Compensation of rate-dependent hysteresis nonlinearities in a magnetostrictive actuator using an inverse Prandtl–Ishlinskii model

Magnetostrictive actuators invariably exhibit hysteresis nonlinearities that tend to become significant under high rates of inputs, and could cause oscillations and error in the micro-positioning tasks. This study presents a methodology for compensation of hysteresis nonlinearity in a magnetostrictive actuator subject to a wide range of input rates in an open-loop manner. The hysteresis compensation is attained through application of an inverse rate-dependent Prandtl–Ishlinskii model formulated on the basis of the rate-dependent Prandtl–Ishlinskii hysteresis model and laboratory-measured hysteresis properties of the magnetostrictive actuator under inputs at frequencies up to 200 Hz. The effectiveness of the inverse rate-dependent Prandtl–Ishlinskii model compensator for mitigating the major and minor loop hysteresis nonlinearities is demonstrated through simulation results and hardware-in-the-loop laboratory measurements of a magnetostrictive actuator (stroke ±50 μm) under inputs in the 1–200 Hz frequency range. Both the simulation and experimental results revealed reduction of peak hysteresis from 4.7 to 0.645 μm, when the proposed inverse rate-dependent model is applied as a feedforward hysteresis compensator, which occurred under excitations at the lowest frequency of 1 Hz. The results suggest that the inverse Prandtl–Ishlinskii model could provide hysteresis compensation under different rates of inputs in a simple and effective manner.