  In this paper we address the problem of sensorless control of the 1-DOF
magnetic levitation system. Assuming that only the current and the voltage are
measurable, we design an adaptive state observer using the technique of signal
injection. Our main contribution is to propose a new filter to identify the
virtual output generated by the signal injection. It is shown that this filter,
designed using the dynamic regressor extension and mixing estimator,
outperforms the classical one. Two additional features of the proposed observer
are that (i) it does not require the knowledge of the electrical resistance,
which is also estimated on-line and (ii) exponential convergence to a tunable
residual set is guaranteed without excitation assumptions. The observer is then
applied, in a certainty equivalent way, to a full state-feedback control law to
obtain the sensorless controller, whose performance is assessed via simulations
and experiments.
