1.5.1 Luenberger Observer

The Luenberger Observer is a general method used to find out the internal state of a linear system, when the inputs and the outputs are known.

Here the implementation of Reduced Order Luenberger Observer is described for the BEMF. The BEMF vector position is found with an arctan() operation from the BEMF components, which are derived from the Luenberger observer internal state variables. Now the flux vector position is found since its position lags BEMF by 90°.

The speed is obtained from the position derivative. This needs to be heavily filtered to give good results. A fourth order filter can be used, composed by a first order FIR filter (moving average) followed by three equal first order IIR filters.

The Reduced Order Luenberger Observer provides good results for both steady state and dynamic operating conditions.