Abstract

This paper proposed an equivalent input disturbance (EID)-based approach to control the vertical down-hole drilling process. To describe a drill string which is typically long with large axial-to-radius ratio, a neutral-type model is used to accurately capture dynamics of this type of slender string structure. The axial-torsional coupling effect due to drill bit/rock interaction is also included in the model. A new controller is then designed based on the coupled neutral model, and the coupling effect is specifically addressed in the design. To address the uncertainty of the bit/rock interaction, the EID method is used. A new Lyapunov–Krasovskii functional is proposed for the control design. To this end, a series of numerical simulation results are presented to demonstrate the effectiveness of the proposed control scheme.

References

References
1.
Serrarens
,
A.
,
1997
, “
H-Infinite Control as Applied to Torsional Drillstring Dynamics
,” M.S. thesis, Eindhoven University of Technology, Eindhoven, The Netherlands.
2.
Navarro-López
,
E. M.
, and
Licéaga-Castro
,
E.
,
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
.10.1016/j.chaos.2008.08.008
3.
Abdulgalil
,
F.
, and
Siguerdidjane
,
H.
,
2005
, “
Backstepping Design for Controlling Rotary Drilling System
,”
IEEE Conference on Control Applications (CCA)
, Toronto, ON, Canada, Aug. 28, pp.
120
124
.
4.
Fubin
,
S.
,
Linxiu
,
S.
,
Lin
,
L.
, and
Qizhi
,
Z.
,
2010
, “
Adaptive PID Control of Rotary Drilling System With Stick Slip Oscillation
,”
Second International Conference on Signal Processing Systems (ICSPS),
Dalian, China, July 5, pp. V2-289-V2292.
5.
Karkoub
,
M.
,
Abdel-Magid
,
Y.
, and
Balachandran
,
B.
,
2009
, “
Drill-String Torsional Vibration Suppression Using GA Optimized Controllers
,”
J. Can. Pet. Technol.
,
48
(
12
), pp.
32
38
.10.2118/132161-PA
6.
Feng
,
T.
,
Zhang
,
H.
, and
Chen
,
D.
,
2017
, “
Dynamic Programming Based Controllers to Suppress Stick-Slip in a Drilling System
,”
American Control Conference (ACC),
Seattle, WA, May 24, pp.
1302
1307
.
7.
Tucker
,
R. W.
, and
Wang
,
C.
,
2003
, “
Torsional Vibration Control and Cosserat Dynamics of a Drill-Rig Assembly
,”
Meccanica
,
38
(
1
), pp.
145
161
.10.1023/A:1022035821763
8.
Navarro-López
,
E. M.
, and
Cortés
,
D.
,
2007
, “
Sliding-Mode Control of a Multi-DOF Oilwell Drillstring With Stick-Slip Oscillations
,”
American Control Conference (ACC'07)
, New York, July 9, pp.
3837
3842
.
9.
Nandakumar
,
K.
, and
Wiercigroch
,
M.
,
2013
, “
Stability Analysis of a State Dependent Delayed, Coupled Two DOF Model of Drill-String Vibration
,”
J. Sound Vib.
,
332
(
10
), pp.
2575
2592
.10.1016/j.jsv.2012.12.020
10.
Liu
,
X.
,
Vlajic
,
N.
,
Long
,
X.
,
Meng
,
G.
, and
Balachandran
,
B.
,
2014
, “
Coupled Axial-Torsional Dynamics in Rotary Drilling With State-Dependent Delay: Stability and Control
,”
Nonlinear Dyn.
,
78
(
3
), pp.
1891
1906
.10.1007/s11071-014-1567-y
11.
Gupta
,
S. K.
, and
Wahi
,
P.
,
2016
, “
Global Axial-Torsional Dynamics During Rotary Drilling
,”
J. Sound Vib.
,
375
, pp.
332
352
.10.1016/j.jsv.2016.04.021
12.
Ke
,
C.
, and
Song
,
X.
,
2018
, “
Control of Down-Hole Drilling Process Using a Computationally Efficient Dynamic Programming Method
,”
ASME J. Dyn. Syst. Meas. Control
,
140
(
10
), p.
101010
.10.1115/1.4039787
13.
Saldivar
,
B.
,
Mondié
,
S.
,
Loiseau
,
J.-J.
, and
Rasvan
,
V.
,
2011
, “
Stick-Slip Oscillations in Oilwell Drillstrings: Distributed Parameter and Neutral Type Retarded Model Approaches
