Holonomicity analysis of electromechanical systems

Abstract

Electromechanical systems are described using state variables that contain electrical and mechanical components. The equations of motion, both electrical and mechanical, describe the relationships between these components. These equations are obtained using Lagrange functions. On the basis of the function and Lagrange -d'Alembert equation the methodology of obtaining equations for electromechanical systems was presented, together with a discussion of the nonholonomicity of these systems. The electromechanical system in the form of a single-phase reluctance motor was used to verify the presented method. Mechanical system was built as a system, which can oscillate as the element of physical pendulum. On the base of the pendulum oscillation, parameters of the electromechanical system were defined. The identification of the motor electric parameters as a function of the rotation angle was carried out. In this paper the characteristics and motion equations parameters of the motor are presented. The parameters of the motion equations obtained from the experiment and from the second order Lagrange equations are compared.

Vectorized Mathematical Model of a Slip-Ring Induction Motor

“…The Lagrange function is the difference of kinetic and potential energies and it does not take into account the friction and external forces. Consequently, the Lagrange function does not describe the energy flow [15].…”

“…Basing on the Lagrange function the d'Alembert-Lagrange equation may be formulated [15]. Using the equation with virtual velocities as variations of virtual coordinates it may be easy checked that induction motors are holonomic systems.…”

Modelling the power losses in the ferromagnetic materials

“…Wciślik et al [10] noted that determination of power losses in a core is difficult due to the fact that occurrence of losses is considered on a microscopic scale, and their description on the macroscopic scale is based on the assumption of homogeneity of magnetic field. In the cited paper, modelling of losses in magnetic materials used in electrical motors was proposed by introducing an equivalent winding including one turn, modelling eddy currents in the magnetic core.…”

“…The significant influence of flux density amplitude, frequency and temperature on * E-mail: k.gorecki@we.am.gdynia.pl power losses in a core is given in catalogue data and the problem of formulating the universal dependence describing losses of power in different ferromagnetic materials is pointed out in the literature [8][9][10].…”

Research of an oscillatory electro-mechanical system consisting of two DC motors

“…between the oscillatory system and the energy source were developed in [1][2][3][4][5][6][7][8][9][10].…”