An evolutionary approach to physics-based modelling of piezoelectric actuators, supported by a critical review and experimental results

Abstract

This paper reviews different physics-based (inspired by physics) modelling methods of piezoelectric actuators, which are the foremost actuators in nanopositioning, manipulating material at nano/micro metre scale, applicable in AFM (atomic force microscopy), highly precise manufacturing and … Applying electric charge/voltage on piezoelectric materials deforms their shapes; using this characteristics; the structures in contact with them can be actuated; in this case, piezoelectric material plays the role of an actuator. In nanopositioning, models of piezoelectric actuators can estimate displacement of piezoelectric actuators, based on the voltage across them, to eliminate expensive displacement sensors from control systems, also these models can be used in controller design. Therefore, several models have been developed for piezoelectric actuators either merely based on data mapping, black box models, or inspired by physical phenomena, physics-based models. As an advantage, physics-based models have smaller number and physically meaningful parameters compared to black box models such as artificial neural networks. These models together with their features such as frequency-dependency, reversibility and validity area are critically reviewed in this paper using a uniform and comparable notation to facilitate model selection by engineers and researchers. The main challenge of physics-based models is parameter identification which is currently partially solved using complicated ad-hoc methods. A standard parameter identification method based on an evolutionary algorithm is presented in this paper, and a discretised Voigt model is identified and experimentally verified using the proposed method.