Active vibration suppression of non-linear beams using optimal dynamic inversion

Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering

Volumn 223, Issue 5, 2009, Pages 657-672

  Ali, Sk F ^a   Padhi, R ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

Dynamic inversion; Euler Bernoulli beams; Non linear beams; Non linear structural control; Optimal dynamic inversion

Indexed keywords

DYNAMIC INVERSION; EULER-BERNOULLI BEAMS; NON-LINEAR BEAMS; NON-LINEAR STRUCTURAL CONTROL; OPTIMAL DYNAMIC INVERSION;

AIRCRAFT ENGINES; COMPUTER SIMULATION; CONTROL THEORY; EQUATIONS OF MOTION; NONLINEAR CONTROL SYSTEMS; OPTIMIZATION; PARTIAL DIFFERENTIAL EQUATIONS; STATE FEEDBACK; STRUCTURAL DYNAMICS; SYSTEMS ENGINEERING; VIBRATION CONTROL; VIBRATION MEASUREMENT;

CONTROLLERS;

EID: 70349254121     PISSN: 09596518     EISSN: None     Source Type: Journal    
DOI: 10.1243/09596518JSCE688     Document Type: Article

References (26)

1. Nayfeh, A. H. and Pai, P. F. Linear and nonlinear structural mechanics, 2004 (Wiley, Berlin).
2. Kar, I. N., Seto, K., and Doi, F. Multimode vibration control of a flexible structure using H' based robust control. IEEE/ASME Trans. Mecha-tron., 2000, 5(1), 23-31. (Pubitemid 30584001)
3. Yang, J. B., Jiang, L. J., and Chen, D. C. H. Dynamic modeling and control of a rotating Euler-Bernoulli beam. J. Sound Vib., 2004, 274(3-5), 863-875.
4. Jalili, N. An infinite dimensional distributed base controller for regulation of flexible robot arms. Trans. ASME, J. Dyn. Syst., Meas. Control, 2001, 123, 712-718.
5. Lasiecka, I. Control of systems governed by partial differential equations: a historical perspective. In Proceedings of the 34th IEEE Conference on Decision and control, New Orleans, LA, 1995, pp. 2792-2796 (IEEE, Piscataway, NJ).
6. Padhi, R. and Faruque, Ali Sk. An account of chronological developments in control of distributed parameter systems. Ann. Rev. Control (in press). DOI: 10.1016/j.arcontrol.2009.01.003.
7. Burns, J. and King, B. B. Optimal sensor location for robust control of distributed parameter systems. In Proceedings of the 33rd IEEE Conference on Decision and control, 1994, pp. 3967-3972 (IEEE, Florida, USA).
8. Carlos Mazzilli, E. N., Soares, M. E. S., and Baracho Neto, O. G. P. Non-linear normal modes of a simply supported beam: continuous system and finite-element models. Comput. Struct, 2004, 82 , 2683-2691.
9. Fung, R. F., Wu, J. W., and Lu, P. Y. Adaptive boundary control of an axially moving string system. Trans. ASME, J. Vib. Acoust., 2002, 124, 435-440.
10. Wu, Z. and Yildizoglu, S. E. Distributed parameter-dependent modeling and control of flexible structures. Trans. ASME, J. Dyn. Syst. Meas. Control, 2005, 127, 230-239.
11. Gunzburger, M. D., Peterson, J. S., and Shadid, J. N. Reduced order modeling of time dependent PDEs with multiple parameters in the boundary data. Comput. Methods Appl. Mech. Engng, 2007, 196(4-6), 1030-1047.
12. Holmes, P., Lumley, J. L., and Berkooz, G. Turbulence, coherent structures, dynamical systems and symmetry, 1996 (Cambridge University Press, Cambridge, UK).
13. Yang, B. Transfer function of constrained/combined one dimensional continuous dynamic systems. J. Sound Vib., 1992, 156(3), 425-443.
14. Yang, B. and Mote, C. D. Active vibration control of axially moving string in S domain. J. Appl. Mech., 1991, 58(1), 189-196.
15. Tadi, M. Nonlinear feedback control of slewing beams. Comput. Methods Appl. Mech. Engng, 2006, 195(1-3), 133-147.
16. Canbolat, H., Dawson, D., Rahn, C., and Veda-garbha, P. Boundary control of a cantilevered flexible beam with point-mass dynamics at the free end. Mechatronics, 1998, 8, 163-186.
17. Pang, S. T., Sao, T. C., and Bergman, L. A. Active and passive damping of Euler-Bernoulli beam and their interaction. Trans. ASME, J. Dyn. Syst., Meas. Control, 1993, 115, 379-384.
18. Curtain, R. F. and Zwart, H. J. An introduction to infinite dimensional linear systems theory, 1995 (Springer-Verlag, New York, NY).
19. Bameih, B. The structure of optimal controllers of spatially-invariant distributed parameter systems. In Proceedings of the IEEE Conference on Decision and control, 1997, pp. 1056-1061 (IEEE, San Diego, California, USA).
20. Sun, D. and Mills, J. K. Control of a rotating cantilever beam using a torque actuator and a distributed piezoelectric polymer actuator. Appl. Acoustics, 2002, 63, 885-899.
21. Bourquin, F., Branchet, B., and Collet, M. Computational methods for the fast boundary stabilization of flexible structures. Part 1: the case of beams. Comput. Methods Appl. Mech. Engng, 2007, 196(4-6), 988-1005.
22. Padhi, R. and Balakrishnan, S. N. An optimal dynamic inversion approach for controlling a class of one-dimensional nonlinear distributed parameter systems. In Proceedings of the American Control Conference, 2006, pp. 57-62 (IEE, Minnesota, USA).
23. Slotine, J. E. and Li, W. Applied nonlinear control, 1991 (Prentice Hall, New Jersey).
24. Khalil, H. K. Nonlinear systems, 1996 (Prentice Hall, New Jersey).
25. Bryson, A. E. and Ho, Y. C. Applied optimal control, 1975 (Taylor and Francis, London).
26. Crandall, S. H. Optimum recurrence formulas for a fourth order parabolic partial differential equation. J. Assoc. Comput. Mach., 1957, 4(4), 467-471.