A comparative study on the use of black box modelling for piezoelectric actuators

In this article, different approaches of the use of black box modelling techniques for piezoelectric actuators are particularly addressed, regardless of the employed technique/algorithm. A modelling approach in this paper refers to two matters: the first, the role of black box techniques in modelling (i.e. if physics-based techniques are also involved in modelling; if so, how and to what extent). From this aspect, the spectrum of approaches ranges from those merged with/inspired by classical phenomenological models to an approach based on purely system identification-based techniques. The second aspect of modelling approaches, in this article, is the input variables to the model. Current and previous values of input voltage, previous values of the output (displacement), derivatives and extremum values of the system's input/output have been used as the inputs to the model so far. Both aforementioned aspects of modelling approaches are addressed appropriately in this article, and various modelling approaches in the literature are categorized and presented in a uniform and comparable manner, so that readers can easily identify research trends in this area and the gaps in the literature. One of the identified unanswered questions in the literature is whether the extremum values of the system's input/output should/should not be used as an input to black box models of piezoelectric actuators. There are works in the literature which have/have not used the aforementioned input variables, but there is no published investigation to evidently answer the proposed question. This article, in the last section, answers this question by reporting and discussing an experimental study.