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Interval Modeling and Robust Feedback Control of Piezoelectric-Based Microactuators

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Smart Materials-Based Actuators at the Micro/Nano-Scale

Abstract

This chapter presents the modeling and the control of piezoelectric-based microactuators. Typified by uncertainties of models, we propose to use intervals to bound the uncertain parameters. These uncertainties are particularly due to the difficulties to perform precise identification and to the high sensivity of the systems at the micro/nanoscale. In order to account the models uncertainties, we propose therefore to combine interval tools and classical control theory to derive robust controllers. Experimental results confirm the predicted theory and demonstrate the efficiency of the proposed method.

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References

  1. S.-J. An, L. Huang, E. Wang, On the parametric H problems of weighted interval plants, IEEE Trans. Automat. Contr. 45, 332–335 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  2. S.-J. An, X. Hu, B. Vucetic, W. Liu, Vertex results for parametric shifted H performance of weighted interval plants. IEEE Conf. Decis. Contr. 5, 4195–4196 (2000)

    Google Scholar 

  3. G.J. Balas, J.C. Doyle, K. Glover, A. Packard, R. Smith, \(\mu\) -synthesis and synthesis toolbox for use with Matlab. The Mathworks (2001)

    Google Scholar 

  4. L. Iorga, H. Baruh, I. Ursu, A review of H robust control of piezoelectric smart structures. Appl. Mech. Rev. 61(4), 04082-1–04082-15 (2008)

    Google Scholar 

  5. L. Jaulin, E. Walter, Set inversion via interval analysis for nonlinear bounded-error estimation. Automatica. 29(4), 1053–1064 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  6. L. Jaulin, M. Kieffer, O. Didrit, E. Walter, Applied Interval Analysis (Springer, London, 2001)

    Book  MATH  Google Scholar 

  7. S. Khadraoui, Calcul par intervalles et outils de l’automatique permettant la micromanipulation prcision qualifie pour le microassemblage, Thse de Doctorat, Universit de Franche-Comt Besanon, 2012

    Google Scholar 

  8. S. Khadraoui, M. Rakotondrabe, P. Lutz, PID-structured controller design for interval systems: application to piezoelectric microactuators, in American Control Conference (ACC), San Francisco, CA, USA, 2011, pp. 3477–3482

    Google Scholar 

  9. S. Khadraoui, M. Rakotondrabe, P. Lutz, Combining H and interval techniques to design robust low order controllers: application to piezoelectric actuators, in American Control Conference (ACC), Montral, Canada, 2012

    Google Scholar 

  10. S. Khadraoui, M. Rakotondrabe, P. Lutz, Combining H approach and interval tools to design a low order and robust controller for systems with parametric uncertainties: application to piezoelectric actuators. Int. J. Contr. 85(3), 251–259 (2012)

    Article  MathSciNet  Google Scholar 

  11. S. Khadraoui, M. Rakotondrabe, P. Lutz, Interval modeling and robust control of piezoelectric microactuators. IEEE Trans. Contr. Syst. Technol. 20(2),486–494 (2012)

    Article  Google Scholar 

  12. R.E. Moore, Interval Analysis (Prentice-Hall, Englewood Cliffs, 1966)

    MATH  Google Scholar 

  13. M. Rakotondrabe, Performances inclusion for stable interval systems, in American Control Conference (ACC), San Francisco, CA, USA, June–July 2011, pp. 4367–4372

    Google Scholar 

  14. M. Rakotondrabe, C. Clevy, P. Lutz, Modelling and robust position/force control of a piezoelectric microgripper, in IEEE - International Conference on Automation Science and Engineering (CASE), Scottsdale, AZ, USA, 2007, pp. 39–44

    Google Scholar 

  15. M. Rakotondrabe, Y. Haddab, P. Lutz, Quadrilateral modelling and robust control of a nonlinear piezoelectric cantilever. IEEE Trans. Contr. Syst. Technol. 17(3), 528–539 (2009)

    Article  Google Scholar 

  16. A. Sebastian, A. Pantazi, S.O.R. Moheimani, H. Pozidis, E. Eleftheriou, Achieving subnanometer precision in a MEMS-based storage device during self-servo write process. IEEE Trans. Nanotechnol. 7(5), 586–595 (2008)

    Article  Google Scholar 

  17. L. Wang, H performance of interval systems. eprint arXiv:math/0211013 1, 1–8 (2002)

    Google Scholar 

  18. K. Zhou, J. Doyle, K. Glover, Robust and Optimal Control (Prentice-Hall, Englewood Cliffs, New Jersey 07632, Upper Saddle River, 1996)

    Google Scholar 

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Correspondence to Micky Rakotondrabe .

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Khadraoui, S., Rakotondrabe, M., Lutz, P. (2013). Interval Modeling and Robust Feedback Control of Piezoelectric-Based Microactuators. In: Rakotondrabe, M. (eds) Smart Materials-Based Actuators at the Micro/Nano-Scale. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6684-0_6

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  • DOI: https://doi.org/10.1007/978-1-4614-6684-0_6

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