Use of mathematical modeling for solving tasks of optimal control of an electric drive

Abstract

The object of study in this article is the control processes of electromechanical systems with an electric drive. The subject matter is a mathematical model in the problem of optimal control of the following electric drive. This article is devoted to the mathematical modeling of the control processes of electromechanical systems with an electric drive. In this paper, we use the approximation of vector-valued functions of one variable by splines of the first degree to solve the problem of rotation of the motor shaft in electromechanical system. As you know, it is not always possible to find exact solutions in optimal control problems. In this regard, there is a need to obtain approximate solutions for optimal control problems. Therefore, an urgent task is the development of new methods for the approximate solution to the problems of optimal control of the electric drive, which provide higher approximation accuracy. The following results are presented: Graphs of phase coordinates and optimal control of approximation by splines of the first order are obtained. The results obtained were compared with the exact solution. The given examples illustrate the high accuracy of approximate solutions to the control problem obtained using the proposed method. Conclusions. The scientific novelty of the results obtained lies in the fact that a method is proposed for an approximate solution to the problem of optimal control of a servo drive using spline functions, in which unknown control parameters are found simultaneously with unknown parameters of phase coordinates, which gives the best approximation to the exact solution.