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.Narges Miri, Morteza Mohammadzaheri and Lei Che

A comparative study of different physics-based approaches to modelling of piezoelectric actuators

This article reviews different approaches to modelling of piezoelectric actuators (PZA). The electric charge/voltage variation causes shape deformation of piezoelectric materials. If the piezoelectric material is in contact with a structure, it has the tendency to actuate that structure; in this case, the piezoelectric material plays the role of an actuator. Piezoelectric actuators are the foremost actuators in nanopositioning, manipulating material at nano/micro metre scale, applicable in Atomic Force Microscopy (AFM), highly precise manufacturing and .... In nanopositioning, displacement of piezoelectric actuators should be precisely controlled. However, the application of displacement sensors is limited by their high expense and practical constraints. Estimating displacement of piezoelectric actuators, based on their input voltage, can eliminate expensive displacement sensors from control systems. Therefore, several models have been developed to predict the displacement of piezoelectric actuators based on their input voltage. Models are basically created either merely based on data mapping, black box models, or inspired by physical phenomena, physics-based models. Physics-based models are superior in offering a clear definition of the relationship between all parts of the system dynamics. The main physics-based models are Kelvin-Voigt, Maxwell-Slip, Duhem, Preisach and Prandtl-Ishlinskii models; for each one some critical features such as rate-dependency and reversibility are addressed in this paper. This article compares the mentioned approaches and states advantages/disadvantages of each method. Parameter identification in these models is done by adhoc and non-optimal methods motivating researchers to look for alternative methods.Narges Miri, Morteza Mohammadzaheri, Lei Che