Modeling amplitude-modulation atomic force microscopy using direct-quadrature transformation

Xu, Yuchen

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https://hdl.handle.net/2142/108135 Copy

Description

Title

Modeling amplitude-modulation atomic force microscopy using direct-quadrature transformation

Author(s)

Xu, Yuchen

Issue Date

2020-05-13

Director of Research (if dissertation) or Advisor (if thesis)

Salapaka, Srinivasa M

Department of Study

Mechanical Sci & Engineering

Discipline

Mechanical Engineering

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

M.S.

Degree Level

Thesis

Date of Ingest

2020-08-26T23:57:20Z

Keyword(s)

• AFM
• Dynamics

Abstract

This thesis presents modeling of amplitude-modulated atomic force microscopy. The existing models of AM-AFM rely on averaging of dynamic models, where second order ordinary differential equations are considered with sinusoidal forcing which are perturbed with small forces that model cantilever tip and sample interactions. The resulting models that relate cantilever amplitude to sample motions are complex and inaccurate. These challenges have forced using model-free control design approaches, which can provide only limited performance; especially limited in disturbance rejection bandwidth, which severely impede imaging quality and bandwidth. The approach proposed in this thesis relies on deriving models in a rotating frame, whereby the resulting models are simple and accurate. Here, the proposed model is derived using direct-quadrature (dq) frame (rotating frame) transformation, which is commonly used in electrical power systems literature to describe dynamical systems driven by near-harmonic oscillating signals. This coordination transformation requires at least two-dimensional coordinate system; accordingly a fictitious AFM system is assumed running in parallel with the original AFM system. In the rotating frame, the trajectories are represented by dynamics of phasors, where the orthogonal components of these phasors closely relate to the amplitudes of the solutions of the real and fictitious systems. The resulting dynamical model is simple which can be used to enable model-based analysis and control design. We demonstrate that this model provides an accurate (5.5 % estimation error) over a bandwidth of up to 2.5% of the cantilever resonance frequency. This is sufficient for control design since current AM-AFM implementations typically use bandwidths in the range of 0.01%-0.1% of the cantilever resonance frequency. We modify our design with extra signal processing of our amplitude estimate, where we designed a notch filter to gives a to reduce the unwanted higher harmonics and other frequency components that hinder the estimation accuracy. The notch filter design reduced the unwanted high frequency components by over 80% giving much more accuracy with amplitude and phase estimation errors less than 1.5% over a bandwidth of 2.5 % of cantilever resonance frequency. The resulting model is also in a structure more suitable for sample physical property estimation than existing models such as Krylov-Bogoliubov-Mitropolsky models.

Graduation Semester

2020-05

Type of Resource

Thesis

Permalink

http://hdl.handle.net/2142/108135

Copyright and License Information

Copyright 2020 Yuchen Xu

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