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Technical Brief

Observer-Based Boundary Control Design for the Suppression of Stick–Slip Oscillations in Drilling Systems With Only Surface Measurements

[+] Author and Article Information
Halil Ibrahim Basturk

Department of Mechanical Engineering,
Bogazici University,
Istanbul 34342, Turkey
e-mail: halil.basturk@boun.edu.tr

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received February 3, 2016; final manuscript received March 17, 2017; published online June 28, 2017. Assoc. Editor: Mazen Farhood.

J. Dyn. Sys., Meas., Control 139(10), 104501 (Jun 28, 2017) (7 pages) Paper No: DS-16-1074; doi: 10.1115/1.4036549 History: Received February 03, 2016; Revised March 17, 2017

We develop an observer-based boundary controller for the rotary table to suppress stick–slip oscillations and to maintain the angular velocity of the drill string at a desired value during a drilling process despite unknown friction torque and by using only surface measurements. The control design is based on a distributed model of the drill string. The obtained infinite dimensional model is converted to an ordinary differential equation–partial differential equation (ODE–PDE) coupled system. The observer-based controller is designed by reformulating the problem as the stabilization of an linear time-invariant (LTI) system which is affected by a constant unknown disturbance and has simultaneous actuator and sensor delays. The main contribution of the controller is that it requires only surface measurements. We prove that the equilibrium of the closed-loop system is exponentially stable, and that the angular velocity regulation is achieved with the estimations of unknown friction torque and drill bit velocity. The effectiveness of the controller is demonstrated using numerical simulations.

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References

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Figures

Grahic Jump Location
Fig. 1

The illustration of a drilling system and a string [15]

Grahic Jump Location
Fig. 2

The angular velocities of the drill bit and the rotary table are given when the stick–slip oscillation occurs in the system. The angular velocity of the rotary table (dashed) is almost constant, whereas the velocity of the drill bit (solid) oscillates in a wide range [6].

Grahic Jump Location
Fig. 3

The plot of normalized friction torque (top) and its derivative with respect to angular velocity are given (bottom). The value of torque changes dramatically around ω = 0, but its value is almost constant for higher magnitudes. A reasonable penetration is obtained for ω>5, and usually ω = 10 is chosen for an optimal drilling process. As it is shown by the marker, the change of friction torque is approximately zero at around ω=10 (i.e., (dT(ω)/dω)|ω=10≈0).

Grahic Jump Location
Fig. 4

Simulation results of angular velocities of the drill pipe. The controllers are turned on at around t=17 s: (a) The system responses for the proposed controller and the one given in Ref. [17]. Until the controller is activated, the drill bit is oscillating in a wide range due to the stick–slip phenomena. When the controllers are turned on at around t=17 s, from top to bottom, the drill string starts rotating at the desired value, 10 rad/s. The performances of the controllers are almost the same. (b) The angular velocities of drill bit, i.e., the bottom (solid) and its estimate (dashed), which is obtained by the proposed observer are given. The estimation is almost perfect when the system gets closer to the linearization point of friction torque and the error becomes zero once the controller is activated.

Grahic Jump Location
Fig. 5

The angular velocities of the rotary table for both the proposed controller (solid) and the one given in Ref. [17] (dashed) are given

Grahic Jump Location
Fig. 6

The estimations of unknown parameter d and its actual value are given. Both controllers achieve to estimate the real value of d when the controllers are activated.

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