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.