Analysis of Flux Observers for Brushless Machines

In this thesis the observation of magnetic fluxes of brushless machines is investigated. Given the time varying nature of the equations that describe the brushless machines electrical behaviour, the stability of time varying systems is studied adopting Lyapunov theory. Three observers are proposed for the estimation of the fluxes: the Luenberger Observer, the Kalman Filter and the Extended Kalman Filter. These algorithms are implemented in Simulink. The solutions found are tested and verified using a full Model in the Loop available at the LEMAD (Laboratory for Electric Machine and Drives) of the University of Bologna. The observers are tested also with uncertainties in the resistance and inductances parameters, which is a common scenario in practice. A stability band for a diagonal observer gain, in discrete time, has been successfully found. In both the simulations with the known parameters and with variation of the statoric resistance, the estimated fluxes converge to the actual fluxes, but the RMS value of the error is better for the Extended Kalman Filter. For the simulations with the variations of the inductances, the estimation of the fluxes have worsened with more similar RMS error value among the three. In conclusion it was found that the Extended Kalman Filter has a better behaviour all around but it does not perform significantly better in the more realistic case. For this reason the proposed simpler Luenberger observer, designed using Lyapunov theory, can be a valid alternative.