  In this paper, we present a hybrid sensorless observer for Permanent Magnets
Synchronous Machines, with no a priori knowledge of the mechanical dynamics and
without the typical assumption of constant or slowly-varying speed. Instead, we
impose the rotor speed to have a constant (unknown) sign and a non-zero
magnitude at all times. For the design of the proposed scheme, meaningful Lie
group formalism is adopted to describe the rotor position as an element of the
unit circle. This choice, however, leads to a non-contractible state space, and
therefore it introduces topological constraints that complicate the achievement
of global/semi-global and robust results. In this respect it is shown that the
proposed observer, which employs a clock to periodically reset the estimates,
is semi-globally practically asymptotically stable, and thus it improves a
continuous-time version designed under the same assumptions. As highlighted in
the simulation results, the novel hybrid strategy leads to enhanced transient
performance, notably without any modification of the gains employed in the
continuous-time solution. These features motivate to augment the observer with
a discrete-time identifier, leading to significantly faster rotor flux
reconstruction.
