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Paper details
Number 2 - June 2016
Volume 26 - 2016
The control of drilling vibrations: A coupled PDE-ODE modeling approach
Belem Saldivar, Sabine Mondié, Juan Carlos Ávila Vilchis
Abstract
The main purpose of this contribution is the control of both torsional and axial vibrations occurring along a rotary oilwell
drilling system. The model considered consists of a wave equation coupled to an ordinary differential equation (ODE)
through a nonlinear function describing the rock–bit interaction. We propose a systematic method to design feedback
controllers guaranteeing ultimate boundedness of the system trajectories and leading consequently to the suppression of
harmful dynamics. The proposal of a Lyapunov–Krasovskii functional provides stability conditions stated in terms of the
solution of a set of linear and bilinear matrix inequalities (LMIs, BMIs). Numerical simulations illustrate the efficiency of
the obtained control laws.
Keywords
drilling vibrations, LMI approach, ultimate boundedness, coupled wave-ODE system