Application of a fuzzy tree based dynamic hysteresis model to precise tracking control for a smart structure

This paper addresses a method of modeling hysteresis of a class of smart structures generated by both varying input current and mechanical loads on account of effective application in trajectory tracking with a precision under sub-micron level. The proposed hysteresis model is a modification of the classical Preisach operator by introducing the dependence of the density function on the stress. The parameter identification procedure of the model including an adaptive-tree-structure-based fuzzy method, abbreviated as fuzzy tree, is provided. Based on the model, a feedback control scheme combined with a feed-forward inverse compensator is implemented to a magnetostrictive smart structure (MSS) for real-time precise trajectory tracking. Compared with a classical hysteresis model, the proposed model and control scheme experimentally showed a dramatically improved performance of the MSS.