The paper presents an algorithm for the construction of an approximation of a highly nonlinear current-flux characteristic of a synchronous reluctance machine. Such an approximation is required in a Hamiltonian model of an electric machine and the constructed approximation is suited to be used in such a model. It employs a simplicial approximation based on irregular points sets in the spaces of currents and fluxes. The sets are constructed by the iterative insertion of new points. Initially the sets contain an arbitrarily small number of elements. The insertion is based on an approximation error calculation. Based on the sets containing possibly small number of elements, the proposed procedure leads to smooth and precise approximation. Due to the nonlinearity of the approximated characteristics, ambiguities can occur. A method for the triangulation refinement of the sets of currents and fluxes that eliminates them is also presented. In the paper, a reluctance machine model using the constructed approximation is described and compared with a model using the approximation based on regular sets.

The Synchronous Reluctance Machine (SynRM) is an electrical machine in which the useful electromagnetic torque is produced due to rotor saliency. Its high power- and torque-to-mass ratio and very good efficiency make it a cheap and simple alternative for permanent magnet or induction motors, e.g. in electromobility applications. However, because of magnetic nonlinearities, the rotational speed and torque control of a SynRM is a nontrivial task. In the paper, a control algorithm based on a Hamiltonian mathematical model is presented. The model is formulated using measurement results, obtained by the drive controller. An algorithm is tested in the drive system consisting of a SynRM with the classical rotor and a fast prototyping card. The drive dynamic response in transient states is very good, but the proposed algorithm does not ensure the best efficiency after steady state angular velocity is achieved.