{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/108135"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/108135","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Modeling amplitude-modulation atomic force microscopy using direct-quadrature transformation","abstract":"The student, Yuchen Xu, accepted the attached license on 2020-04-29 at 12:03.","abstract_html":"The student, Yuchen Xu, accepted the attached license on 2020-04-29 at 12:03.","abstract_has_math":false,"creators":["Xu, Yuchen"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Mechanical Engineering","degree_department":null,"school":null,"contributors":["Salapaka, Srinivasa M"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-08-26T23:57:20Z","date_published":"2020-08-26T23:57:20Z","updated_at":"2026-07-22T22:24:47Z","subjects":["AFM","Dynamics"],"languages":["en"],"rights":["Copyright 2020 Yuchen Xu"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/108135","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Salapaka, Srinivasa M"]},{"key":"dc:creator","label":"Author","values":["Xu, Yuchen"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2020-08-26T23:57:20Z","2022-08-26T23:58:55Z","2020-05-13","2020-05"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["AFM","Dynamics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2020 Yuchen Xu"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/108135"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The student, Yuchen Xu, accepted the attached license on 2020-04-29 at 12:03.","The student, Yuchen Xu, submitted this Thesis for approval on 2020-04-29 at 12:11.","This Thesis was approved for publication on 2020-05-13 at 07:16.","DSpace SAF Submission Ingestion Package generated from Vireo submission #15114 on 2020-08-25 at 17:28:29","Made available in DSpace on 2020-08-26T23:57:20Z (GMT). No. of bitstreams: 2 XU-THESIS-2020.pdf: 1008405 bytes, checksum: b7626eea95acf60604673efebd6c6e1b (MD5) LICENSE.txt: 4206 bytes, checksum: 32c50101d92c4a7e1ba441be44f1dcb2 (MD5) Previous issue date: 2020-05-13","Embargo set by: Seth Robbins for item 115747 Lift date: 2022-08-26T23:57:28Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system","Embargo set by: Seth Robbins for item 115747 Lift date: 2022-08-26T23:58:55Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system","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.","Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2022-05-01","Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system","U of I Only"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Modeling amplitude-modulation atomic force microscopy using direct-quadrature transformation"]}]}],"canonical_facts":{"dc:contributor":["Salapaka, Srinivasa M"],"dc:creator":["Xu, Yuchen"],"dc:date":["2020-08-26T23:57:20Z","2022-08-26T23:58:55Z","2020-05-13","2020-05"],"dc:description":["The student, Yuchen Xu, accepted the attached license on 2020-04-29 at 12:03.","The student, Yuchen Xu, submitted this Thesis for approval on 2020-04-29 at 12:11.","This Thesis was approved for publication on 2020-05-13 at 07:16.","DSpace SAF Submission Ingestion Package generated from Vireo submission #15114 on 2020-08-25 at 17:28:29","Made available in DSpace on 2020-08-26T23:57:20Z (GMT). No. of bitstreams: 2 XU-THESIS-2020.pdf: 1008405 bytes, checksum: b7626eea95acf60604673efebd6c6e1b (MD5) LICENSE.txt: 4206 bytes, checksum: 32c50101d92c4a7e1ba441be44f1dcb2 (MD5) Previous issue date: 2020-05-13","Embargo set by: Seth Robbins for item 115747 Lift date: 2022-08-26T23:57:28Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system","Embargo set by: Seth Robbins for item 115747 Lift date: 2022-08-26T23:58:55Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system","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.","Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2022-05-01","Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system","U of I Only"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/108135"],"dc:language":["en"],"dc:rights":["Copyright 2020 Yuchen Xu"],"dc:subject":["AFM","Dynamics"],"dc:title":["Modeling amplitude-modulation atomic force microscopy using direct-quadrature transformation"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Mechanical Engineering"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:47Z"}