Optimization of actuating elements of transport control systems with magnetic levitation based on the solution of inverse problems

¹ Department of Applied Mathematics, SRSPU (NPI), 346428 Novocherkassk, Russia
² Department of Information and Measuring Systems and Technologies, SRSPU (NPI), 346428 Novocherkassk, Russia

^* Corresponding author: vgrech@mail.ru

Abstract

The designing of optimal energy-saving actuating elements for transport control systems with magnetic levitation (electromagnets with current windings and permanent magnets) is reduced to solving the following inverse problem. It is necessary to determine the dimensions and magnetomotive force of the actuating element, providing a given levitation force, magnetic induction in ferromagnets and a minimum mass of the actuating element. The solution of the direct problem (determination of the force of levitation and magnetic induction) is carried out by the finite element method. In the problem, the objective function is the mass of the actuating element and the restrictions are superimposed on the force and magnetic induction. Solving this optimization problem by the Lagrange method leads to inefficient algorithm. The article describes the proposed optimization method based on the transformation of constraints into objective functions, that is, the reduction of the problem to the multicriteria problem with consistent minimization of objective functions with a limited number of required parameters. A number of criteria are minimized analytically. The application of the complex criterion is considered. To reduce the time of solving the problem, the hierarchy of models is used: chain and field model. The proposed optimization method allows reducing the time of solving the problem by about two times. The cost of electricity due to the use of permanent magnets is reduced by four times. An example of optimization of the design of the actuating element of transport control system with magnetic levitation is considered.