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Backstepping boundary observer based-control for hyperbolic PDE in rotary drilling system

Author

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  • Mlayeh, Rhouma
  • Toumi, Samir
  • Beji, Lotfi

Abstract

It is well known that torsional vibrations in oil well system affect the drilling directions and may be inherent for drilling systems. The drill pipe model is described by second order hyperbolic Partial Differential Equation (PDE) with mixed boundary conditions in which a sliding velocity is considered at the top end. In this paper, we consider the problem of boundary observer design for one-dimensional PDE with the usually neglected damping term. The main purpose is the construction of a control law which stabilizes the damped wave PDE, using only boundary measurements. From the Lyapunov theory, we show an exponentially vibration stability of the partially equipped oil well drilling system. The observer-based control law is found using the backstepping approach for second-order hyperbolic PDE. The numerical simulations confirm the effectiveness of the proposed PDE observer based controller.

Suggested Citation

  • Mlayeh, Rhouma & Toumi, Samir & Beji, Lotfi, 2018. "Backstepping boundary observer based-control for hyperbolic PDE in rotary drilling system," Applied Mathematics and Computation, Elsevier, vol. 322(C), pages 66-78.
    • Handle: RePEc:eee:apmaco:v:322:y:2018:i:c:p:66-78
    DOI: 10.1016/j.amc.2017.11.034
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    Cited by:

    1. Mathiyalagan, K. & Nidhi, A. Shree & Su, H. & Renugadevi, T., 2022. "Observer and boundary output feedback control for coupled ODE-transport PDE," Applied Mathematics and Computation, Elsevier, vol. 426(C).
    2. Song, Xiaona & Zhang, Renzhi & Song, Shuai & Zhang, Yijun, 2022. "Fuzzy adaptive-event-triggered control for semi-linear parabolic PDE systems with stochastic actuator failures," Applied Mathematics and Computation, Elsevier, vol. 426(C).

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