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.

This paper presents a predictive torque and flux control algorithm for the synchronous reluctance machine. The algorithm performs a voltage space phasor pre-selection, followed by the computation of the switching instants for the optimum switching space phasors, with the advantages of inherently constant switching frequency and time equidistant implementation on a DSP based system. The criteria used to choose the appropriate voltage space phasor depend on the state of the machine and the deviations of torque and flux at the end of the cycle. The model of the machine has been developed on a d-q frame of coordinates attached to the rotor and takes into account the magnetic saturation in both d-q axes and the cross saturation phenomenon between both axes. Therefore, a very good approximation of this effect is achieved and the performance of the machine is improved. Several simulations and experimental results using a DSP and a commercially available machine show the validity of the proposed control scheme.