Nonlinear Dynamics

, Volume 92, Issue 1, pp 59–74 | Cite as

Modeling and closed loop control of a polymer composite-based hard-magnetic micromirror for optical switching applications

Original Paper
  • 196 Downloads

Abstract

In this paper, a mathematical model is first established for an electromagnetic actuated polymer composite-based MEMS hard-magnetic micromirror. The model consists of the analyses of the mechanical parts for torsional scanner, the electro-coils parts and the magnetic actuator parts of the hard-magnetic films. To illustrate the effectiveness of such a model, the static and dynamic performance is further analyzed using both finite element method and it is experimentally validated. The experimental results show that our models are valid. Finally, considering the high performance requirements of optical switching applications proportional-integral-derivative (PID) controller with incomplete differentials and the integral sliding mode surface with PID form controller which is based on the established mathematical model is designed to improve its transient response. And the experimental results of set-point regulation have demonstrated that the 95% setting time is shortened from 45 to 10 ms while improving the overshoot.

Keywords

MEMS Electromagnetic micromirror Hard-magnetic PID Sliding mode control Angle tracking 

Notes

Acknowledgements

This work is supported by National Natural Science Foundation (NNSF) of China under Grants 61273121, 61374036 and Science and Technology Project of Guangdong Province (No. 2017A010101009).

