Your browser does not support JavaScript!
http://iet.metastore.ingenta.com
1887

access icon free Adaptive boundary control for a class of inhomogeneous Timoshenko beam equations with constraints

In this study, integral-Barrier Lyapunov function (IBLF)-based boundary controls are proposed for a class of inhomogeneous Timoshenko beam equations with boundary output constraints. An IBLF which depends explicitly on time, is employed to prevent the constraint violation. The adaption laws are designed to compensate for the system uncertainties. By using the proposed adaptive IBLF-based boundary control, the vibration of the Timoshenko beam system is suppressed greatly, without any discretisation or simplification of the dynamics in the time and space. The proposed adaptive IBLF-based boundary controls also guarantee that boundary outputs always remain in the constrained space, subject to significantly relaxed feasibility conditions. In the end, numerical simulations are displayed to illustrate the performance of the proposed control.

References

    1. 1)
      • 30. Rahn, C.: ‘Mechatronic control of distributed noise and vibration’ (Springer, New York, USA, 2001).
    2. 2)
    3. 3)
    4. 4)
      • 23. Krstic, M., Siranosian, A., Smyshlyaev, A.: ‘Backstepping boundary controllers and observers for the Slender Timoshenko beam: part I – design’. 2006 American Control Conf., 2006, pp. 24122417.
    5. 5)
    6. 6)
    7. 7)
    8. 8)
      • 24. Krstic, M., Siranosian, A., Smyshlyaev, A., Bement, M.: ‘Backstepping Boundary Controllers and Observers for the Slender Timoshenko Beam: Part II – Stability and Simulations’. 45th IEEE Conf. on Decision and Control, 2006, pp. 39383943.
    9. 9)
    10. 10)
    11. 11)
    12. 12)
      • 31. Hardy, G.H., Littlewood, J.E., Polya, G.: ‘Inequalities’ (Cambridge University Press, Cambridge, UK, 1959).
    13. 13)
    14. 14)
    15. 15)
    16. 16)
    17. 17)
    18. 18)
    19. 19)
    20. 20)
    21. 21)
    22. 22)
      • 19. Luo, B., Wu, H.-N.: ‘Approximate optimal control design for nonlinear one-dimensional parabolic pde systems using empirical eigenfunctions and neural network’, IEEE Trans. Syst. Man Cybern. B, Cybern., 2011, 42, (6), pp. 15381549.
    23. 23)
    24. 24)
    25. 25)
    26. 26)
    27. 27)
      • 20. Li, H.-X., Qi, C.: ‘Spatio-temporal modeling of nonlinear distributed parameter systems: a time/space separation based approach’ (Springer Verlag, 2011), vol. 50.
    28. 28)
    29. 29)
    30. 30)
      • 36. Ioannou, P., Sun, J.: ‘Robust adaptive control’ (Prentice-Hall, Eaglewood Cliffs, New Jersey, 1996).
    31. 31)
    32. 32)
    33. 33)
      • 35. He, W., Ge, S.S., How, B.V.E., Choo, Y.S.: ‘Dynamics and control of mechanical systems in offshore engineering’ (Springer, London, UK, 2013).
    34. 34)
    35. 35)
    36. 36)
      • 12. Queiroz, M.S., Dawson, D.M., Nagarkatti, S.P., Zhang, F.: ‘Lyapunov based control of mechanical systems’ (Birkhauser, Boston, USA, 2000).
    37. 37)
      • 13. He, W., Ge, S.S.: ‘Robust adaptive boundary control of a vibrating string under unknown time-varying disturbance’, IEEE Trans. Control Syst. Technol., 2012, 20, (1), pp. 4858.
    38. 38)
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2013.0601
Loading

Related content

content/journals/10.1049/iet-cta.2013.0601
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address