,”
IFAC Proc. Vol.
,
44
(
1
), pp.
284
289
.10.3182/20110828-6-IT-1002.00084
14.
Boussaada
,
I.
,
Cela
,
A.
,
Mounier
,
H.
, and
Niculescu
,
S.-I.
,
2013
, “
Control of Drilling Vibrations: A Time-Delay System-Based Approach
,”
IFAC Proc. Vol.
,
46
(
3
), pp.
226
231
.10.3182/20130204-3-FR-4031.00162
15.
Saldivar
,
B.
,
Knüppel
,
T.
,
Woittennek
,
F.
,
Boussaada
,
I.
,
Mounier
,
H.
, and
Niculescu
,
S.-I.
,
2014
, “
Flatness-Based Control of Torsional-Axial Coupled Drilling Vibrations
,”
IFAC Proc. Vol.
,
47
(
3
), pp.
7324
7329
.10.3182/20140824-6-ZA-1003.02205
16.
Saldivar
,
B.
,
Mondié
,
S.
,
Loiseau
,
J.-J.
, and
Rasvan
,
V.
,
2011
, “
Exponential Stability Analysis of the Drilling System Described by a Switched Neutral Type Delay Equation With Nonlinear Perturbations
,”
50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC),
Orlando, FL, Dec. 12, pp.
4164
4169
.
17.
Detournay
,
E.
,
Richard
,
T.
, and
Shepherd
,
M.
,
2008
, “
Drilling Response of Drag Bits: Theory and Experiment
,”
Int. J. Rock Mech. Min. Sci.
,
45
(
8
), pp.
1347
1360
.10.1016/j.ijrmms.2008.01.010
18.
She
,
J.-H.
,
Fang
,
M.
,
Ohyama
,
Y.
,
Hashimoto
,
H.
, and
Wu
,
M.
,
2008
, “
Improving Disturbance-Rejection Performance Based on an Equivalent-Input-Disturbance Approach
,”
IEEE Trans. Ind. Electron.
,
55
(
1
), pp.
380
389
.10.1109/TIE.2007.905976
19.
She
,
J.-H.
,
Xin
,
X.
, and
Pan
,
Y.
,
2011
, “
Equivalent-Input-Disturbance Approach Analysis and Application to Disturbance Rejection in Dual-Stage Feed Drive Control System
,”
IEEE/ASME Trans. Mechatronics
,
16
(
2
), pp.
330
340
.10.1109/TMECH.2010.2043258
20.
Ke
,
C.
, and
Song
,
X.
,
2017
, “
Computationally Efficient Down-Hole Drilling System Dynamics Modeling Integrating Finite Element and Transfer Matrix
,”
ASME J. Dyn. Syst. Meas. Control
,
139
(
12
), p.
121003
.10.1115/1.4037165
21.
Germay
,
C.
,
Denoël
,
V.
, and
Detournay
,
E.
,
2009
, “
Multiple Mode Analysis of the Self-Excited Vibrations of Rotary Drilling Systems
,”
J. Sound Vib.
,
325
(
1–2
), pp.
362
381
.10.1016/j.jsv.2009.03.017
22.
Di Meglio
,
F.
, and
Aarsnes
,
U. J. F.
,
2015
, “
A Distributed Parameter Systems View of Control Problems in Drilling
,”
IFAC-PapersOnLine
,
48
(
6
), pp.
272
278
.10.1016/j.ifacol.2015.08.043
23.
Edelman
,
K.
, and
Gendelman
,
O.
,
2013
, “
Dynamics of Self-Excited Oscillators With Neutral Delay Coupling
,”
Nonlinear Dyn.
,
72
(
3
), pp.
683
694
.10.1007/s11071-012-0745-z
24.
Hale
,
J. K.
, and
Lunel
,
S. M. V.
,
2013
,
Introduction to Functional Differential Equations
, Vol.
99
,
Springer Science & Business Media
,
New York
.
25.
Zhou
,
B.
, and
Liu
,
Q.
,
2017
, “
Input Delay Compensation for Neutral Type Time-Delay Systems
,”
Automatica
,
78
, pp.
309
319
.10.1016/j.automatica.2016.12.015
26.
Cheng
,
J.
,
Wu
,
M.
,
Lu
,
C.
,
Chen
,
L.
,
Chen
,
X.
,
Cao
,
W.
, and
Lai
,
X.
,
2017
, “
A Stick-Slip Vibration Suppression Method for the Drillstring System Based on Neutral Type Model
,”
11th Asian Control Conference (ASCC),
Gold Coast, Australia, Dec. 17, pp.
2837
2842
.
27.
Boyd
,
S.
,
El Ghaoui
,
L.
,
Feron
,
E.
, and
Balakrishnan
,
V.
,
1994
,
Linear Matrix Inequalities in System and Control Theory
,
SIAM
,
Philadelphia, PA
.
28.
Ho
,
D. W.
, and
Lu
,
G.
,
2003
, “
Robust Stabilization for a Class of Discrete-Time Non-Linear Systems Via Output Feedback: The Unified LMI Approach
,”
Int. J. Control
,
76
(
2
), pp.
105
115
.10.1080/0020717031000067367
You do not currently have access to this content.