Adaptive estimation of the shear force in the cantilever dynamics of the Transverse Dynamic Force Microscope

The dynamics of the cantilever in a Transverse Dynamic Force Microscope (TDFM) are presented by means of irrational transfer functions. An approximate model of the cantilever can then be obtained using a finite number of rational transfer functions. The shear force for this model can be estimated by adaptive schemes. Numerical simulations are presented to show the effectiveness of the proposed methods.

[1]  A. Raman,et al.  Comparative dynamics of magnetically, acoustically, and Brownian motion driven microcantilevers in liquids , 2007 .

[2]  Jing Na,et al.  An adaptive observer-based parameter estimation algorithm with application to road gradient and vehicle's mass estimation , 2012, Proceedings of 2012 UKACC International Conference on Control.

[3]  Murti V. Salapaka,et al.  Multimode and multitone analysis of the dynamic mode operation of the Atomic Force Microscope , 2013, 2013 American Control Conference.

[4]  A. Raman,et al.  Dynamics of tapping mode atomic force microscopy in liquids: Theory and experiments , 2007 .

[5]  Carsten Trunk,et al.  Analyticity and Riesz basis property of semigroups associated to damped vibrations , 2008 .

[6]  J. Hörber,et al.  Methods for imaging DNA in liquid with lateral molecular-force microscopy , 2012, Nanotechnology.

[7]  A Ulcinas,et al.  A new detection system for extremely small vertically mounted cantilevers , 2008, Nanotechnology.

[8]  S. Sastry,et al.  Adaptive Control: Stability, Convergence and Robustness , 1989 .

[9]  Guido Herrmann,et al.  Shear force reconstruction in a vertically oriented probe microscope using a super-twisting observer , 2013, 52nd IEEE Conference on Decision and Control.

[10]  Massimo Antognozzi,et al.  Observation of molecular layering in a confined water film and study of the layers viscoelastic properties , 2001 .

[11]  Murti V. Salapaka,et al.  Damping mechanisms in dynamic mode atomic force microscopy applications , 2009, 2009 American Control Conference.

[12]  Guido Herrmann,et al.  Estimation of the shear force in Transverse Dynamic Force Microscopy using a sliding mode observer , 2013, 2013 American Control Conference.

[13]  Ulrich Eggers,et al.  Introduction To Infinite Dimensional Linear Systems Theory , 2016 .

[14]  Bao-Zhu Guo,et al.  Riesz Basis Approach to the Stabilization of a Flexible Beam with a Tip Mass , 2000, SIAM J. Control. Optim..

[15]  G. Weiss,et al.  Observation and Control for Operator Semigroups , 2009 .

[16]  X. Ren,et al.  Robust adaptive finite-time parameter estimation for linearly parameterized nonlinear systems , 2013, Proceedings of the 32nd Chinese Control Conference.

[17]  Kathy L. Rowlen,et al.  Tip Characterization from AFM Images of Nanometric Spherical Particles , 1998 .

[18]  Gerber,et al.  Atomic Force Microscope , 2020, Definitions.