Structural Engineering and Mechanics

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Modal-based model reduction and vibration control for uncertain piezoelectric flexible structures

  • Yalan, Xu (School of Electronic & Mechanical Engineering, Xidian University) ;
  • Jianjun, Chen (School of Electronic & Mechanical Engineering, Xidian University)
  • Received : 2006.10.16
  • Accepted : 2008.03.31
  • Published : 2008.07.30
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Abstract

In piezoelectric flexible structures, the contribution of vibration modes to the dynamic response of system may change with the location of piezoelectric actuator patches, which means that the ability of actuators to control vibration modes should be taken into account in the development of modal reduction model. The spatial $H_2$ norm of modes, which serves as a measure of the intensity of modes to system dynamical response, is used to pick up the modes included in the reduction model. Based on the reduction model, the paper develops the state-space representation for uncertain flexible tructures with piezoelectric material as non-collocated actuators/sensors in the modal space, taking into account uncertainties due to modal parameters variation and unmodeled residual modes. In order to suppress the vibration of the structure, a dynamic output feedback control law is designed by imultaneously considering the conflicting performance specifications, such as robust stability, transient response requirement, disturbance rejection, actuator saturation constraints. Based on linear matrix inequality, the vibration control design is converted into a linear convex optimization problem. The simulation results show how the influence of vibration modes on the dynamical response of structure varies with the location of piezoelectric actuators, why the uncertainties should be considered in the reductiom model to avoid exciting high-frequency modes in the non-collcated vibration control, and the possiblity that the conflicting performance specifications are dealt with simultaneously.

Keywords

References

  1. Bala, G.L. (1995), 'Control design for variation in structural natural frequencies', J. Guid., Control Dynam., 18(2), 325-332 https://doi.org/10.2514/3.21387
  2. Balas, M.J. (1978), 'Feedback control of flexible systems', IEEE T. Automat. Contr., 23(4), 673-679 https://doi.org/10.1109/TAC.1978.1101798
  3. Cao, W.W. and Cudney, H.H. (1999), 'Smart materials and structures', Proceeding of National Academic Science, USA
  4. Carten, Scherer and Pascal, Gahinet (1989), 'Multiobjective output-feedback control via LMI optimization', IEEE T. Automat. Contr., 42(7), 896-910 https://doi.org/10.1109/9.599969
  5. Chen, H. and Guo, K.H. (2005), 'Constrained $H_{\infty}$ control of active suspensions: an LMI approach', IEEE T. Contr. Syst. T., 13(3), 412-421 https://doi.org/10.1109/TCST.2004.841661
  6. Lu, C.Y., Tsai, J.S.H., Jong, G.J. and Su, T.J. (2003), 'An LMI-based approach for robust stabilization of uncertain stochastic systems with time-varying delays', IEEE T. Automat. Contr., 48(2), 286-289 https://doi.org/10.1109/TAC.2002.808482
  7. Clark, R.L., Saunders, W.R. and Gibbs, G.P. (1998), Adaptive Structures: Dynamics and Control, John Wiley, New York
  8. Fuller, C.R., Elliott, S.J. and Nelson, P.A. (1996), Active Control of Vibration, Academic Press, London
  9. Fuller, C.R., Maillard, J.P. and Mercadal, M. (2002), 'Active-passive piezoelectric absorbers for systems under multi non-stationary harmonic excitions', J. Sound Vib., 255, 685-700 https://doi.org/10.1006/jsvi.2001.4184
  10. Gao, W. and Chen, J.J. (2003), 'Optimal placement of active bars in active vibration control for piezoelectric intelligent truss structures with random parameters', Comput. Struct., 81(1), 53-60 https://doi.org/10.1016/S0045-7949(02)00331-0
  11. Gawronski, W. (1996), Balanced Control of Flexible Structures, Springer, Berlin
  12. Ha, S.K., Keilers, C. and Chang, F.K. (1992), 'Finite element analysis of composite structures containing distributed piezoceramic sensors and actuators', AIAA J., 30(3), 772-780 https://doi.org/10.2514/3.10984
  13. Hu, Qinglei and Ma, Guangfu (2004), 'Active vibration control of a flexible plate structure using LMI-based $H_{\infty}$ output feedback control law', Proceedings of the 5th World Congress on Intelligent Control and Automation, Hangzhou, June
  14. Jiang, L., Tang, J. and Wang, K.W. (2006), 'An enhanced frequency-shift based damage identification method using tunable piezoelectric transducer circuitry', J. Smart Mater. Struct., 15, 799-808 https://doi.org/10.1088/0964-1726/15/3/016
  15. Kusculuoglu, Z.K. and Fallahi, B. (2004), 'Finite element model of a beam with a piezoceramic patch actuator', J. Sound Vib., 275, 27-44 https://doi.org/10.1016/S0022-460X(03)00740-5
  16. Meirovitch, L. and Baruh, H. (1983), 'A comparison of control techniques for large flexible systems', J. Guidance, 6(4), 302-310 https://doi.org/10.2514/3.19833
  17. Moheimani, S.O.R. (2000), 'Minimizing the out-of bandwidth dynamics in the model of reverberant system that arises in the modal analysis: Implication on spatial $H_{\infty}$ control', Automatica, 36, 1023-1033 https://doi.org/10.1016/S0005-1098(00)00012-1
  18. Narayanan, S. and Balamurugan, V. (2003), 'Finite element modelling of piezolaminated smart structures for active vibration control with distributed sensors and actuators', J. Sound Vib., 262, 529-562 https://doi.org/10.1016/S0022-460X(03)00110-X
  19. Da Silva, S., Lopes Junior, V. and Brennan, M.J. (2006), 'Design of a control system using linear matrix inequalities for the active vibration control of a plate', J. Intel. Mat. Syst. Struct., 17(1), 81-93 https://doi.org/10.1177/1045389X06056341
  20. Sana, S. and Rao, V.S. (2000), 'Application of linear matrix inequalities in the control of smart structural systems', J. Intel. Mat. Syst. Struct., 11, 311-323 https://doi.org/10.1106/E2AY-BY64-H0E4-WRHQ
  21. Xu, Y.L. and Chen, J.J. (2004), 'Vibration control of piezoelectric flexible structures using multiobjective technique', Proceeding of the First Asia International Symposium on Mechatronics Theory, Method, and Application, Xi'an, May
  22. Yu, H. and Wang, K.W. (2007), 'Piezoelectric networks for vibration suppression of mistuned bladed disks', J. Vib. Acoustics, ASME, 129(5), 559-566 https://doi.org/10.1115/1.2775511
  23. Zhang, X. and Shao, C. (2001), 'Robust $H_{\infty}$ vibration control for flexible linkage mechanism systems with piezoelectric sensors and actuators', J. Sound Vib., 243(1), 145-155 https://doi.org/10.1006/jsvi.2000.3413

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