text: Model Reduction and Active Control for a Flexible Plate | Springer for Research & Development
  October 2011 , Volume 24, Issue 5, pp 467–476 | Cite as
  Model Reduction and Active Control for a Flexible Plate
  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.
  flexible plate internal balance model reduction active control experiment
  Project supported by the Key Project (No. 11132001) and the General Projects (Nos. 11072146 and 11002087) of the National Natural Science Foundation of China.
  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
  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
  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
  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
  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
  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
  Skelton, R.E. and Yousuff, A., Component cost analysis of large scale systems. International Journal of Control, 1983, 37(2): 285–304.MathSciNetCrossRefGoogle Scholar
  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
  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
  Gregory, C.Z., Reduction of large flexible model using internal balancing theory. Journal of Guidance, 1984, 7(6): 725–732.CrossRefGoogle Scholar
  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
  Jonchherre, E.A., Principal component analysis of flexible system open-loop case. IEEE Transaction on Automatic Control, 1984, 29(12): 1059–1097.MathSciNetGoogle Scholar
  Gawronski, W. and Willams, T., Model reduction for flexible space structures. Journal of Guidance, 1991, 14(1): 68–76.CrossRefGoogle Scholar
  Willams, T., Closed-form grammians and model reduction for flexible space structures. IEEE Transaction on Automatic Control, 1990, 35(3): 379–382.MathSciNetCrossRefGoogle Scholar
  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
  Laub, A.J., Computation of balancing transformations. In: Proceedings of the Joint Automatic Control Conference, FA8-E, 1980.Google Scholar
  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
  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).MathSciNetzbMATHGoogle Scholar
  Xie, Y., Zhao, T. & Cai, G. Acta Mech. Solida Sin. (2011) 24: 467. https://doi.org/10.1016/S0894-9166(11)60046-3