A Review of Feedforward Control Approaches in Nanopositioning for High-Speed SPM

[+] Author and Article Information
Garrett M. Clayton

Department of Mechanical Engineering, Villanova University, Villanova, PA 19085garrett.clayton@villanova.edu

Szuchi Tien

Department of Mechanical Engineering, National Cheng Kung University, Tainan 701, Taiwansctien@mail.ncku.edu.tw

Kam K. Leang

Department of Mechanical Engineering, University of Nevada, Reno, NV 89557kam@unr.edu

Qingze Zou

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

Santosh Devasia1

Department of Mechanical Engineering, University of Washington, Seattle, WA 98195devasia@u.washington.edu


Corresponding author.

J. Dyn. Sys., Meas., Control 131(6), 061101 (Oct 28, 2009) (19 pages) doi:10.1115/1.4000158 History: Received February 06, 2008; Revised April 28, 2009; Published October 28, 2009

Control can enable high-bandwidth nanopositioning needed to increase the operating speed of scanning probe microscopes (SPMs). High-speed SPMs can substantially impact the throughput of a wide range of emerging nanosciences and nanotechnologies. In particular, inversion-based control can find the feedforward input needed to account for the positioning dynamics and, thus, achieve the required precision and bandwidth. This article reviews inversion-based feedforward approaches used for high-speed SPMs such as optimal inversion that accounts for model uncertainty and inversion-based iterative control for repetitive applications. The article establishes connections to other existing methods such as zero-phase-error-tracking feedforward and robust feedforward. Additionally, the article reviews the use of feedforward in emerging applications such as SPM-based nanoscale combinatorial-science studies, image-based control for subnanometer-scale studies, and imaging of large soft biosamples with SPMs.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 1

AFM imaging in contact mode. The AFM probe is positioned using a piezoscanner in the lateral scan (x,y) and vertical (z) axes. Other possible positioning schemes include the sample being moved rather than the AFM probe and the use of separate scanners or multiple stages for different axes.

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Figure 2

Precision vertical positioning allows the AFM probe to follow the sample profile (plot (a)) along each scan line without excessive probe deflection and, therefore, without excessive probe-sample force. If the AFM probe does not follow the sample profile (plot (b)), then the probe can “dig” into the sample, causing excessive probe deflection, thereby resulting in excessive probe-sample forces.

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Figure 3

Experimental (a) frequency response with sharp resonances and (b) hysteresis nonlinearity for a tube-type piezoscanner. The input is the applied voltage to a piezoscanner preamplifier and the output is the lateral displacement. Additional details are provided in Ref. 31.

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Figure 4

Scan frequency is around 1/100 to 1/10 of the lowest resonant-vibrational frequency for a variety of SPM positioning systems and different positioning controllers (38-44)

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Figure 5

SPM scan frequency ωsf versus scan size S with a variety of positioning systems operating in air (represented by solid triangles), and in liquid over soft samples (represented by ∗). The lines are linear least-square-error fits of the data points, solid line for air imaging, and dashed line for liquid imaging. When not reported, the scan frequency and scan size were estimated (if possible) from the images, frame rates, and number of pixels (51-57).

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Figure 6

Three different approaches to linearize hysteresis nonlinearity in piezoscanners

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Figure 7

Experimental (a) frequency response G and (b) residual hysteresis nonlinearity for the tube-type piezoscanner and output range of 4 μm as in Fig. 3. The input is the voltage applied to the charge amplifier as in Fig. 6 and the output is the lateral displacement. Additional details are in Ref. 31.

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Figure 8

Integrating feedforward with feedback in SPM: (a) Closed-loop-inversion approach (38,82-83) and (b) plant-inversion approach (27,84)

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Figure 9

(a) Magnitude response of example system G in Eq. 8 and (b) percentage error %emax in Eq. 14 for a sinusoidal position trajectory. The percentage error reaches 2% at 43.3 Hz, which is slightly less than one-tenth of the first resonant-vibrational frequency at 500 Hz.

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Figure 10

Inversion for periodic position trajectory. (a) Feedforward input Vff and desired position Pd for system G in Eq. 8. (b) Simulated transient error (Pd−P) in position P when the periodic inverse input Vff is applied to G.

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Figure 11

Noncausal, exact-inverse feedforward Vff for a desired output acceleration P̈d and the associated desired output trajectory Pd. Note that the inverse feedforward Vff is nonzero before the output acceleration P̈d starts to change.

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Figure 12

Comparison of exact inverse G−1, optimal inverse Gopt−1, and ZPET inverse GZPET−1. (a) Magnitude and (b) phase. Note that the phase plots for the optimal inverse and ZPET inverse are shifted to distinguish them from the phase plot of the exact inverse.

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Figure 13

Comparison of STM images of HOPG surface without (plot (a)) and with (plot (b)) the optimal inverse input (12). The distortion of the uniform lattice pattern of the sample (in plot (a)) is substantially reduced with the use of the optimal inverse (in plot (b)).

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Figure 14

Hysteresis curve with two branches: ascending Ba and descending Bd

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Figure 15

Schematic of nanoscale combinatorial science: screening a library of samples with an AFM probe

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Figure 16

Zoom approach (148-149): the three scanning phases (expanding zoom-out phase, fixed phase, and shrinking zoom-in phase) to maintain small tip-sample forces during the iteration process

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Figure 17

Block diagram of image-based SPM control method (90). At each iteration step, k, the SPM (in this case a STM) is used to acquire a low-speed and a high-speed image (I and Ik, respectively). These two images are compared with to determine the positioning error ek, which is used by the IIC algorithm to determine the input Vk+1 for the next iteration step to improve the SPM’s positioning accuracy.

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Figure 18

Image-based control has been applied to enable high-speed imaging of a HOPG sample in Refs. 90-91. (a) Accurate low-speed (100 Hz) STM image of graphite. (b) High-speed (2 kHz) STM image of the same graphite surface showing the distortion caused by positioning error. (c) High-speed (2 kHz) STM image obtained using image-based control (91).

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Figure 19

Two approaches to increase positioning bandwidth of piezoscanner, where the system model is G in Eq. 8. (a) Flattening the frequency response by using the optimal inverse as feedforward (Gopt−1 in Sec. 42 with dc-gain G(0) as in Eq. 9). (b) Stiffening the system by increasing each resonant-vibrational frequency ωz, ωp1, and ωp2 and the gain k of G (in Eq. 8) by an order of magnitude.




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