Fuzzy modeling of a piezoelectric actuator

In this research, a piezoelectric actuator was modeled using fuzzy subtractive clustering and neuro-fuzzy networks. In the literature, the use of various modeling techniques (excluding techniques used in this article) and different arrangements of inputs in black box modeling of piezoelectric actuators for the purpose of displacement prediction has been reported. Nowadays, universal approximators are available with proven ability in system modeling; hence, the modeling technique is no longer such a critical issue. Appropriate selection of the inputs to the model is, however, still an unsolved problem, with an absence of comparative studies. While the extremum values of input voltage and/or displacement in each cycle of operation have been used in black box modeling inspired by classical phenomenological methods, some researchers have ignored them. This article focuses on addressing this matter. Despite the fact that classical artificial neural networks, the most popular black box modeling tools, provide no visibility of the internal operation, neuro-fuzzy networks can be converted to fuzzy models. Fuzzy models comprise of fuzzy rules which are formed by a number of fuzzy or linguistic values, and this lets the researcher understand the role of each input in the model in comparison with other inputs, particularly, if fuzzy values (sets) have been selected through subtractive clustering. This unique advantage was employed in this research together with consideration of a few critical but subtle points in model verification which are usually overlooked in black box modeling of piezoelectric actuators.