Modeling of dynamic hysteresis for piezoelectric actuator via IGSA-IELM-based Hammerstein block structure

In this paper, A novel two-stage Hammerstein model is presented to describe the dynamic hysteresis. In the first stage, a hysteresis operator is introduced to transform the multi-valued mapping of the hysteresis into one-to-one mapping. Then the nonlinear static part is approximated by Extreme Learning Machine Algorithm combining with an Isomap method. Before this, an improved Gravitational Search Algorithm is used to optimize the parameter of ELM Algorithm. The obtained model assumes that the hysteretic behavior does not depend on the history of voltage rate, so in the second stage, an ARX model is adopted which can estimate the rate dependency of hysteresis as the linear dynamic system of Hammerstein structure. The effectiveness of the algorithm is verified by piezoelectric actuator (PEA) experiments.