Inversion of an extended generalized Prandtl-Ishlinskii hysteresis model: Theory and experimental results

The Prandtl-Ishlinskii (PI) model is a popular hysteresis model that has been widely adopted for smart material-based systems. Recently, an analytical inversion of a generalized PI model was formulated, facilitating the modeling and control of systems with hysteresis. The approach, however, does not allow the inclusion of a memoryless nonlinearity. In this paper we consider an extended generalized PI model, where a memoryless function is added to improve modeling accuracy. An inversion algorithm for the extended generalized PI hysteresis model is derived based on the fixed-point theorem along with the convergence conditions. Experiments involving a new class of smart materials, vanadium dioxide (VO
2
), are conducted to illustrate the effectiveness of the extended generalized PI modeling approach and the inverse algorithm.