Mathematical models of hysteresis and their applications

By I. Mayergoyz. 2003

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Integral Resonant Control of a Piezoelectric Tube Actuator for Fast Nanoscale Positioning (2008, background): “constructing a good model is both complex and computationally involved [31].”
Development of the rate-dependent Prandtl–Ishlinskii model for smart actuators (2008, background): “For describing smartmaterial-based actuators, perhaps the most popular hysteresis model is the phenomenological Preisach operator [1], where the hysteresis is modeled as an aggregate effect (density function) of all possible delayed relay elements, which are parameterized by a pair of threshold vari”
Modeling and Control of Piezo-Actuated Nanopositioning Stages: A Survey (2016, positive): “3) Operator-Based Hysteresis Models: Operator-based hysteresis models are kinds of models with an integral of weighed elementary hysteresis operators [62], [84]–[86].”
Modeling and Compensation of Asymmetric Hysteresis Nonlinearity for Piezoceramic Actuators With a Modified Prandtl–Ishlinskii Model (2014, methodology): “Inspired by the validation approach of the wiping-out property for the operator-based hysteresis models [15], [27], [28], [39], the wiping-out property of the proposed MPI model is asserted in a geometrical interpretation with the memory curve structure.”
Position Control of Shape Memory Alloy Actuators by Using Self Tuning Fuzzy PID Controller (2006, background): “Usually the Preisach model of hysteresis based on phenomenological nature [7-9] is developed.”