Parameter Estimation in Linear Electromagnetic Devices

The parameters of electrical machines can change considerably during operation due to thermal effects. Therefore, the corresponding models and the estimates of parameters can be subject to a significant bias and uncertainty, which degrade the performance of the system. In this paper, a method is developed to estimate the resistance of the coil of a linear electromagnetic actuator, i.e., of a single-coil linear solenoid. In the electrical model of the solenoid actuator, the inductance depends on the current. The inductance is identified from the transient waveform of the current (step response), and an estimate of the resistance is provided by extrapolating to the steady state of the current. Thus, the resistance can be estimated before the system reaches the steady state. The presented method is generalized to pulsewidth-modulation (PWM) drive conditions by considering the average of the current of the coil in the successive PWM cycles. This improves the suppression of measurement noise. The developed approach is demonstrated through numerical and experimental analyses.