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.
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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).
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.
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).
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.
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.
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).
Hughes, P.C., Modal identities for elastic bodies with application to vehicle dynamics and control. Journal of Applied Mechanics, 1980, 47: 177–184.
Skelton, R.E. and Yousuff, A., Component cost analysis of large scale systems. International Journal of Control, 1983, 37(2): 285–304.
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.
Moore, B.C., Principal component analysis in linear system: controllability, observability and model reduction. IEEE Transaction on Automatic Control, 1981, 26(1): 17–31.
Gregory, C.Z., Reduction of large flexible model using internal balancing theory. Journal of Guidance, 1984, 7(6): 725–732.
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.
Jonchherre, E.A., Principal component analysis of flexible system open-loop case. IEEE Transaction on Automatic Control, 1984, 29(12): 1059–1097.
Gawronski, W. and Willams, T., Model reduction for flexible space structures. Journal of Guidance, 1991, 14(1): 68–76.
Willams, T., Closed-form grammians and model reduction for flexible space structures. IEEE Transaction on Automatic Control, 1990, 35(3): 379–382.
Zhou, K., Salomon G. and Wu, E., Balanced realization and model reduction for unstable system. International Journal Robust Nonlinear Control, 1999, 9: 183–198.
Laub, A.J., Computation of balancing transformations. In: Proceedings of the Joint Automatic Control Conference, FA8-E, 1980.
Bartels, R.H. and Stewart, G.W., Solution of the matrix equation AX+XB=C. Communications of the ACM, 1972, 15(9): 820–826.
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).
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Project supported by the Key Project (No. 11132001) and the General Projects (Nos. 11072146 and 11002087) of the National Natural Science Foundation of China.
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Xie, Y., Zhao, T. & Cai, G. Model Reduction and Active Control for a Flexible Plate. Acta Mech. Solida Sin. 24, 467–476 (2011). https://doi.org/10.1016/S0894-9166(11)60046-3
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DOI: https://doi.org/10.1016/S0894-9166(11)60046-3