Active estimation of the initial phase for brushless synchronous motors

This paper addresses the initial phase estimation problem for brushless synchronous motors. Only displacement measurements are used (no current) and friction, load and motor parameters are supposed to be unknown. Because of friction, the system is modelled by a differential equation with discontinuous right-hand side. Specific open-loop inputs are designed (active method) to get the initial phase as a function of the magnitude of the displacements along the corresponding trajectories. The estimation relies on a complete classification of the possible dynamical behaviours of the considered discontinuous right-hand side system with periodic input, whatever values the unknown parameters may take. We propose an approximated formula of the initial phase. Some experimental results are given, together with a comparison of our method to a classical procedure