An enhanced physics-based model to estimate the displacement of piezoelectric actuators

Piezoelectric actuators are the foremost actuators in the area of nanopositioning. However, the sensors employed to measure the actuator displacement are expensive and difficult, if not impossible, to use. Mathematical models can map the easy-to-measure electrical signals to the displacements of the actuators as the displacement sensors are replaced with the models. In addition, these models can be used in model-based control system design. Two main groups of mathematical models are used for this purpose: black box and physics-based models. As an advantage, the latter has a much smaller number of parameters reducing computational demand in real-time applications. However, physics-based models suffer from (1) the relatively low accuracy of the models and (2) non-standard and ad-hoc parameter identification methods. In this research, to improve the model accuracy, mathematical structure of a well-known physics-based model, the Voigt model, is enhanced by adding two complementary terms inspired by another model, the Preisach model. Then, a standard method based on the evolutionary algorithms is proposed to identify the model's parameters. The proposed ideas are substantiated to increase the applicability and accuracy of the model, and they are easily extendable to other physics-based models of piezoelectric actuators. The newly proposed enhanced structure of the Voigt model doubles the estimation accuracy of the original model and results in accuracies comparable with black box models.