістю в кінці переводу, оптимальної за критерієм максимальної швидкодії. Подано математичне формулювання мети керування, критерію оптимальності й обмеження на керуючий вплив. Розроблено математичну модель привода з двигуном постійного струму. Проведено аналіз керованості об'єкта і нормальності варіаційної задачі. Синтез оптимальної системи керування виконано з використанням принципу максимуму Л. С. Понтрягіна.

EN: The algorithm of operation of switch electric drives (the electric motor together with a reducer and a safety friction clutch) in railway transport is constructed in such a way that at the moment of completion of the working stroke of the tongue, its linear speed has the maximum value, and the braking process is provided only by the mechanical counteraction of the frame rail on the moving tongue. This process is accompanied by increased wear of the contacting parts, the deformation of the tongue, the rods and the elements of the hinged joints. To reduce the intensity of mechanical wear on the parts of the electric drive and the switch it is necessary to reduce the kinetic energy of the moving masses by reducing the velocity at the time the transfer is completed to zero or to a sufficiently small value. On the other hand, from the time of switching tongue depends the time of setting the routes, processing capacity of stations, sorting hills, that is, the efficiency of the transport complex as a whole. The aim of the article is to synthesize the control system of an switch electric motor with zero speed at the end of the translation, optimal by the criterion of maximum speed. The mathematical formulation of the goal of management, the criterion of optimality and the constraints on the control action are presented. A mathematical model of a drive with a DC motor is developed. The controllability of the object and the normality of the variational problem are analyzed. Synthesis of the optimal control system is performed using the maximum principle of L.S. Pontryagin. The analysis of the problem of practical implementation of the speed-optimal control system is briefly analyzed.