System identification of proportional solenoid valve dynamics

We present a system identification technique for the characterisation of the linearity and dynamic response of a PSOL valve and its corresponding electronic control unit (ECU) using bandlimited white noise, as well as pseudo random "non-sum non-difference" (NSND) waveforms consisting of mutually prime frequencies to mitigate the effects of nonlinear distortions. The parameters of several transfer function models were simultaneously estimated from the voltage-flow frequency response using a nonlinear gradient descent technique. Candidate transfer function models were assessed using the mean squared residual (MSR) criterion and the corrected Akaike information criterion (AICc). The MSR yielded a transfer function consisting of 10 poles and 9 zeros, while the AICc yielded a simpler transfer function consisting of 5 poles and 3 zeros. Monte Carlo analysis demonstrated fragile stability for the MSR-selected model with respect to varying parameter values within estimated uncertainties, yet a robust stability for the AICc-selected model.