Reduction of phase error between sinusoidal motions and vibration of a tube scanner during spiral scanning using an AFM

Regular Papers Control Theory and Applications

Abstract

The design of a phase-locked loop (PLL)-based proportional integral (PI) controller for compensating the phase error between motions from the lateral axes of a piezoelectric tube scanner (PTS) during spiral scanning for an atomic force microscope (AFM) is proposed in this paper. Spiral motion of the PTS for scanning of material surfaces or biological samples using an AFM is achieved by applying two sinusoidal signals with a 90 degree phase-shift and of varying amplitudes to the X and Y-axes of the scanner. The phase error between the X and Y-axes positions and scanner’s vibration due to its mechanical properties increase with increasing scanning speeds which reduce the imaging performance of the AFM at high frequencies. In the proposed control scheme, a vibration compensator is used with the X and Y-PTS to damp the vibration of the PTS at its resonant frequency and the phase error between the displacements of the two lateral axes of the scanner is measured by a phase detector and a PI controller is used to reduce the error. Comparisons of experimental results for reference tracking and imaging performance with the AFM PI controller demonstrate the efficiency of the proposed control method.

Keywords

Atomic force microscope phase-locked loop control piezoelectric tube scanner vibration control 

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References

  1. [1]
    R. Young, J. Ward, and F. Scire, “The topografiner: an instrument for measuring surface microtopography,” Review of Scientific Instruments, vol. 43, no. 7, pp. 999–1011, 1972. [click]CrossRefGoogle Scholar
  2. [2]
    G. Binnig, C. F. Quate, and C. Gerber, “Atomic force microscope,” Physical Review Letters, vol. 56, no. 9, p. 930, 1986. [click]CrossRefGoogle Scholar
  3. [3]
    P. Ge and M. Jouaneh, “Modeling hysteresis in piezoceramic actuators,” Precision Engineering, vol. 17, no. 3, pp. 211–221, 1995. [click]CrossRefGoogle Scholar
  4. [4]
    H. Habibullah, H. R. Pota, I. R. Petersen, and M. S. Rana, “Tracking of triangular reference signals using lqg controllers for lateral positioning of an afm scanner stage,” IEEE/ASME Transactions on Mechatronics, vol. 19, no. 4, pp. 1105–1114, 2014. [click]CrossRefGoogle Scholar
  5. [5]
    H. Habibullah, O. U. Rehman, H. R. Pota, and I. R. Petersen, “Internal reference model based optimal lqg controller for atomic force microscope,” Proc. of 12th International Conference on Control Automation Robotics & Vision (ICARCV), pp. 294–299, 2012. [click]Google Scholar
  6. [6]
    I. Mahmood and S. R. Moheimani, “Making a commercial atomic force microscope more accurate and faster using positive position feedback control,” Review of Scientific Instruments, vol. 80, no. 6, p. 063705, 2009. [click]CrossRefGoogle Scholar
  7. [7]
    H. Habibullah, H. R. Pota, I. R. Petersen, and M. S. Rana, “Reduction of cross-coupling between x-y axes of piezoelectric scanner stage of atomic force microscope for faster scanning,” Proc. of IEEE International Conference on Control Applications (CCA), pp. 455–460, 2013. [click]Google Scholar
  8. [8]
    D. Zhiqiang, Z. Zude, A. Wu, and C. Youping, “A linear drive system for the dynamic focus module of sls machines,” The International Journal of Advanced Manufacturing Technology, vol. 32, no. 11-12, pp. 1211–1217, 2007. [click]CrossRefGoogle Scholar
  9. [9]
    N. Tamer and M. Dahleh, “Feedback control of piezoelectric tube scanners,” Proceedings of the 33rd IEEE Conference on Decision and Control, vol. 2. IEEE, pp. 1826–1831, 1994. [click]Google Scholar
  10. [10]
    H. Habibullah, H. R. Pota, I. R. Petersen, and M. S. Rana, “Creep, hysteresis, and cross-coupling reduction in the high-precision positioning of the piezoelectric scanner stage of an atomic force microscope,” IEEE Transactions on Nanotechnology, vol. 12, no. 6, pp. 1125–1134, 2013. [click]CrossRefGoogle Scholar
  11. [11]
    K. K. Leang and S. Devasia, “Feedback-linearized inverse feedforward for creep, hysteresis, and vibration compensation in AFM piezoactuators,” IEEE Transactions on Control Systems Technology, vol. 15, no. 5, pp. 927–935, 2007. [click]CrossRefGoogle Scholar
  12. [12]
    M. Rana, H. Pota, and I. R. Petersen, “High-speed afm image scanning using observer-based mpc-notch control,” IEEE Transactions on nanotechnology, vol. 12, no. 2, pp. 246–254, 2013. [click]CrossRefGoogle Scholar
  13. [13]
    A. Bazaei, Y. K. Yong, S. R. Moheimani, and A. Sebastian, “Tracking of triangular references using signal transformation for control of a novel afm scanner stage,” IEEE Transactions on Control Systems Technology, vol. 20, no. 2, pp. 453–464, 2012. [click]CrossRefGoogle Scholar
