Open AccessSynthesis of quasioptimal control of the technical systems with the direct current drive
Author(s) -
В. С. Ловейкін,
Yuriy Romasevych,
M. M. Korobko
Publication year - 2019
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/708/1/012014
Subject(s) - smoothness , mathematics , nonlinear system , control theory (sociology) , euler's formula , boundary value problem , optimal control , mathematical analysis , mathematical optimization , computer science , control (management) , physics , quantum mechanics , artificial intelligence
The paper presents an approximate solution of the optimal control problem of the technical system driven by the direct current motor. The braking mode of the system is under consideration. The optimization criterion was a nonlinear integral functional, which reflects the root-mean-square value of the electric drive power during the system’s braking mode. It was found, that the necessary condition of the criterion minimum – Euler-Poisson equation – is a sixth-order nonlinear differential equation. It is impossible to find its analytical solution. In order to find the approximate solution a direct variational method was applied. Proper selection of the class of the basis functions allowed to reach the absolute minima of the terminal criteria and meeting the boundary conditions of the system’s movement. The first provides decreasing of the dynamical forces in the system transmission; the latter is connected with the statement of the problem. Among the class of functions, the one was found, which minimizes the integral criterion. In order to illustrate the approximate solution of the optimal control problem, the plots have been built. They show the smoothness of the system movement and practicability of the obtained result. All calculations have carried out in an analytical form.