A compact model representing the dynamics between piezoelectric voltage inputs and cantilever probe positioning, including nonlinear surface interaction forces, for atomic force microscopes (AFM) is considered. By considering a relatively large cantilever stiffness, singular perturbation methods reduce complexity in the model and allows for faster responses to Van der Waals interaction forces experienced by the cantilever's tip and measurement sample. In this study, we outline a nonlinear near-optimal feedback control approach for non-contact mode imaging designed to move the cantilever tip laterally about a desired trajectory and maintain the tip vertically about the equilibrium point of the attraction and repulsion forces. We also consider the universal instance when the tip-sample interaction force is unknown, and we construct cascaded high-gain observers to estimate these forces and multiple AFM dynamics for the purpose of output feedback control. Our proposed output feedback controller is used to accomplish the outlined control objective with only the piezotube position available for state feedback. / Master of Science / In this thesis, the idea of an atomic force microscope (AFM), specifically the applications of the non-contact mode, will be discussed. An atomic force microscope (AFM) is a tool that measures the surface height of nanometer sized samples. To improve the speed and precision of the machine under a non-contact mode objective, a controller is designed based on optimality and is applied to the system. The system contains a series of equations designed to steer the system towards a desired trajectory and minimal vibrations. Given the complexity of the system, resulting from nonlinearities, we will apply singular perturbation principles on the system's stiffness property to separate the larger problem into two smaller ones. These two problems are inserted into a near-optimal controller and a series of simulations are conducted to demonstrate performance. Alongside this, we will outline an observer to estimate the unknown dynamics of the system. These estimates are then applied to our controller to demonstrate that only the AFM's piezotube position is to be known in order to estimate and control the remaining dynamics of the system.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/110770 |
| Date | 13 June 2022 |
| Creators | Sutton, Joshua Lee |
| Contributors | Electrical and Computer Engineering, Boker, Almuatazbellah M., Doan, Thinh Thanh, Mili, Lamine M. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | ETD, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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