The conventional methods for estimating the rotor position of permanent magnet synchronous machines, at low speed range and characterized by rotor saliency, rely on high frequency voltage injection in the stator windings. Ordinarily, the rotor position estimation is achieved through the demodulation of the high frequency current response. In this paper, an alternative method is presented for detecting rotor position from the rotating high frequency injection current response. The proposed ellipse fitting technique is not affected by signal processing delay effects and it requires the tuning of only one parameter, called forgetting factor, making the studied method suitable for industrial application thanks to its minimal setup effort. The inverse problem related to the ellipse fitting is solved implementing a QR recursive least squares algorithm. Efficient updating QR factorization has been adopted because of its features in terms of numerical stability and required limited computational effort. The proposed sensorless control scheme is validated by means of many experiments.

In this paper, we introduce a new column selection strategy, named here “Deviation Maximization”, and apply it to compute rank-revealing QR factorizations as an alternative to the well-known block version of the QR factorization with the column pivoting method, called QP3 and currently implemented in LAPACK’s routine. We show that the resulting algorithm, named QRDM, has similar rank-revealing properties of QP3 and better execution times. We present experimental results on a wide data set of numerically singular matrices, which has become a reference in the recent literature.