An evolutionary approach to physics-based modelling of piezoelectric actuators

Abstract

The objective of this research is to improve physics-based models of piezoelectric actuators through developing a global parameter identification method for the models and introducing a new high performance model. Piezoelectric actuators produce nano-metre scale displacements making them the dominant actuators in nanopositioning applications. In nanopositioning, the control of actuators’ displacement requires highly accurate displacement sensors. The sensors are expensive and difficult, if not impossible, to use. Therefore, the models are employed to estimate the displacement of piezoelectric actuators, using the voltage across them, without any displacement sensors. Accordingly, several mathematical models have been developed to estimate the displacement of piezoelectric actuators. However, due to the nonlinear behaviour of the actuators, the models cannot capture their behaviour precisely. Therefore, developing a model to simulate the nonlinear behaviour of the actuator would constitute an important contribution to the development of high precision sensorless nanopositioning systems. Models can also be used in control system design. To model piezoelectric actuators, this research utilises physics-based models that have a small number of parameters compared with standard black box models of piezoelectric actuators minimising the computation efforts in real-time applications. In this thesis, the physics-based models are enhanced by dealing with two main diagnosed weaknesses of these models: (1) the lack of a global parameter identification method and, (2) the relatively low accuracy of the models due to their inadequate mathematical structure. The method for identifying the parameters of the physics-based models is one of the main challenges for these models. In general, the parameters of physics-based models are determined by non-optimal ad-hoc methods. Hence, this research adopts a standard, optimal and global (non-ad-hoc) method to identify the parameters of the nonlinear models of the piezoelectric actuators. Another challenge for the physics-based models of piezoelectric actuators is the relatively low accuracy of the models compared with the black box models, partially arising from the rather simple mathematical structure and a small number of parameters of these models. Therefore, improving the model structure will increase the model accuracy. To address this matter, complementary terms/inputs are added to a physics-base model constructing an enhanced structure for the model. The new model doubles the estimation accuracy of the original model and results in accuracies comparable with those of the best reported models of piezoelectric actuators. The proposed ideas are substantiated to increase the applicability and accuracy of the models of piezoelectric actuators. From the range of physics-based models, the Voigt model is a particular focus for this research. The Voigt model can capture the rate-dependent and nonlinear behaviour of piezoelectric actuators. Furthermore, this model has been reported to be adequate for a broad excitation frequency range (1-1000) Hz. However, the proposed ideas are easily extendable to other physics-based models of piezoelectric actuators.