Suppressing stick‐slip oscillations in underactuated multibody drill‐strings with parametric uncertainties using sliding‐mode control

Abstract

This paper is a postprint of a paper submitted to and accepted for publication in IET Control Theory and Applications and is subject to Institution of Engineering and Technology Copyright. AbstractStabilization of multibody drill-strings which exhibit stick-slip oscillations is studied in this paper from the point of view of underactuated system. The model has one control torque input acting on the rotary table from the land surface and multi-degree-of-freedom downhole parts to be controlled. Three motion regimes of the model including bit sticking, stick-slip oscillation, and rotating at a constant speed are identified and their equilibria are analyzed accordingly. The control objective of the system is to avoid the undesired bit sticking and stick-slip oscillation while tracking a desired angular velocity. Three slidingmode controllers are studied for the drill-string with estimated physical parameters. The stabilities of the proposed controllers are proved by using the Lyapunov direct method ensuring that any trajectory of the system can reach and stays thereafter on the predesigned sliding surface where the desired equilibrium is asymptotically stable. Extensive simulation results are given to demonstrate the effectiveness of the proposed controllers and their robustness to parametric uncertainties.

Numerical and experimental studies of stick–slip oscillations in drill-strings

“…2, in such a way to achieve a sound agreement between theoretical and experimental observations. This will allow a series of experimental and numerical tests of different control mechanisms to suppress stick-slip oscillations, based on previous theoretical investigations (see, e.g., [3]). …”

“…The generalized lumped-parameter model can be written in a single-input and multi-output form as follows Fig. 2 Schematics of a drill-string and b simplified drill-string system as considered in [3] (a) (b)…”

Proportional-Derivative Control of Stick-Slip Oscillations in Drill-Strings

“…The drilling system, which is illustrated in Fig.1 Making use of the dynamic theory, the government equation of motion for the discrete system [8] can be written as…”

Suppression of Drill-String Stick-Slip Vibration

“…This class of models has been widely employed in studies focusing in drill-string torsional vibration. The number of disks varies in those studies, for example 2 disks [8], 3 disks [9], 4 disks [10] and even 18 disks [11]. In the current work a 2-disk model has been employed (see Fig.2(b)) to model the CADR experimental drilling rig, following the work presented in [8].…”