Acta Mechanica Solida Sinica

, Volume 24, Issue 5, pp 467–476 | Cite as

Model Reduction and Active Control for a Flexible Plate

Article

Abstract

The internal balance technique is effective for model reduction in flexible structures, especially those with dense frequencies. However, due to the difficulty in extracting the internal balance modal coordinates from the physical sensor readings, research so far on this topic has been mostly theoretic and little on experiment or engineering applications. This paper, by working on a DSP TMS320F2812-based experiment system with a flexible plate and bringing forward an approximating approach to accessing the internal balance modal coordinates, studies the internal balance method theoretically as well as experimentally, and further designs an active controller based on the reduced model. Simulation and test results have proven the proposed approximating approach feasible and effective, and the designed controller successful in restraining the plate vibration.

Key words

flexible plate internal balance model reduction active control experiment 

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References

  1. [1]
    Li, F.M., Kikuo, K., Wang, Y.S., Chen, Z.B. and Huang, W.H., Vibration control of beams with active constrained layer damping. Smart Materials and Structures, 2008, 17: 065036(9pp).CrossRefGoogle Scholar
  2. [2]
    Li, C.C., Li, F.M. and Huang, W.H., Active vibration control of finite L-shaped beam with traveling wave approach. Acta Mechanica Solida Sinica, 2010, 23(5): 377–385.CrossRefGoogle Scholar
  3. [3]
    Song, Z.G. and Li, F.M., Active aeroelastic flutter analysis and vibration control of supersonic beams using the piezoelectric actuator/sensor pairs. Smart Materials and Structures, 2011, 20: 055013(12pp).CrossRefGoogle Scholar
  4. [4]
    Qiu, Z.C., Zhang, X.M., Wu, H.X. and Zhang, H.H., Optimal placement and active vibration control for piezoelectric smart flexible cantilever plate. Journal of Sound and Vibration, 2007, 301: 521–543.MathSciNetCrossRefGoogle Scholar
  5. [5]
    Chen, L.X., Cai, G.P. and Pan, J., Experimental study of delayed feedback control for a flexible plate. Journal of Sound and Vibration, 2009, 322: 629–651.CrossRefGoogle Scholar
  6. [6]
    Miao, B.Q., Qu, G.J. and Cheng, D.S., A study on dynamics modeling of flexible spacecraft. Chinese space science and Techology, 1999, 5: 35–40 (in Chinese).Google Scholar
  7. [7]
    Hughes, P.C., Modal identities for elastic bodies with application to vehicle dynamics and control. Journal of Applied Mechanics, 1980, 47: 177–184.MathSciNetCrossRefGoogle Scholar
  8. [8]
    Skelton, R.E. and Yousuff, A., Component cost analysis of large scale systems. International Journal of Control, 1983, 37(2): 285–304.MathSciNetCrossRefGoogle Scholar
  9. [9]
    Skelton, R.E. and Gregory, C.Z., Measurement feedback and model reduction by modal cost analysis. In: Joint Automatic Control Conference, Denver, 1979: 211–218.Google Scholar
  10. [10]
    Moore, B.C., Principal component analysis in linear system: controllability, observability and model reduction. IEEE Transaction on Automatic Control, 1981, 26(1): 17–31.MathSciNetCrossRefGoogle Scholar
  11. [11]
    Gregory, C.Z., Reduction of large flexible model using internal balancing theory. Journal of Guidance, 1984, 7(6): 725–732.CrossRefGoogle Scholar
  12. [12]
    Jonckherre, E.A. and Opdencker, P.H., Singular value analysis balancing and model reduction of large space structures. In: American Control Conference, USA: San Diego, CA, 1984: 141–149.Google Scholar
  13. [13]
    Jonchherre, E.A., Principal component analysis of flexible system open-loop case. IEEE Transaction on Automatic Control, 1984, 29(12): 1059–1097.MathSciNetGoogle Scholar
  14. [14]
    Gawronski, W. and Willams, T., Model reduction for flexible space structures. Journal of Guidance, 1991, 14(1): 68–76.CrossRefGoogle Scholar
  15. [15]
    Willams, T., Closed-form grammians and model reduction for flexible space structures. IEEE Transaction on Automatic Control, 1990, 35(3): 379–382.MathSciNetCrossRefGoogle Scholar
  16. [16]
    Zhou, K., Salomon G. and Wu, E., Balanced realization and model reduction for unstable system. International Journal Robust Nonlinear Control, 1999, 9: 183–198.MathSciNetCrossRefGoogle Scholar
  17. [17]
    Laub, A.J., Computation of balancing transformations. In: Proceedings of the Joint Automatic Control Conference, FA8-E, 1980.Google Scholar
  18. [18]
    Bartels, R.H. and Stewart, G.W., Solution of the matrix equation AX+XB=C. Communications of the ACM, 1972, 15(9): 820–826.CrossRefGoogle Scholar
  19. [19]
    Han, J.Q. and Yuan, L.L., The discrete form of tracking-differentiator. Journal of systems science and mathematical sciences, 1999, 19: 268–273 (in Chinese).MathSciNetMATHGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2011

Authors and Affiliations

  1. 1.Department of Engineering Mechanics, State Key Laboratory of Ocean EngineeringShanghai Jiaotong UniversityShanghaiChina

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