Real-Time Hysteresis Modeling of a Reluctance Actuator Using a Sheared-Hysteresis-Model Observer

We present a method for real-time estimation of the hysteresis in an electromagnetic actuator in the presence of a changing air gap. We model the actuator with a lumped-parameter model, which enables us to model the ferromagnetic hysteresis separately from the air gap reluctance. This allows us to use a single-input hysteresis model with the magnetic field in the actuator core as the input, rather than having to use a two-input hysteresis model that requires the air gap as an additional input. Since the core magnetic field is not measured, we design an observer of the lumped-parameter model to estimate the core magnetic field and air gap flux as the gap changes. We introduce a change of variables in order to model a sheared version of the ferromagnetic hysteresis that takes advantage of the linearizing effect of the nominal air gap. We use the Preisach model to model the ferromagnetic hysteresis. The observer with sheared-hysteresis model is shown to be much more accurate compared to an observer using a standard unsheared-hysteresis model and is numerically stable in the face of a dynamically changing air gap. We test our real-time flux estimation scheme on a reluctance actuator prototype mounted to a 1-DoF air bearing stage. We experimentally demonstrate that the observer with the sheared-hysteresis model is capable of accurately estimating the actuator air gap flux in the presence of a dynamic gap change with a peak-to-peak amplitude of 35 μm.