Abstract—Solenoids can be used as linear or incremental
motion actuators, most often by coupling the solenoid armature to
a linear spring. In this configuration, its limited open-loop stable
range (less than one-third of the full range) affects performance
and limits applications. The input–output linearization control
method is an effective technique to extend the stable range. But in
practice, however, the time-delay effect from both measurement
and actuation can make the system less damped and therefore
more sensitive to disturbances. This effect was analyzed and a
digital proportional and integrator controller plus extended state
observer (ESO) is proposed to enhance the performance of the
electromagnetic actuator. Simulation and experimental tests show
that this combined proportional and integral and ESO technique
can extend the stable range of motion to 77.6% of full stroke
with less sensitivity to external disturbances.