Flux observer for spool displacement sensing in self-sensing push-pull solenoids

Spool position feedback in an electrohydraulic valve typically requires a spool displacement sensing device such as a LVDT. Self-sensing is the methodology to obtain spool displacement information directly from the solenoid spool actuators, thus obviating the additional cost and footprint of a LVDT or another displacement sensing device. A self-sensing scheme that uses only the measurement of electrical signals to the pair of push-pull solenoids was first proposed in [1]. It uses the position dependence of electrical inductance in the solenoids to infer the spool displacement. The scheme in [1] relies on a flux observer and several infinite dimensional filters that require explicit resets, and is prone to singularity. The present paper proposes a modified scheme in which the flux observer (and hence the self-sensing) problem is cast in a linear time varying system setting so that standard linear observer design techniques can be brought to bear.