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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Christoforou, A. , and Yigit, A. S. , 2003, “ Fully Coupled Vibrations of Actively Controlled Drillstrings,” J. Sound Vib., 267(5), pp. 1029–1045. [CrossRef]
Dunayevsky, V. A., and Abbasian, F., 1998, “ Application of Stability Approach to Bit Dynamics,” SPE Drill. Completion, 13(2), pp. 99–107. [CrossRef]
Belokobylskii, S. V. , and Prokopv, V. K. , 1982, “ Friction-Induced Self-Excited Vibrations of Drill Rig With Exponential Drag Law,” Sov. Appl. Mech., 18(12), pp. 1134–1138. [CrossRef]
Azar, J. J. , and Samuel, G. R. , 2007, Drilling Engineering, Penn Well Corporation, Tulsa, OK.
Kyllingstad, A. , and Halsey, G. W. , 1988, “ A Study of Slip/Stick Motion of the Bit,” SPE Drill. Eng., 3–4(4), pp. 369–373. [CrossRef]
Jansen, J. D. , and van den Steen, L. , 1995, “ Active Damping of Self-Excited Torsional Vibrations in Oil Well Drillstrings,” J. Sound Vib., 179(4), p. 647. [CrossRef]
Christoforou, A. P. , and Yigit, A. S. , 2000, “ Coupled Torsional and Bending Vibrations of Actively Controlled Drilstrings,” J. Sound Vib., 234(1), pp. 67–83. [CrossRef]
Serrarens, A. F. A. , van de Molengraft, M. J. G. , Kok, J. J. , and van den Steen, L. , 1998, “ H Control for Suppressing Stick-Slip in Oil Well Drillstrings,” IEEE Control Syst., 18(2), pp. 19–30. [CrossRef]
Navarro-Lopez, E. M. , and Cortes, D. , 2009, “ Non-Desired Transitions and Sliding-Mode Control of a Multi-DOF Mechanical System With Stick-Slip Oscillations,” Chaos, Solitons Fractals, 41(4), pp. 2035–2044. [CrossRef]
Jijon, R. B. , Canudas-de-Wit, C. , Niculescu, S. , and Dumon, J. , 2010, “ Adaptive Observer Design Under Low Data Rate Transmission With Applications to Oil Well Drill-String,” American Control Conference (ACC), Baltimore, MD, June 30–July 2, pp. 1973–1978.
Canudas-de-Wit, C. , Rubio, F. R. , and Corchero, M. A. , 2008, “ D-OSKIL: A New Mechanism for Controlling Stick-Slip in Oil Well Drillstrings,” IEEE Trans. Control Syst. Technol., 16(6), pp. 1177–1191. [CrossRef]
Balanov, A. G. , Janson, N. B. , McClintock, P. V. E. , Tucker, R. W. , and Wang, C. H. T. , 2003, “ Bifurcation Analysis of a Neutral Delay Differential Equation Modelling the Torsional Motion of a Driven Drill-String,” Chaos, Solutions Fractals, 15(2), pp. 381–394. [CrossRef]
Saldivar, M. B. , Mondie, S. , and Loiseau, J. J. , 2009, “ Reducing Stick-Slip Oscillations in Oilwell Drillstrings,” 6th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE), Toluca, Mexico, Jan. 10–13.
Saldivar, M. B. , Mondie, S. , Loiseau, J. J. , and Rasvan, V. , 2013, “ Suppressing Axial Torsional Coupled Vibrations in Oilwell Drillstrings,” J. Control Eng. Appl. Inf., 15(1), pp. 3–10.
Sagert, C. , Di Meglio, F. , Krstic, M. , and Rouchon, P. , 2013, “ Backstepping and Flatness Approaches for Stabilization of the Stick-Slip Phenomenon for Drilling,” IFAC Symposium on System, Structure and Control, Grenoble, France, Feb. 4–6 https://doi.org/10.3182/20130204-3-FR-2033.00126.
Bekiaris-Liberis, N. , and Krstic, M. , 2014, “ Compensation of Wave Actuator Dynamics for Nonlinear Systems,” IEEE Trans. Autom. Control, 59(6), pp. 1555–1570. [CrossRef]
Bresch-Pietri, D. , and Krstic, M. , 2014, “ Adaptive Output Feedback for Oil Drilling Stick-Slip Instability Modeled by Wave PDE With Anti-Damped Dynamic Boundary,” American Control Conference (ACC), Portland, OR, June 4–6.
Qizhi, Z. , Yu yao, H. , Li, L. , and Nurzat, R. , 2010, “ Sliding Mode Control of Rotary Drilling System With Stick Slip Oscillation,” 2nd International Workshop on Intelligent Systems and Applications (ISA), Wuhan, China, May 22–23, pp. 1–4.
Krstic, M. , and Smyshlyaev, A. , 2008, Boundary Control of PDEs: A Course on Backstepping Designs, SIAM, Philadelphia, PA.
Roman, C. , Bresch-Pietri, D. , Prieur, C. , and Sename, O. , 2015, “ Robustness of an Adaptive Output Feedback for an Anti-Damped Boundary Wave PDE in Presence of In-Domain Viscous Damping,” American Control Conference (ACC), Boston, MA, July 6–8, pp. 3455–3460.
Krstic, M. , 2012, Delay Compensation for Nonlinear, Adaptive and PDE Systems, Birkhauser, Basel, Switzerland.
Krstic, M. , and Smyshlyaev, A. , 2008, “ Backstepping Boundary Control for First-Order Hyperbolic PDEs and Application to Systems With Actuator and Sensor Delays,” Syst. Control Lett., 57(9), pp. 750–758. [CrossRef]
Liszka, T. , and Orkisz, J. , 1980, “ The Finite Difference Method at Arbitrary Irregular Grids and Its Application in Applied Mechanics,” Comput. Struct., 11(1–2), pp. 83–95. [CrossRef]
Ritto, T. G. , Soize, C. , and Sampaio, R. , 2009, “ Non-Linear Dynamics of a Drill-String With Uncertain Model of the Bit-Rock Interaction,” Int. J. Non-Linear Mech., 44(8), pp. 865–876. [CrossRef]
Bresch-Pietri, D. , and Krstic, M. , 2014, “ Output-Feedback Adaptive Control of a Wave PDE With Boundary Anti-Damping,” Automatica, 50(5), pp. 1407–1415. [CrossRef]
Krstic, M. , Kanellakopoulos, I. , and Kokotovic, P. , 1995, Nonlinear and Adaptive Control Design, Wiley, Hoboken, NJ.
Ioannou, P. , and Sun, J. , 1996, Robust Adaptive Control, Prentice-Hall, Upper Saddle River, NJ.


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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