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System identification for nano-scale control

Vaqueiro Contreras, Michelle

[Thesis]. Manchester, UK: The University of Manchester; 2015.

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Abstract

Piezoelectric materials are widely used in nanotechnology. In particular they are usedwith scanning tunnelling microscopy (STM) and atomic force microscopy (AFM).Over the last few decades the development of these technologies has underpinned significantprogress in numerous areas, including biology, chemistry, materials science,and physics. Nevertheless, piezoelectric materials have an intrinsically nonlinear conduct,exhibiting hysteresis and creep; these are typical characteristics of ferroelectricmaterials. Such behaviour is undesirable for nanopositioning applications. Consequently,many efforts have been made to compensate/eliminate these nonlinear actions.There are many studies of appropriate models. However, finding a suitable model forthe hysteresis of such materials is non-trivial for control.With the aim of providing new or improved methods and models for identificationin piezo-actuated nanopositioners, we identify a an ARMAX model in series with arecently developed nonlinear model, the hyperbolic model. The hyperbolic model hasbeen demonstrated to be closely related to the well known Preisach model.Correspondingly, throughout this research we have applied some of the well investigatedtools for linear and nonlinear identification, for a proper integration of aWienermodel structure. The Wiener model configuration, which consists of the interconnectionof a dynamic linear model in series with a nonlinear static model, has been usedwidely in the nonlinear identification field however not reported for nanopositioningapplications yet. Additionally, the simulated annealing algorithm commonly used foroptimization objectives has been implemented for parametrization. Accordingly, themodel is identified using a black-box model approach with input and output data obtainedfrom laboratory experiments.Experiments were carried out using a piezo scanned flexure guided stage (NanopositioningStage), as the system to be identified. The calculated response shows a highlevel of affinity with real data in both the time and frequency domains.