  14. [14]
    N. Chuang, I. R. Petersen, and H. R. Pota, “Robust H control in fast atomic force microscopy,” Proc. of American Control Conference (ACC), pp. 2258–2265, 2011. [click]Google Scholar
  15. [15]
    S. Devasia, E. Eleftheriou, and S. O. R. Moheimani, “A survey of control issues in nanopositioning,” IEEE Transactions on Control Systems Technology, vol. 15, no. 5, pp. 802–823, 2007. [click]CrossRefGoogle Scholar
  16. [16]
    B. Bhikkaji and S. R. Moheimani, “Integral resonant control of a piezoelectric tube actuator for fast nanoscale positioning,” IEEE/ASME Transactions on Mechatronics, vol. 13, no. 5, pp. 530–537, 2008. [click]CrossRefGoogle Scholar
  17. [17]
    J. Wang, J. Wang, Y. Hou, and Q. Lu, “Self-manifestation and universal correction of image distortion in scanning tunneling microscopy with spiral scan,” Review of Scientific Instruments, vol. 81, no. 7, p. 073705, 2010. [click]CrossRefGoogle Scholar
  18. [18]
    I. A. Mahmood and S. O. R. Moheimani, “Fast spiral-scan atomic force microscopy,” Nanotechnology, vol. 20, no. 36, p. 365503, 2009. [click]CrossRefGoogle Scholar
  19. [19]
    A. Kotsopoulos, A. Pantazi, A. Sebastian, and T. Antonakopoulos, “High-speed spiral nanopositioning,” Proceedings of the 18th IFAC World Congress, pp. 2018–2023, 2011. [click]Google Scholar
  20. [20]
    H. Habibullah, H. R. Pota, and I. R. Petersen, “High-speed spiral imaging technique for an atomic force microscope using a linear quadratic gaussian controller,” Review of Scientific Instruments, vol. 85, no. 3, p. 033706, 2014. [click]Google Scholar
  21. [21]
    ---, “Developing a spiral scanning method using atomic force microscopy,” Proc. of 9th Asian Control Conference (ASCC), pp. 1–6, 2013. [click]Google Scholar
  22. [22]
    ---, “Phase-locked loop-based proportional integral control for spiral scanning in an atomic force microscope,” Proc. of IFAC-World Congress, vol. 19, no. 1, pp. 6563–6568, 2014. [click]Google Scholar
  23. [23]
    ---, “High-precision spiral positioning control of a piezoelectric tube scanner used in an atomic force microscope,” Proc. of American Control Conference (ACC), pp. 1625–1630, 2014. [click]Google Scholar
  24. [24]
    S.-K. Hung, “Spiral scanning method for atomic force microscopy,” Journal of Nanoscience and Nanotechnology, vol. 10, no. 7, pp. 4511–4516, 2010. [click]CrossRefGoogle Scholar
  25. [25]
    W. Gao, J. Aoki, B.-F. Ju, and S. Kiyono, “Surface profile measurement of a sinusoidal grid using an atomic force microscope on a diamond turning machine,” Precision Engineering, vol. 31, no. 3, pp. 304–309, 2007. [click]CrossRefGoogle Scholar
  26. [26]
    R. D. Hoge, R. K. Kwan, and G. Bruce Pike, “Density compensation functions for spiral MRI,” Magnetic Resonance in Medicine, vol. 38, no. 1, pp. 117–128, 1997. [click]CrossRefGoogle Scholar
  27. [27]
    H. Habibullah, I. R. Petersen, H. R. Pota, and M. S. Rana, “LQG controller with sinusoidal reference signal modeling for spiral scanning of atomic force microscope,” Proc. of 8th IEEE Conference on Industrial Electronics and Applications (ICIEA), pp. 1474–1479, 2013. [click]Google Scholar
  28. [28]
    A. G. Kotsopoulos and T. A. Antonakopoulos, “Nanopositioning using the spiral of archimedes: The probe-based storage case,” Mechatronics, vol. 20, no. 2, pp. 273–280, 2010. [click]CrossRefGoogle Scholar
  29. [29]
    C. Ahn, J. Kim, and Z. Cho, “High-speed spiral-scan echo planar NMR imaging-I,” IEEE Transactions on Medical Imaging, vol. 5, no. 1, pp. 2–7, 1986. [click]CrossRefGoogle Scholar
  30. [30]
    R. Ben Mrad and H. Hu, “A model for voltage-todisplacement dynamics in piezoceramic actuators subject to dynamic-voltage excitations,” IEEE/ASME Transactions on Mechatronics, vol. 7, no. 4, pp. 479–489, 2002. [click]CrossRefGoogle Scholar
  31. [31]
    L. Ljung, “Prediction error estimation methods,” Circuits, Systems and Signal Processing, vol. 21, no. 1, pp. 11–21, 2002. [click]MathSciNetCrossRefGoogle Scholar
  32. [32]
    H. R. Pota, “Phase-locked loop,” University of New South Wales (UNSW), Australia, (Technical Brief Lecture Notes), Tech. Rep., 2005.Google Scholar
  33. [33]
    W. Djatmiko and B. Sutopo, “Speed control dc motor under varying load using phase-locked loop system,” Proc. of the International Conf. on Electrical, Electronics, Communication, and Information CECI, pp. 7–8, 2001.Google Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of Engineering and ITThe University of New South WalesCanberra BCAustralia

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