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

摘要

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.