A new simple asymmetric hysteresis operator and its application to inverse control of piezoelectric actuators
Résumé
Piezoelectric actuators (PEAs) are commonly used as micro-positioning devices due to their high resolution, high stiffness and fast frequency response. Because piezoceramic materials are ferroelectric, they fundamentally exhibit hysteresis behavior in their response to an applied electric field. The positioning precision can be significantly reduced due to nonlinear hysteresis effects when PEAs are used in relatively long range applications. This paper describes a new precise and simple asymmetric hysteresis operator dedicated to PEAs. The complex hysteretic transfer characteristic has been considered in a purely phenomenological way, without taking into account the underlying physics. This operator is based on two curves. The first curve corresponds to the main ascending branch and is modeled by the function f1. The second curve corresponds to the main reversal branch and is modeled by the function g2. f1 and g2 are two very simple hyperbola functions with only three parameters. Particular ascending and reversal branches are deduced from appropriate translations of f1 and g2. The efficiency and preciseness of the proposed approach is demonstrated, in practice, by a real-time inverse feedforward controller for piezoelectric actuators. Advantages and drawbacks of the proposed approach compared to classical hysteresis operators are discussed.