Skip to main content

Systematic Formulation of Model Uncertainties and Robust Control in Smart Structures Using H and μ-Analysis

  • Chapter
  • 2556 Accesses

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 26))

Abstract

The influence of structural uncertainties on actively controlled smart beams is investigated in this paper. The dynamical problem of a model smart composite beam is based on a simplified modelling of the actuators and sensors, both being realized by means of piezoelectric layers. In particular, a practical robust controller design methodology is developed, which is based on recent theoretical results on H control theory and μ-analysis. Numerical examples demonstrate the vibration-suppression property of the proposed smart beams.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Arvanitis, K.G., Zacharenakis, E.C., Soldatos, A.G., Stavroulakis, G.E.: New trends in optimal structural control. In: Selected Topics in Structronic and Mechatronic System, pp. 321–415. World Scientific, Singapore (2003)

    Chapter  Google Scholar 

  2. Bosgra, O., Kwakernaak, H.: Design methods for control systems. Course notes, Dutch Institute for Systems and Control, p. 69 (2001)

    Google Scholar 

  3. Burke, J.V., Henrion, D., Lewis, A.S., Overton, M.L.: HIFOO—a MATLAB package for fixed-order controller design and H optimization. In: Proceedings of the IFAC Symposium on Robust Control Design, Toulouse, France (2006). www.cs.nyu.edu/overton/software/hifoo

    Google Scholar 

  4. Burke, J.V., Henrion, D., Lewis, A.S., Overton, M.L.: Stabilization via nonsmooth, nonconvex optimization. IEEE Trans. Autom. Control 5(11), 1760–1769 (2006)

    Article  MathSciNet  Google Scholar 

  5. Foutsitzi, G., Marinova, D., Hadjigeorgiou, E., Stavroulakis, G.: Finite element modelling of optimally controlled smart beams. In: Venkov, G., Marinov, M. (eds.) 28th Summer School: Applications of Mathematics in Engineering and Economics, Sozopol, Bulgaria (2002)

    Google Scholar 

  6. Foutsitzi, G., Marinova, D., Hadjigeorgiou, E., Stavroulakis, G.: Robust H2 vibration control of beams with piezoelectric sensors and actuators. In: Proceedings of Physics and Control Conference (PhyCon03), St. Petersburg, Russia, 20–22 August, vol. I, pp. 158–163 (2003)

    Google Scholar 

  7. Hou, M., Muller, P.C.: Design of observers for linear systems with unknown inputs. IEEE Trans. Autom. Control 37, 871–875 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  8. Huang, W.S., Park, H.C.: Finite element modelling of piezoelectric sensors and actuators. AIAA J. 31, 930–937 (1993)

    Article  Google Scholar 

  9. Marinova, D., Stavroulakis, G.E., Foutsitzi, D., Hadjigeorgiou, E., Zacharenakis, E.C.: Robust design of smart structures taking into account structural defects. In: Indeitsev, D.A. (ed.) Summer School Conference Advanced Problems in Mechanics, Russian Academy of Sciences, pp. 288–292 (2004)

    Google Scholar 

  10. Miara, B., Stavroulakis, G., Valente, V. (eds.): Topics on Mathematics for Smart Systems: Proceedings of the European Conference, Rome, Italy, 26–28 October 2006. World Scientific, Singapore (2007)

    MATH  Google Scholar 

  11. Moutsopoulou, A., Stavroulakis, G., Pouliezos, A.: Model uncertainties in smart structures. In: Papadrakakis, M., Fragiadakis, M., Plevris, V. (eds.) 3rd Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Corfu, Greece (2011)

    Google Scholar 

  12. Packard, A., Doyle, J., Balas, G.: Linear, multivariable robust control with a perspective. J. Dyn. Syst. Meas. Control 115(2b), 310–319 (1993)

    Google Scholar 

  13. Pouliezos, A.: MIMO control systems. Class notes (2008). http://pouliezos.dpem.tuc.gr

  14. Shahian, B., Hassul, M.: Control System Design Using MATLAB. Prentice Hall, New York (1994)

    Google Scholar 

  15. Sisemore, C., Smaili, A., Houghton, R.: Passive damping of flexible mechanism system: experimental and finite element investigation. In: The 10th World Congress of the Theory of Machines and Mechanisms, Oulu, Finland, vol. 5, pp. 2140–2145 (1999)

    Google Scholar 

  16. Stavroulakis, G.E., Foutsitzi, G., Hadjigeorgiou, E., Marinova, D., Baniotopoulos, C.C.: Design and robust optimal control of smart beams with application on vibrations suppression. Adv. Eng. Softw. 36(11–12), 806–813 (2005)

    Article  Google Scholar 

  17. Tiersten, H.F.: Linear Piezoelectric Plate Vibrations. Plenum Press, New York (1969)

    Google Scholar 

  18. Tits, A.L., Yang, Y.: Globally convergent algorithms for robust pole assignment by state feedback. IEEE Trans. Autom. Control 41, 1432–1452 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  19. Ward, R.C.: Balancing the generalized eigenvalue problem. SIAM J. Sci. Stat. Comput. 2, 141–152 (1981)

    Article  MATH  Google Scholar 

  20. Young, P., Newlin, M., Doyle, J.: Practical computation of the mixed problem. In: Proceedings of the American Control Conference, pp. 2190–2194 (1992)

    Google Scholar 

  21. Zhang, N., Kirpitchenko, I.: Modelling dynamics of a continuous structure with a piezoelectric sensor/actuator for passive structural control. J. Sound Vib. 249, 251–261 (2002)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Amalia Moutsopoulou .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Moutsopoulou, A., Stavroulakis, G.E., Pouliezos, A. (2013). Systematic Formulation of Model Uncertainties and Robust Control in Smart Structures Using H and μ-Analysis. In: Papadrakakis, M., Stefanou, G., Papadopoulos, V. (eds) Computational Methods in Stochastic Dynamics. Computational Methods in Applied Sciences, vol 26. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5134-7_11

Download citation

  • DOI: https://doi.org/10.1007/978-94-007-5134-7_11

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-5133-0

  • Online ISBN: 978-94-007-5134-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics