Miroshnychenko H. Mathematical modeling of electric drive control processes

The object of research – the processes of control electromechanical systems with a monitoring electric drive. The purpose of the work is to improve the quality of the processes of electric drive management by developing a new computational method for solving the problem of optimal control of the electric drive. Research methods – the main results of work are based on general methods of functional analysis, methods of computational mathematics, the theory of solving the Cauchy problem for systems of ordinary differential equations with control, the method of finding the best approximation of the function of one variable splines of the first order in the norm W21[0,t].Theoretical and practical results – the computational method of solving the problem of optimal control of the electric drive, developed in the dissertation, allows to increase the accuracy of approximation in problems of optimal control. The scientific novelty of the obtained results is that for the first time the method of solving the problem of optimal control of a monitoring electric drive using spline functions is proposed, in which unknown control parameters are simultaneously with unknown parameters of phase coordinates, which gives the best approximation to the exact solution in the norm W21[0,t]; has further developed the method of best approximation of the function of one variable splines in the norm W21[0,t] for the solving the Cauchy problem for a system of ordinary differential equations of a given order and the problem of optimal control of a moving electric drive; the method for solving the Cauchy problem for a system of differential equations with right-hand sides in the form of polynomial functions is improved with the choice of basic functions, which allowed to ensure high accuracy of approximation in norm L2[0,1]. The main results of the dissertation research were obtained within the framework of the implementation of the research work «Construction of mathematical models for the management of technological processes» FN 12-5 at the Ukrainian engineering pedagogics academy. The results of the work are used in the educational process at the department of higher and applied mathematics of the Ukrainian engineering pedagogics academy in the presentation of the discipline «Theoretical, physical and Information fundamentals of branch knowledge». Also, the results are implemented in the development of the enterprise «Electromashina», namely in the control devices of electric motors during their testing. The obtained results can be used when creating a package of industrial values and in the design of electric drives.