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DYNAMIC MODELING CONTROL AND MANIPULATION AT THE NANOSCALE

# An Iterative-Based Feedforward-Feedback Control Approach to High-Speed Atomic Force Microscope Imaging

[+] Author and Article Information
Ying Wu

Department of Mechanical Engineering, Iowa State University, Ames, Iowa 50011wuying@iastate.edu

Qingze Zou

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

J. Dyn. Sys., Meas., Control 131(6), 061105 (Nov 06, 2009) (9 pages) doi:10.1115/1.4000137 History: Received June 18, 2008; Revised April 27, 2009; Published November 06, 2009; Online November 06, 2009

## Abstract

This article presents an iterative-based feedforward-feedback control approach to achieve high-speed atomic force microscope (AFM) imaging. AFM-imaging requires precision positioning of the probe relative to the sample in all $x-y-z$ axes directions. Particularly, this article is focused on the vertical $z$-axis positioning. Recently, a current-cycle-feedback iterative-learning-control (CCF-ILC) approach has been developed for precision tracking of a given desired trajectory (even when the desired trajectory is unknown), which can be applied to achieve precision tracking of sample profile on one scanline. In this article, we extend this CCF-ILC approach to imaging of entire sample area. The main contribution of this article is the convergence analysis and the use of the CCF-ILC approach for output tracking in the presence of desired trajectory varation between iterations—the sample topography variations between adjacent scanlines. For general case where the desired trajectory variation occurs between any two successive iterations, the convergence (stability) of the CCF-ILC system is addressed and the allowable size of desired trajectory variation is quantified. The performance improvement achieved by using the CCF-ILC approach is discussed by comparing the tracking error of using the CCF-ILC technique to that of using feedback control alone. The efficacy of the proposed CCF-ILC control approach is illustrated by implementing it to the $z$-axis control during AFM-imaging. Experimental results are presented to show that the AFM-imaging speed can be substantially increased.

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## Figures

Figure 8

Entire Imaging: Comparison of the sample estimation results (cross section view) by using the proposed CCF-ILC approach with that by using the PI control for three different equivalent scan rates of (a) 16 Hz, (b) 32 Hz, and (c) 64 Hz where the lateral scan range is 20 μm

Figure 7

Entire Imaging: Comparison of the sample estimation results by using (the upper row) the proposed CCF-ILC approach with that by using (the bottom row) the PI control for three different equivalent scan rates of ((a1)(b1)) 16 Hz, ((a2)(b2)) 32 Hz, and ((a3)(b3)) 64 Hz where the lateral scan range is 20 μm

Figure 6

Entire Imaging: Comparison of the deflection error (the residual error) by using the proposed CCF-ILC approach with that by using the PI control for four different equivalent scan rates of ((a1)(b1)) 8 Hz, ((a2)(b2)) 16 Hz, ((a3)(b3)) 32 Hz, and ((a4)(b4)) 64 Hz in sample imaging, where the left column shows the deflection error for a total of ten scanline imaging (during the middle of the imaging), the right column shows the zoomed-in view of the deflection error for one scanline imaging within the dashed window in the left column, and the lateral scan range is 20 μm

Figure 5

One Point Imaging: Comparison of the cross section of the estimated sample profiles obtained by using (red-dashed-line) the proposed CCF-ILC approach with that by using (blue-solid-line) the PI control for four different equivalent scan rates of ((a1)(b1)) 8 Hz, ((a2)(b2)) 16 Hz, ((a3)(b3)) 32 Hz, and ((a4)(b4)) 64 Hz in one scanline imaging, where the left column shows the sample estimation, the right column shows the estimation error, and the effective lateral scan range is 20 μm

Figure 4

One Point Imaging: Comparison of the estimated sample images obtained by using (the upper row) the proposed CCF-ILC approach with that by using (the bottom row) the PI control for four different equivalent scan rates of ((a1)(b1)) 8 Hz, ((a2)(b2)) 16 Hz, ((a3)(b3)) 32 Hz, and ((a4)(b4)) 64 Hz, where the effective lateral scan range was assumed to be 20 μm

Figure 3

One point imaging: Comparison of the deflection error (the residual error) by using the proposed CCF-ILC approach with that by using the PI control for four different equivalent scan rates of ((a1)(b1)) 8 Hz, ((a2)(b2)) 16 Hz, ((a3)(b3)) 32 Hz, and ((a4)(b4)) 64 Hz in one-point imaging, where the left column shows the deflection error for a total of ten scanline imaging (during the middle of the imaging) and the right column is the zoomed-in view of the deflection error for one scanline imaging within the dashed window in the left column

Figure 2

(a) The computer generated “sample profile,” (b) the cross section of one scanline, and (c) the line-to-line sample variation

Figure 1

The block diagram of (a) the standard feedback loop, (b) the modified feedback loop, and (c) the proposed CCF-ILC approach for the vertical z-axis positioning in AFM-imaging

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