Smart Structures and Systems

  • 제6권8호
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  • Pages.921-938
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  • 2010
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  • 1738-1584(pISSN)
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  • 1738-1991(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Assessment of velocity-acceleration feedback in optimal control of smart piezoelectric beams

  • Beheshti-Aval, S.B. (Department of Civil Engineering, Khajeh Nasir Toosi University of Technology (KNTU)) ;
  • Lezgy-Nazargah, M. (Department of Civil Engineering, Khajeh Nasir Toosi University of Technology (KNTU))
  • 투고 : 2009.04.21
  • 심사 : 2010.01.21
  • 발행 : 2010.11.25
⟨ 이전 논문 다음 논문 ⟩

초록

Most of studies on control of beams containing piezoelectric sensors and actuators have been based on linear quadratic regulator (LQR) with state feedback or output feedback law. The aim of this study is to develop velocity-acceleration feedback law in the optimal control of smart piezoelectric beams. A new controller which is an optimal control system with velocity-acceleration feedback is presented. In finite element modeling of the beam, the variation of mechanical displacement through the thickness is modeled by a sinus model that ensures inter-laminar continuity of shear stress at the layer interfaces as well as the boundary conditions on the upper and lower surfaces of the beam. In addition to mechanical degrees of freedom, one electric potential degree of freedom is considered for each piezoelectric element layer. The efficiency of this control strategy is evaluated by applying to an aluminum cantilever beam under different loading conditions. Numerical simulations show that this new control scheme is almost as efficient as an optimal control system with state feedback. However, inclusion of the acceleration in the control algorithm increases practical value of a system due to easier and more accurate measurement of accelerations.

