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Fuzzy control for geometrically nonlinear vibration of piezoelectric flexible plates

  • Xu, Yalan (School of Electronic & Mechanical Engineering, Xidian University) ;
  • Chen, Jianjun (School of Electronic & Mechanical Engineering, Xidian University)
  • Received : 2011.01.17
  • Accepted : 2012.05.31
  • Published : 2012.07.25

Abstract

This paper presents a LMI(linear matrix inequality)-based fuzzy approach of modeling and active vibration control of geometrically nonlinear flexible plates with piezoelectric materials as actuators and sensors. The large-amplitude vibration characteristics and dynamic partial differential equation of a piezoelectric flexible rectangular thin plate structure are obtained by using generalized Fourier series and numerical integral. Takagi-Sugeno (T-S) fuzzy model is employed to approximate the nonlinear structural system, which combines the fuzzy inference rule with the local linear state space model. A robust fuzzy dynamic output feedback control law based on the T-S fuzzy model is designed by the parallel distributed compensation (PDC) technique, and stability analysis and disturbance rejection problems are guaranteed by LMI method. The simulation result shows that the fuzzy dynamic output feedback controller based on a two-rule T-S fuzzy model performs well, and the vibration of plate structure with geometrical nonlinearity is suppressed, which is less complex in computation and can be practically implemented.

Keywords

References

  1. Assawinchaichote, W., Nguang, S.K. and Shi, C.P. (2008), "$H_{\infty}$ fuzzy state-feedback control design for nonlinear systems with D-stability constraints: An LMI approach", Math. Comput. Simulat., 78, 514-531. https://doi.org/10.1016/j.matcom.2007.07.002
  2. Belouettar, S. and Azrar, L. (2008), "Active control of nonlinear vibration of sandwich piezoelectric beams: A simplified approach", Comput. Struct., 86, 386-397. https://doi.org/10.1016/j.compstruc.2007.02.009
  3. Chen, H. and Guo, H.H. (2005), "Constrained $H_{\infty}$ control of active suspensions: an LMI approach", IEEE T. Contr. Syst., 13(3), 412-421. https://doi.org/10.1109/TCST.2004.841661
  4. Chen, C.W. (2006), "Stability conditions of fuzzy systems and its application to structural and mechanical systems", Adv. Eng. Softw., 37, 624-629. https://doi.org/10.1016/j.advengsoft.2005.12.002
  5. Chia, C.Y. (1980), Nonlinear Ananlysis of Plates, McGraw-Hill.
  6. Dash, P. and Singh, B.N. (2009), "Nonlinear free vibration of piezoelectric laminated composite plate", Finite Elem. Anal. D., 45, 686-694. https://doi.org/10.1016/j.finel.2009.05.004
  7. FaruqueAli, S. and Ramaswamy, A. (2009), "Optimal fuzzy logic control for MDOF structural systems using evolutionary algorithms", Eng. Appl. Artif. Intel., 22, 407-419. https://doi.org/10.1016/j.engappai.2008.09.004
  8. Fuller, C.R., Elliot, S.J. and Nelson, P.A. (1996), Active Control of Vibration, Academic Press, London.
  9. 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
  10. Hu, Q.L. and Ma, G.F. (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.
  11. Liu, J. and Wang, W. (2010), "A novel fuzzy frame work for nonlinear system control", Fuzzy Set. Syst., 161, 2746-2759. https://doi.org/10.1016/j.fss.2010.04.009
  12. Lu, C.Y. and Tsai, S.H. (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
  13. 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
  14. 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
  15. Panda, S. and Ray, M.C. (2009), "Active control of geometrically nonlinear vibrations of functionally graded laminated composite plates using piezoelectric fiber reinforced composites", J. Sound Vib., 325, 186-205. https://doi.org/10.1016/j.jsv.2009.03.016
  16. Qiu, Z.Q. and Wu, H.X. (2009), "Acceleration sensors based modal identification and active vibration control of flexible smart cantilever plate proportional feedback control", Aeros. Sci. Tech., 13, 277-290. https://doi.org/10.1016/j.ast.2009.05.003
  17. Samuel, D.S. and Vicente, L.J. (2006), "Design of a control system using linear matrix inequalities for the active vibration control of a plate", J. Intel. Mat. Syst. Str., 17(1), 81-93. https://doi.org/10.1177/1045389X06056341
  18. Song, G. and Sethi, V. (2006), "Vibration control of civil structures using piezoceramic smart materials: A review", Eng. Struct., 28, 1513-1524. https://doi.org/10.1016/j.engstruct.2006.02.002
  19. Takagi, T. and Sugeno, M. (1985), "Fuzzy identification of systems and its application on modelling and control", IEEE T. Syst. Man. Cyb., 15(1), 116-132.
  20. Tanaka, K. and Wang, H.O. (2001), Fuzzy Control Systems Design and Analysi, John Wiley & Sons.
  21. Xu, Y.L. and Chen, J.J. (2008), " Modal-based model reduction and vibration control for uncertain piezoelectric flexible structures", Struct. Eng. Mech., 29(5), 489-504. https://doi.org/10.12989/sem.2008.29.5.489
  22. Zheng, Q.W. and Sun, Z. (2004), "Active control of vibration using a fuzzy control method", J. Sound Vib., 275, 917-930. https://doi.org/10.1016/S0022-460X(03)00795-8
  23. Zhou, Y.H. and Wang, J.Z. (2004), "Vibration control of piezoelectric beam-type plates with geometrically nonlinear deformation", Int. J. Nonlin. Mech., 39, 909-920. https://doi.org/10.1016/S0020-7462(03)00074-X

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