Wojciech Burlikowski

Mathematical model of an electromechanical actuator using flux state variables applied to reluctance motor

– Aims to present a new approach for formulating state‐space equations of an electromechanical actuator using magnetic flux linkages as state variables., – The model is based on employment of discrete databases and their interpolation. The algorithm of determination of databases defining the flux/current characteristics of an actuator is described. Graphical interpretation of variable transformation is presented. A simplified, two‐axis model of reluctance motor is used to illustrate the application of the proposed modelling technique. Comparison with the classical model of the motor is used to verify the validity of the method. Analysis is focused on determination of saturation phenomenon influence on formulation methodology and on correctness of obtained results., – A very good agreement is observed between reference dq model and the proposed model. The main problem of the presented method is the existence of undefined entries in databases. Sufficiently dense databases can be used to overcome the problem., – The model is limited to actuators in which eddy currents and hysteresis phenomenon can be neglected. Future research will be concentrated on evaluation of different interpolation strategies of databases used in the model for realistic saturation conditions., – The model can be used as a library block for testing various control strategies for actuators without standard simplifying assumptions (e.g. sinusoidal winding distribution). It can be implemented in any simulational software (e.g. SIMULINK) as its block diagram is simple and no numerical differentiation is necessary in derivation of the model data., – Presents an extension of state‐space model of an actuator based on database discretised description of variables to two or more state variables.

Modification of Park variable transformation for wye‐connected winding without neutral wire

Purpose – The purpose of this paper is to present a modification of the Park variable transformation for a three‐phase wye‐connected winding without neutral wire. A new physical interpretation of the winding equivalent circuit is proposed.Design/methodology/approach – An equivalent circuit representing reluctance motor stator winding is rearranged to enable easier physical interpretation of obtained voltage equation. The Park transformation and constraints resulting from Kirchhofs laws are then applied to obtain a two‐axis mathematical model of the motor.Findings – A new physical two‐phase interpretation of the voltage equation for a three‐phase wye‐connected winding without neutral wire is proposed. A novel two‐axis transformation is formulated for all variables. Compared to the Park transformation, which is the same for all variables, in the proposed transformation its matrices for currents and voltages/flux linkages are different, yet strongly interconnected.Research limitations/implications – The pro...

Hamiltonian model based control algorithm for electromechanical actuator

In the paper a control algorithm of an electrical machine, that is based on its hamiltonian mathematical model described in the dq0 reference frame, is introduced. The algorithm is designed to be specifically useful to control Synchronous Reluctance Machines. In the algorithm flux linkage values in the direct and quadrature axis are treated as state variables. Those flux linkage values and the electromagnetic torque are estimated using the aforementioned model. The algorithm is divided into two modes, first to ensure fast reaching of the commanded angular velocity and second to ensure stable operation of the drive when it is obtained. Additional criterion used in the control algorithm is to minimize the ohmic losses in the phase windings. In the paper the way of formulation of the needed mathematical model by the drive controller, based on the measurement results, is also presented. The performance of the algorithm is examined numerically.

Error analysis in mathematical model of electromechanical actuator using Hamiltonian equations

Streszczenie: W artykule przedstawiono metodyk e analizy boedu w modelu matematycznym przetwornika elektromechanicznego, wykorzystującym rownania Hamiltona w opisie przemiany elektromechanicznej. Jako podstawow ą wielko śc w algorytmie obliczeniowym u zyto koenergie pola magnetycznego Ecm . Wykorzystano w tym celu jednoznaczno śc okre ślenia warto ści koenergii dla danej warto ści zmiennych stanu, wynikającą z pominiecia w modelu pr ądow wirowych oraz zjawiska histerezy.

Comparison of different mathematical models of an electromechanical actuator

In the paper a brief comparison between different models of electromechanical actuator is presented. Main part of the paper is focused on model using Hamiltonian equations which employs flux linkages as state variables in the state space equations. Topological approach is used in the model implementation. This model is compared with one described by Lagrange formalism, which is much more popular in the literature. In both models eddy currents and hysteresis phenomenon are neglected to enable application of state space description. A 3-phase wye connected stator winding without a neutral wire is considered in detail as the most important connection schema in practical applications.

Reluctance motor simulational models using different state variables

In the paper three alternative versions of reluctance motor simulational model are presented. In the state space description flux or current variables are employed without any variable transformation. Simplifying assumptions made in the model formulation are omission of eddy currents and hysteresis phenomenon. Motor parameters were obtained with the help of the finite element method. Influence of mechanical damping on the calculated results for different model implementations was verified.