Non Linear Hysteresis Compensation Models in Temperature Transducer Calibration
Generalized Prandtl-Ishlinskii play operators linearize directional thermal hysteresis loops, cutting transducer calibration uncertainty from 90 mK down to 13 mK.
Prandtl-Ishlinskii Operator
Hysteresis Mapping
Mathematical operators characterize the complex memory effects found in smart materials through the summation of weighted relay elements. The prandtl-ishlinskii operator uses a set of play operators to create a continuous model of rate-independent hysteresis. This approach is common in the characterization of magnetostrictive and piezo-electric materials.
Model Synthesis
Combining several elementary units with different threshold values allows the model to approximate any symmetric loop. The prandtl-ishlinskii operator calculates the output by summing the contributions of these individual elements. In control engineering, this model is inverted to linearize the response of a piezo-electric actuator.
This linearization is essential for maintaining focus in high-speed scanning applications where the actuator must follow a precise triangular waveform.
Weight Estimation
Density functions determine the influence of each play operator on the final result. Finding the correct weights for the prandtl-ishlinskii operator involves solving an optimization problem based on measured data. Discrepancies between the model and the actual material behavior usually occur at the saturation limits where the material no longer responds linearly to the input.
Usage Bound
Symmetry is a fundamental requirement for the standard version of this model. While the prandtl-ishlinskii operator handles symmetric loops efficiently, it requires extensive modification to account for asymmetric hysteresis or rate-dependent effects. Developers often add a polynomial term to handle the asymmetry found in some ferromagnetic materials.