키워드

참고문헌

  1. Alkhatib, R. and Golnaraghi, M.F. (2003), "Active structural vibration control: a review", Shock Vib. Digest, 35(5), 367-383. https://doi.org/10.1177/05831024030355002
  2. Allik, H. and Hughes, T.J.R. (1970), "Finite element method for piezoelectric vibration", Int. J. Num. Meth. Eng., 2(2), 151-157. https://doi.org/10.1002/nme.1620020202
  3. Benjeddou, A. (2000), "Advances in piezoelectric finite element modeling of adaptive structural elements: a survey", Comput. Struct., 76, 347-363. https://doi.org/10.1016/S0045-7949(99)00151-0
  4. Benjeddou, A. (2004), Modeling and simulation of adaptive structures and composites: current trends and future directions, Progress in computational structures technology, (Eds. Topping, B.H.V. and Soares, C.A.M.), Saxe Coburg Publications.
  5. Blanguernon, A., Lene, F. and Bernadou, M. (1999), "Active control of a beam using a piezoceramic element", Smart Mater. Struct., 8(1), 116-124. https://doi.org/10.1088/0964-1726/8/1/013
  6. Bruant, I., Coffignal, G., Lené, F. and Vergé, M. (2001), "Active control of beam structures with piezoelectric actuators and sensors: modeling and simulation", Smart Mater. Struct., 10(2), 404-408. https://doi.org/10.1088/0964-1726/10/2/402
  7. Burl, J.B. (1999), Linear optimal control, Addison-Wesley, California.
  8. Chandrashekhara, K. and Smyser, C.P. (1998), "Dynamic modeling and neural control of composite shells using piezoelectric devices", J. Intel. Mat. Syst. Str., 9(1), 29-43. https://doi.org/10.1177/1045389X9800900103
  9. Crawley, E.F. and de Luis, J. (1987), "Use of piezoelectric actuators as element of intelligent structures", AIAA J., 25, 1373-1385. https://doi.org/10.2514/3.9792
  10. Fukunaga, H., Hu, N. and Ren, G.X. (2001), "FEM modeling of adaptive composite structures using a reduced higher-order plate theory via penalty functions", Int. J. Solids Struct., 38, 8735-8752. https://doi.org/10.1016/S0020-7683(01)00072-5
  11. Heyliger, P., Ramirez, G. and Saravanos, D. (1994), "Coupled discrete-layer finite elements for laminated piezoelectric plates", Commun. Numer. Meth. En., 10(12), 971-981. https://doi.org/10.1002/cnm.1640101203
  12. Irschik, H. (2002), "A review on static and dynamic shape control of structures by piezoelectric actuation", Eng. Struct., 24, 5-11. https://doi.org/10.1016/S0141-0296(01)00081-5
  13. Kwakernaak, H. and Sivan, R. (1972), Linear optimal control systems, New York, John Whiley and Sons.
  14. Lage, R.G., Soares, C.M.M., Soares, C.A.M. and Reddy, J.N. (2004a), "Analysis of laminated adaptive plate structures by mixed layerwise finite element models", Compos. Struct., 66, 269-276. https://doi.org/10.1016/j.compstruct.2004.04.048
  15. Lage, R.G., Soares, C.M.M., Soares, C.A.M. and Reddy, J.N. (2004b), "Modeling of piezolaminated plates using layerwise mixed finite element models", Comput. Struct., 82(23-26), 1849-1863. https://doi.org/10.1016/j.compstruc.2004.03.068
  16. Lim, Y.H., Varadan, V.V. and Varadan, V.K. (1997), "Closed loop finite element modeling of active structural damping in the frequency domain", Smart Mater. Struct., 6(2), 161-168. https://doi.org/10.1088/0964-1726/6/2/005
  17. Moita, J.M.S., Correia, I.F.P., Soares, C.M.M. and Soares, C.A.M. (2004), "Active control of adaptive laminated structures with bonded piezoelectric sensors and actuators", Comput. Struct., 82(17-19), 1349-1358. https://doi.org/10.1016/j.compstruc.2004.03.030
  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. Oshima, K., Takigami, T. and Hayakawa, Y. (1997), "Robust vibration control of a cantilever beam using selfsensing actuator", JSME Int. J. C-Mech. Sy., 40, 681-687. https://doi.org/10.1299/jsmec.40.681
  20. Petyt, M. (1990), Introduction to finite element vibration analysis, Cambridge University Press, Cambridge.
  21. Qiu, J. and Tani, J. (1995), "Vibration control of a cylindrical shell using distributed piezoelectric sensors and actuators", J. Intel. Mat. Syst. Str., 6(4), 474-481. https://doi.org/10.1177/1045389X9500600404
  22. Saravanos, D.A., Heyliger, P.R. and Hopkins, D.A. (1997), "Layerwise mechanics and finite element model for the dynamic analysis of piezoelectric composite plates", Int. J. Solids Struct., 34(3), 359-378. https://doi.org/10.1016/S0020-7683(96)00012-1
  23. Sunar, M. and Rao, S.S. (1999), "Recent advances in sensing and control of flexible structures via piezoelectric material technology", Appl. Mech. Rev., 52, 1-16. https://doi.org/10.1115/1.3098923
  24. Sung, C.K., Chen, T.F. and Chen, S.G. (1996), "Piezoelectric modal sensor actuator design for monitoring generating flexural and torsional vibrations of cylindrical shells", J. Vib. Acoust., 118, 48-55. https://doi.org/10.1115/1.2889634
  25. Tzou, H.S. and Gadre, M. (1989), "Theoretical-analysis of a multi-layered thin shell coupled with piezoelectric shell actuators for distributed vibration controls", J. Sound Vib., 132, 433-450. https://doi.org/10.1016/0022-460X(89)90637-8
  26. Vasques, C.M.A. and Rodrigues, J.D. (2006), "Active vibration control of smart piezoelectric beams: Comparison of classical and optimal feedback control strategies", Comput. Struct., 84(22-23), 1402-1414. https://doi.org/10.1016/j.compstruc.2006.01.026
  27. Veley, D.E. and Rao, S.S. (1996), "A comparison of active, passive and hybrid damping in structural design", Smart Mater. Struct., 5(5), 660-671. https://doi.org/10.1088/0964-1726/5/5/014
  28. Vidal, P. and Polit, O. (2008), "A family of sinus finite elements for the analysis of rectangular laminated beams", Compos. Struct., 84, 56-72. https://doi.org/10.1016/j.compstruct.2007.06.009
  29. Wang, B.T. and Rogers, C.A. (1991), "Laminate plate-theory for spatially distributed induced strain actuators", J. Compos. Mater., 25, 433-452. https://doi.org/10.1177/002199839102500405
  30. Xu, K.M., Noor, A.K. and Tang, Y.Y. (1995), "3-dimensional solutions for coupled thermoelectroelastic response of multilayered plates", Comput. Method. Appl. M., 126(3-4), 355-371. https://doi.org/10.1016/0045-7825(95)00825-L

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