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Practical Stability Analysis of a Drilling Pipe under Friction with a PI-Controller

Matthieu Barreau 1 Frédéric Gouaisbaut 1 Alexandre Seuret 1 
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : This paper deals with the stability analysis of a drilling pipe controlled by a PI controller. The model is a coupled ODE / PDE and is consequently of infinite dimension. Using recent advances in time-delay systems, we derive a new Lyapunov functional based on a state extension made up of projections of the Riemann coordinates. First, we will provide an exponential stability result expressed using the LMI framework. This result is dedicated to a linear version of the torsional dynamic. On a second hand, the influence of the nonlinear friction force, which may generate the well-known stick-slip phenomenon, is analyzed through a new stability theorem. Numerical simulations show the effectiveness of the method and that the stick-slip oscillations cannot be weaken using a PI controller.
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https://hal.laas.fr/hal-02099459
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Submitted on : Monday, September 23, 2019 - 10:33:31 AM
Last modification on : Monday, July 4, 2022 - 9:05:00 AM

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Matthieu Barreau, Frédéric Gouaisbaut, Alexandre Seuret. Practical Stability Analysis of a Drilling Pipe under Friction with a PI-Controller. IEEE Transactions on Control Systems Technology, Institute of Electrical and Electronics Engineers, 2019, ⟨10.1109/TCST.2019.2943458⟩. ⟨hal-02099459v2⟩

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