References

  1. 1.
    Cao, J., Hao, Q., Xia, W., et al.: Design and realization of retina-like three-dimensional imaging based on a MOEMS mirror. Opt. Lasers Eng. 82, 1–13 (2016)CrossRefGoogle Scholar
  2. 2.
    Kainz, A., Hortschitz, W., Steiner, H., et al.: Accurate analytical model for air damping in lateral MEMS/MOEMS oscillators. Sens. Actuators A 255, 154–159 (2017)CrossRefGoogle Scholar
  3. 3.
    Abdel-Rahman, E.M., Younis, M.I., Nayfeh, A.H.: Characterization of the mechanical behavior of an electrically actuated microbeam. J. Micromech. Microeng. 12(6), 759 (2002)CrossRefGoogle Scholar
  4. 4.
    Tan, J., Sun, W., Yeow, J.T.: Internal model-based robust tracking control design for the MEMS electromagnetic micromirror. Sensors 17(6), 1215 (2017)CrossRefGoogle Scholar
  5. 5.
    Kim, S.J., Cho, Y.H., Nam, H.J., et al.: Piezoelectrically pushed rotational micromirrors using detached PZT actuators for wide-angle optical switch applications. J. Micromech. Microeng. 18(12), 125022 (2008)CrossRefGoogle Scholar
  6. 6.
    Frangi, A., Guerrieri, A., Carminati, R., Mendicino, G.: Parametric resonance in electrostatically actuated micromirrors. IEEE Trans. Ind. Electron. 64(2), 1544–1551 (2017)CrossRefGoogle Scholar
  7. 7.
    Kim, H., Jeong, H., Lee, K., Ji, H., Park, H.: Electromagnetically actuated biaxial scanning micromirror fabricated with silicon on glass wafer. Microsyst. Technol. 23(6), 2075–2085 (2017)CrossRefGoogle Scholar
  8. 8.
    Grinberg, I.H., Maccabi, N., Kassie, A., Shmulevich, S., et al.: Direct torsion of bulk PZT using directional interdigitated electrodes. Procedia Eng. 168, 1483–1487 (2016)CrossRefGoogle Scholar
  9. 9.
    Pallapa, M., Yeow, J.T.W.: Design, fabrication and testing of a polymer composite based hard-magnetic mirror for biomedical scanning applications. J. Electrochem. Soc. 161(2), B3006–B3013 (2013)CrossRefGoogle Scholar
  10. 10.
    Zhang, X.M., Chau, F.S., Quan, C., et al.: A study of the static characteristics of a torsional micromirror. Sens. Actuators A Phys. 90(1), 73–81 (2001)CrossRefGoogle Scholar
  11. 11.
    Imam, H.T., Adamson, R., Brown, J. et al.: Two-dimensional (2D) micromirror with enhanced tilting angle using active control methods. In: 2012 International Conference on Optical MEMS and Nanophotonics (OMN), pp. 113–114. IEEE (2012)Google Scholar
  12. 12.
    Tilmans, H.A.C., De Raedt, W., Beyne, E.: MEMS for wireless communications: from RF-MEMS components to RF-MEMS-SiP. J. Micromech. Microeng. 13(4), S139 (2003)CrossRefGoogle Scholar
  13. 13.
    Mizukami, M., Yamaguchi, J., Nemoto, N.: 128128 3D-MEMS optical switch module with simultaneous optical paths connection for optical cross-connect systems. In: PS’09. International Conference on Photonics in Switching, pp. 1–2. IEEE (2009)Google Scholar
  14. 14.
    Wolter A, Hsu S.T., Schenk H, et al.: Applications and requirements for MEMS scanner mirrors, MOEMS-MEMS MicroNanofabrication. In: International Society for Optics and Photonics, pp. 64–75 (2005)Google Scholar
  15. 15.
    Isikman, S.O., Urey, H.: Dynamic modeling of soft magnetic film actuated scanners. IEEE Trans. Magn. 45(7), 2912–2919 (2009)CrossRefGoogle Scholar
  16. 16.
    Myung, N.V., Park, D.Y., Yoo, B.Y., et al.: Development of electroplated magnetic materials for MEMS. J. Magn. Magn. Mater. 265(2), 189–198 (2003)CrossRefGoogle Scholar
  17. 17.
    Cetraro, M., Lacarbonara, W., Formica, G.: Nonlinear dynamic response of carbon nanotube nanocomposite microbeams. J. Comput. Nonlinear Dyn. 12(3), 031007 (2017)CrossRefGoogle Scholar
  18. 18.
    Ando, B., Baglio, S., L’Episcopo, G.: A low-cost, disposable, and contactless resonant mass sensor. IEEE Trans. Instrum. Meas. 62(1), 246–52 (2013)CrossRefGoogle Scholar
  19. 19.
    Wilcox, B., Dankowicz, H., Lacarbonara, W.: Response of electrostatically actuated flexible MEMS structures to the onset of low-velocity contact. In: Proceedings of IDETC/CIE (2009)Google Scholar
  20. 20.
    Cugat, O., Reyne, G., Delamare, J., et al.: Novel magnetic micro-actuators and systems (MAGMAS) using permanent magnets. Sens. Actuators A 129(1), 265–269 (2006)CrossRefGoogle Scholar
  21. 21.
    Borovic, B., Liu, A.Q., Popa, D., et al.: Open-loop versus closed-loop control of MEMS devices: choices and issues. J. Micromech. Microeng. 15(10), 1917 (2005)CrossRefGoogle Scholar
  22. 22.
    Zhao, Z., Liu, Y., Guo, F., Fu, Y.: Vibration control and boundary tension constraint of an axially moving string system. Nonlinear Dyn. (2017). doi: 10.1007/s11071-017-3595-x
  23. 23.
    Grade J.D., Jerman, H.: MEMS electrostatic actuators for optical switching applications. In: Optical Fiber Communication Conference and Exhibit, vol. 3 (2001)Google Scholar
  24. 24.
    Lim M, Mao M, Ostrom R.: Bistable latching actuator for optical switching applications: U.S. Patent 6, 865, 313 (2005)Google Scholar
  25. 25.
    Bernstein, J.J., Taylor, W.P., Brazzle, J.D., et al.: Electromagnetically actuated mirror arrays for use in 3-D optical switching applications. J. Microelectromech. Syst. 13(3), 526–535 (2004)CrossRefGoogle Scholar
  26. 26.
    Fei, J., Ding, H.F.: Adaptive sliding mode control of dynamic system using RBF neural network. Nonlinear Dyn. 70(2), 1563–1573 (2012)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Nayfeh, A.H., Younis, M.I., Abdel-Rahman, E.M.: Dynamic pull-in phenomenon in MEMS resonators. Nonlinear Dyn. 48(1–2), 153–163 (2007)CrossRefMATHGoogle Scholar
  28. 28.
    Towfighian, S., Heppler, G.R., Abdel-Rahaman, E.M.: Low-voltage closed loop MEMS actuators. Nonlinear Dyn. 69(1–2), 565–575 (2011)Google Scholar
  29. 29.
    Daqaq, M.F., Reddy, C.K., Nayfeh, A.H.: Input-shaping control of nonlinear MEMS. Nonlinear Dyn. 54(1), 167–179 (2008)CrossRefMATHGoogle Scholar
  30. 30.
    And, B., Baglio, S., et al.: Numerical and experimental investigation on contactless resonant sensors. Sens. Actuators A 162(2), 329–335 (2010)CrossRefGoogle Scholar
  31. 31.
    Urey, H., Kan, C., Davis, W.O.: Vibration mode frequency formulae for micromechanical scanners. J. Micromech. Microeng. 15(9), 1713–1721 (2005)CrossRefGoogle Scholar
  32. 32.
    Chen, I.G., Liu, J., Weinstein, R., Lau, K.: Characterization of YBa\(_2\)Cu\(_3\)O\(_7\), including critical current density J c, by trapped magnetic field. J. Appl. Phys. 72(3), 1013–1020 (1992)Google Scholar
  33. 33.
    Judy, J.W., Muller, R.S.: Magnetically actuated addressable microstructures. J. Microelectromech. Syst. 6(3), 249–256 (1997)CrossRefGoogle Scholar
  34. 34.
    Piazzi, A., Visioli, A.: A noncausal approach for PID control. J. Process Control 16(8), 831–843 (2006)CrossRefGoogle Scholar
  35. 35.
    Chen, H., Pallapa, M., Sun, W.J., et al.: Nonlinear control of an electromagnetic polymer MEMS hard-magnetic micromirror and its imaging application. J. Micromech. Microeng. 24(4), 57–63 (2014)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  • Yi Qin
    • 1
  • Weijie Sun
    • 1
  • Peng Zuo
    • 1
  • John T. W. Yeow
    • 2
  1. 1.College of Automation Science and EngineeringSouth China University of TechnologyGuangzhouPeople’s Republic of China
  2. 2.Systems Design EngineeringUniversity of WaterlooWaterlooCanada

Personalised recommendations