General Bond Graph model for piezoelectric actuators and methodology for experimental identification

Abstract

Piezoelectric actuators are becoming very popular in applications such as nanopositioning, active vibration control or noise reduction, sometimes as part of so called smart structures. The possibility of accurately moving big loads on a micrometric scale and over a wide range of frequencies has resulted in an intense growth of this technology. This interest has prompted the development of a wide variety of mathematical models available for describing their behaviour, whose suitability depends on the specific application involved. This work overcomes this limitation by unifying the different modelization options for stack and stack-based actuators in a general Bond Graph model structure capable of handling the most important physical phenomena observed in these actuators, both linear, such as direct and indirect piezoelectric effects or rate dependence, and nonlinear, such as hysteresis. This model structure represents a basis for specific applications, and can be used for control or simulation purposes thanks to its high generality and adjustment capabilities. The proposed Bond Graph structure graphically shows the power flow between the electrical and mechanical frameworks of the piezoelectric actuator, and uses a modular structure for separately representing the electrical polarization of the material and its macroscopic electrical and mechanical effects. Finally, the model is successfully applied to describe the rate dependent behaviour of the Cedrat Groupe APA-120ML actuator. In this connection, an experimental identification method is described and adapted for implementing hysteresis descriptions based on simple operators or in differential equations in the model structure (O-based and DE-based models). These two typologies cover the majority of the models available, proving the generality of the proposed piezoelectric model for implementing less general or specific phenomenon descriptions into its structure. In consequence, the main contribution of this work is the development of a general framework for modelling piezoelectric actuators, comprising a graphical Bond Graph model and an adjustment procedure, which is flexible enough to embody different representations of the phenomena present in these actuators, and with a modular structure that admits different levels of complexity depending on the phenomena incorporated in the model.