Identification and control of a 3DOF metrological AFM

Identification and control of a 3DOF metrological AFM

Merry, R. J. E., Uyanik, M., Koops, K. R., Molengraft, van de, M. J. G., Veghel, van, M. G. A., & Steinbuch, M. (2008). Identification and control of a 3DOF metrological AFM. In 27th Benelux Meeting on Systems and Control, Heeze, The Netherlands, March 18-20, 2008. Book of abstracts (pp. paper-199).

Document status and date: Published: 01/01/2008 Document Version:

Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication:

• A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.

• The final author version and the galley proof are versions of the publication after peer review.

• The final published version features the final layout of the paper including the volume, issue and page numbers.

Link to publication

General rights

Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain

• You may freely distribute the URL identifying the publication in the public portal.

If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement:

www.tue.nl/taverne Take down policy

If you believe that this document breaches copyright please contact us at: openaccess@tue.nl

providing details and we will investigate your claim.

Identification and control of a 3DOF metrological AFM

Roel Merry

, Mustafa Uyanik,

Ren´e van de Molengraft and Maarten Steinbuch

Department of Mechanical Engineering

Eindhoven University of Technology

P.O. Box 513, 5600 MB Eindhoven

The Netherlands

Email:

r.j.e.merry@tue.nl

Richard Koops and Marijn van Veghel

NMi Van Swinden Laboratorium

Thijsseweg 11

2629 JA Delft

The Netherlands

1 Introduction

The metrological AFMs are used to calibrate transfer stan-dards for commercial AFMs. In contrast to commercial AFMs, the accuracy of the measurements is much more im-portant than the scanning speed. In current AFMs MIMO aspects are commonly disregarded and the positioning of the sample is often done in an open-loop manner [1].

In this research, nonparametric MIMO identification of the AFM in all 3 degrees of freedom (DOFs) is used to investi-gate the amount of coupling between the various axes. Fur-thermore, feedback control is applied to all 3 DOFs.

2 Identification

The AFM and the feedback control loops of all 3 DOFs are shown schematically in Fig. 1. Although the different axes are theoretically decoupled, practically some amount of cross coupling will be inevitable in the 3DOF stage, e.g. due to alignment errors.

ez t z rz sample topography ry rx ex ey x y z cantilever sample stage

C

Figure 1:Schematic representation of the AFM and the feedback control.

Using the non-parametric open-loop identification method, a full non-parametric MIMO identification is performed. The frequency-dependent relative gain array shows that the different axes can be assumed decoupled for frequencies

f ≤ 100 Hz.

3 Control

Three SISO feedback controllers are designed resulting in bandwidths fBW <<100 Hz. The characteristic loci show that the MIMO system with SISO controllers has a good MIMO phase margin. The feedback control in scanning di-rection also significantly reduces the effect of hysteresis in the piezo driven stage.

Since the piezo actuators act as position actuators, a position feedforward is added to the scanning axes. Fig. 2 shows that the feedforward reduces the tracing error by a factor 2 for a scan in x direction.

Future research includes the design and application of a hys-teresis feedforward and MIMO control to remove the small amount of coupling that is present.

0 10 20 30 40 −20 0 20 x (µ m ) 0 10 20 30 40 −60 0 60 time (s) ex (n m )

Figure 2: Position and tracing errors; reference (dashed), with (black) and without (dark-grey) feedforward.

References

[1] L. Y. Pao, A. Butterworth, and D. Y. Abramovich. Combined feedforward/feedback control of atomic force microscopes. American Control Conference, pages 3509– 3515, 2007.