Recursive Memory-based Hysteresis Modeling for Solid-state Smart Actuators

This article presents a new modeling approach for the memory-dependent hysteresis phenomenon in a broad class of smart structures and systems. We propose a recursive formulation to relate the minor hysteresis trajectories to their surrounding loops. More specifically, each internal (minor) trajectory targets its previous turning point and converges to its neighboring loop with a tunable exponential rate. By applying the ‘curve alignment’ and the ‘wiping out’ properties at the turning points, we present a new strategy within the context of a memory-based hysteresis modeling framework. A Galfenol-driven micropositioning actuator and a piezoelectrically driven nanopositioning stage are used to experimentally validate the model. Galfenol exhibits large butterfly-type nonlinearity with a small hysteresis effect, while the piezoelectric actuator exhibits wide hysteresis loops. The model is able to precisely predict the major and minor hysteresis loops in both the Galfenol and piezoelectric actuators, and is expected to be effectively and conveniently applicable to general systems exhibiting memory-dependent hysteresis.