Research Papers

A New Approach to Scan-Trajectory Design and Track: AFM Force Measurement Example

[+] Author and Article Information
Kyong-Soo Kim

Mechanical Engineering Department,  Iowa State University, Ames, IA 50011kyongsoo@iastate.edu

Qingze Zou1

Mechanical Engineering Department,  Iowa State University, Ames, IA 50011qzzou@iastate.edu

Chanmin Su

 Veeco Instruments Inc., Santa Barbara, CA 93117csu@veeco.com

The numerical results are available via email to Kyong-Soo Kim.


Corresponding author.

J. Dyn. Sys., Meas., Control 130(5), 051005 (Aug 01, 2008) (10 pages) doi:10.1115/1.2936841 History: Received October 18, 2006; Revised March 31, 2008; Published August 01, 2008

In this article, two practical issues encountered in the design and track of scan trajectories are studied: One issue is the large output oscillations occurring during the scanning, and the other one is the effect of modeling errors on trajectory tracking. Output oscillations need to be small in scanning operations, particularly for lightly damped systems, such as the piezoelectric actuators and the flexible structures. Moreover, modeling errors are ubiquitous in practical applications. The proposed approach extends the recently developed optimal scan-trajectory design and control method by introducing the prefilter design to reduce the output oscillations. Furthermore, a novel enhanced inversion-based iterative control (EIIC) algorithm is proposed. The EIIC algorithm is then integrated with the optimal scan-trajectory design method to compensate for the effect of modeling errors on the scanning. The convergence of the iterative control law is discussed, and the frequency range of the convergence is quantified. The proposed approach is illustrated by implementing it to the high-speed adhesion-force measurements using atomic force microscope. Simulation and experimental work are presented and discussed to demonstrate the efficacy of the proposed approach. The experimental results show that compared to the conventional DC-gain method, the proposed approach can reduce the tracking error by over 25 times during the force-curve measurements.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 1

The scan trajectory consisting of a transition section (for t0⩽t<ti) and a tracking section (for ti⩽t<tf), where the desired output trajectory is prespecified for the tracking section only

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Figure 2

The augmented system consisting of a prefilter Gpre(s) followed by the plant dynamics G(s)

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Figure 3

(a) The scheme of AFM adhesion-force measurement and (b) a schematic drawing of the force-distance curve to measure the adhesion force (denoted as Fadh in (b))

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Figure 4

(a) Comparison of the experimentally measured frequency response of the z-axis AFM dynamics (from the piezoactuator input to the cantilever deflection output under the contact-mode condition) with the frequency response of the transfer function model obtained via curve-fitting method. (b) The frequency response of the augmented system model (the prefilter followed by the AFM-dynamics model).

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Figure 5

The estimated magnitude uncertainty of the AFM-dynamics (red, dotted), the upper bound of the iterative coefficient (green, dash-dotted), ρsup(ω) (see Eq. 3), and the iterative coefficient used in the experiments (blue, solid), ρ(ω)

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Figure 6

Comparison of the optimal inputs (plot (a)) and the corresponding optimal output trajectories (plot (b)) obtained by using the OSDC technique for the augmented system with (solid) and without (dashed) the prefilter. The signal frequency is 100Hz with the duty ratio Rd=50%.

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Figure 7

Left column: Comparison of the experimental tracking results obtained by using the DC-gain method, the OSDC technique, and the EIIC technique for the scan rate of (a1)100Hz, (a2)260Hz, and (a3)320Hz. Right column: Comparison of the corresponding tracking errors.

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Figure 8

Left column: The comparison of the experimentally measured probe-sample force trajectory (i.e., force-time curve) for adhesion-force measurements, obtained by using the DC-gain method with the curves by using the EIIC technique at the scan rates of (a1)100Hz. (b1)260Hz, and (c1)320Hz. Right column: The comparison of the corresponding deviations of the force curve from the constant force rate during the pulling-up section for the scan rates of (a2)100Hz, (b2)260Hz, and (c2)320Hz.



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