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Feedforward control of a closed-loop piezoelectric translation stage for atomic force microscope

Rev. Sci. Instrum. 78, 013702 (2007); doi:10.1063/1.2403839

Published 11 January 2007

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Yang Li and John Bechhoefer
Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
Simple feedforward ideas are shown to lead to a nearly tenfold increase in the effective bandwidth of a closed-loop piezoelectric positioning stage used in scanning probe microscopy. If the desired control signal is known in advance, the feedforward filter can be acausal: the information about the future can be used to make the output of the stage have almost no phase lag with respect to the input. This keeps in register the images assembled from right and left scans. We discuss the design constraints imposed by the need for the feedforward filter to work robustly under a variety of circumstances. Because the feedforward needs only to modify the input signal, it can be added to any piezoelectric stage, whether closed or open loop. ©2007 American Institute of Physics
History: Received 4 October 2006; accepted 7 November 2006; published 11 January 2007
Permalink: http://link.aip.org/link/?RSINAK/78/013702/1
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KEYWORDS and PACS

Keywords
PACS
  • 07.79.Lh
    Atomic force microscopes
  • YEAR: 2006

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PUBLICATION DATA

ISSN:
0034-6748 (print)   1089-7623 (online)
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REFERENCES (34)
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  16. The group at MIT led by W. P. Seering has been a particular champion of feedforward (or “input shaping”) techniques. For a detailed and lucid introduction, see W. E. Singhose, Ph.D. thesis, MIT (1997).
  17. “Dynamic Digital Linearization” and “Input Shaping” for Polytec PI (Karlsruhe, Germany) translation stages. See www.polytecpi.com. The algorithms are licensed from Convolve, Inc.; see www.convolve.com.
  18. We implement an acausal feedforward filter to eliminate phase shifts. In addition, we use an infinite-impulse-response (IIR) filter, rather than a finite-impulse-response (FIR) filter.
  19. P. S. Maybeck, Stochastic Models, Estimation, and Control (Academic, New York, 1979), Vol. 1.
  20. Mad City Labs, Madison, WI. Stage Nano-H100, with a range of 100 µm. Another model, the Nano-PDQ series, is specified to have a resonant frequency five times that of our stage (the H100). See madcitylabs.com.
  21. For simplicity, we discuss only the X-stage response. The Y-stage has a similar response, with a lower mechanical resonance frequency, since the Y-stage supports the X-stage.
  22. Stanford Research Systems, SR850. The excitation was an 8 mV rms sine wave (equivalent to about 220 nm, peak-to-peak). The time constant was 1 s, with 8 s/data point in the sweep. See thinksrs.com.
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  24. The bandwidth is here defined, in the standard way, as being the frequency where the response amplitude first falls below 1/sqrt(2). The stage's manufacturer claims a bandwidth of 200 Hz. Apparently, this discrepancy stems from their use of a nonstandard definition of bandwidth.
  25. S. W. Smith, The Scientist and Engineer's Guide to Digital Signal Processing, 2nd ed. (California Technical Publishing, San Diego, 1999). Available on the web at DSPguide.com.
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  27. One subtlety of going from the continuous to the discrete domain is that the discrete filter constructed using Eq. (7) has a different bandwidth. But, because the sampling rate is over 20 times the filter bandwidth, the bandwidth of the discrete filter differs from that of its continuous counterpart by only ~0.3 Hz. Thus, although one can compensate for the shift by using “prewarping,” we did not. See, for example, Ref. 26, Chap. 6.1.
  28. SCILAB is available from scilab.org.
  29. The term “noncausal” is also used. Both terms refer to the feature that a desired future behavior of the system is achieved by modifying the inputs in the present.
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  34. K. K. Leang and S. Devasia, Mechatronics 16, 141 (2006).

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