The design of a vibration control system for an aluminum plate with piezo-stripes based on residues analysis of model

  • Andrzej KoszewnikEmail author
Open Access
Regular Article


The design process of an active vibration control system for many mechanical structures using smart devices requires determining reduced and precise mathematical models. Such requirements cause orthogonal methods to be used and carefully analyzed. In the present paper, a plate with two simple supported edges and two free edges (SFSF) is an object of consideration. It is known that this structure represents a flexible structure wherein high natural frequencies are separated from low frequencies because they are naturally damped. Thus, in order to estimate the dynamical features of the control system, some orthogonal methods, such as the Schur and modal decomposition, were applied. A detailed analysis of the chosen methods showed us that each of them properly generates resonance frequencies while calculating different values of the anti-resonance frequencies. From the strategy control point of view, it is known that the anti-resonances play an essential role because they directly influence the dynamics of the whole control system. Thus, in order to check this behavior, different controllers are designed for various reduced models and, next, they are applied in a real mechanical structure. The dynamical behavior of the control systems with such controllers was analyzed and tested on a laboratory stand. In conclusion, we should carefully choose model reduction methods in the design process of the vibration control system. The sum of the residues of the reduced model appeared to be the best indicator during the choice process of the reduction method. It is particularly important when we design the vibration control system for a non-existent yet, but newly designed, structure.


  1. 1.
    W. Gawroński, K.B. Lim, Balanced Control of Flexible Structures (Springer, London,1996)Google Scholar
  2. 2.
    M.J. Balas, IEEE Trans. Autom. Control 23, 4 (1978)CrossRefGoogle Scholar
  3. 3.
    E.H. Maslen, G. Schweitzer, Magnetic Bearings Theory, Design and Application to Rotating Machinery (Springer Publisher, Dordrecht Heidelberg London, 2009)Google Scholar
  4. 4.
    N. Chailet, M. Grossard, S. Regnier, Flexible Robotics, Applications to Multiscale Manipulators (ISTE Ltd., London, John Wiley & Sons, Hoboken, 2013)Google Scholar
  5. 5.
    Z. Kulesza, J. Vib. Control 21, 8 (2015)CrossRefGoogle Scholar
  6. 6.
    A. Preumont, Vibration Control of Active Structures, An Introduction, second edition (Kluwer Academic Publisher, Dordrecht, 2002)Google Scholar
  7. 7.
    M.S. Tombs, I. Postlethwaite, Int. J. Control 46, 1319 (1987)CrossRefGoogle Scholar
  8. 8.
    J.N. Juang, Applied System Identification (Prentice Hall, Inc. UK, 1994)Google Scholar
  9. 9.
    Z. Osiński, Theory of Vibrations (PWN Press, Warsaw, 1990) (in Polish)Google Scholar
  10. 10.
    Z. Gosiewski, Z. Kulesza, in Proceedings of 14th International Carpathian Control Conference, 2013 (Poland, Rytro, 2013)Google Scholar
  11. 11.
    A. Mystkowski, A. Koszewnik, Mech. Syst. Signal Process. 78, 18 (2016)CrossRefGoogle Scholar
  12. 12.
    L. Meirovitch, H. Oz, J. Guid. Control 3, 3 (1980)Google Scholar
  13. 13.
    L. Meirovitch, H. Oz, H.F. Van Landingham, J. Guid. Control 2, 5 (1979)Google Scholar
  14. 14.
    Z. Gosiewski, A. Koszewnik, J. Vibroeng. 14, 2 (2012)Google Scholar
  15. 15.
    Z. Gosiewski, A. Koszewnik, Solid State Phenom. 144, 59 (2007)CrossRefGoogle Scholar
  16. 16.
    A. Quarteroni, R. Sacco, F. Saleri, Numerical Mathematics, Approximation of Eigenvalues and Eigenvectors, Part II (Springer, New York, 2007)Google Scholar
  17. 17.
    S.G. Kelly, Advanced Vibration Analysis (CRC Press, Taylor & Francis Group, 2007)Google Scholar
  18. 18.
    B. Sapiński, Smart Mater. Struct. 20, 105007 (2011)CrossRefGoogle Scholar
  19. 19.
    Z. Gosiewski, A. Mystkowski, Mech. Syst. Signal Process. 22, 66 (2013)Google Scholar
  20. 20.
    Z. Gosiewski, A. Koszewnik, Mech. Syst. Signal Process. 36, 136 (2013) Special Issue of Piezoelectric TechnologyCrossRefGoogle Scholar
  21. 21.
    J. Konieczny, J. Kowal, B. Sapiński, Proceedings of the International Symposium on Active Control of Sound and Vibration, Vols. 1 & 2 (Florida, USA, 1999)Google Scholar
  22. 22.
    G.L. Anderson, H.S. Tzou, Intelligent Structural Systems (Kluwer Academic Publishers, 1992)Google Scholar
  23. 23.
    J.J. Hollkamp, H.S. Tzou, J.P. Zhong, J. Sound Vib. 177, 3 (1994)Google Scholar
  24. 24.
    Z. Gosiewski, J. Theor. Appl. Mech. 46, 4 (2008)Google Scholar
  25. 25.
    A. Koszewnik, Z. Gosiewski, Solid State Phenom. 248, 119 (2016)CrossRefGoogle Scholar
  26. 26.
    A. Koszewnik, Z. Gosiewski, Eur. Phys. J. Plus 131, 232 (2016)CrossRefGoogle Scholar
  27. 27.
    A. Preumont, Twelve Lectures on Structural Dynamics (Springer, New York, 2013)Google Scholar
  28. 28.
    A.J.M. Ferreira, Matlab Code for Finite Element Analysis: Solids and Structures (Springer Publisher, 2009)Google Scholar

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© The Author(s) 2018

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  1. 1.Bialystok University of TechnologyFaculty of Mechanical Engineering, Department of Automatics and RoboticsBialystokPoland

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