Impact Solenoid Modeling for Current-Dependent Piston Position Estimation

Impact solenoids create wide-band acoustic signals in the materials they hit, which can be used to measure physical properties, geometry, and distances. Heuristic signal approximations are insufficient at smaller timescales, or when the impactor bounces. We seek a way to estimate the impact profile, and therefore piston position, from the current passing through the solenoid. Existing models focus on position control applications, and so make assumptions such as low piston velocity and pulse-width modulation excitation. We present a physically-derived solenoid model which includes the effects of piston velocity, and thus is suitable for impact applications with a step excitation. The associated differential equation is solved to determine the location of the piston, giving an impact model relating the piston position to a measured solenoid current via dead reckoning. These models are assessed by firing impact solenoids at a target and recording the drawn current and supply voltage. The position estimates each model produces are compared against ground truth readings taken from a laser vibrometer for each individual firing, both for fitting and validation replicates. The validation RMS position error of the models is less than 3 % of the piston stroke over full impact durations.