Abstract

Active and passive control techniques have been devised over the years to mitigate the effect of vibrations on drill-string life with varying degrees of success. Here, it is proposed to design a robust trajectory tracking controller, which ultimately forces the rotary table and the drill-bit to move with the same speed (speed synchronization), hence reducing/eliminating torsional vibrations from the drill pipes. A model of the rotary drilling system, which includes torsional stick-slip, is first developed; then, an integral sliding mode control with time-varying exponent (ISMC-TVE) scheme is developed such that the bit motion tracks that of the rotary table to mitigate the effects of the induced vibrations. The ISMC-TVE is able to control the transient stage of the drill-string system’s response, maintain the system in the sliding state even under abrupt or existing external disturbances, and guarantee asymptotic stability of the rotary drilling system. The Lyapunov stability theorem is used here to analyze the performance of the closed-loop system, and the simulation results showed that the ISMC-TVE law is capable of accurately synchronizing the bit and rotary table speeds.

References

References
1.
Nygaard
,
G.
, and
Nævdal
,
G.
,
2006
, “
Nonlinear Model Predictive Control Scheme for Stabilizing Annulus Pressure During Oil Well Drilling
,”
J. Process Control
,
16
(
7
), pp.
719
732
. 10.1016/j.jprocont.2006.01.002
2.
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
, pp.
386
391
.
3.
Ritto
,
T. G.
, and
Ghandchi-Tehrani
,
M.
,
2019
, “
Active Control of Stick-Slip Torsional Vibrations in Drill-Strings
,”
J. Vib. Control
,
25
(
1
), pp.
194
202
. 10.1177/1077546318774240
4.
Vaziri
,
V.
,
Kapitaniak
,
M.
, and
Wiercigroch
,
M.
,
2018
, “
Suppression of Drill-String Stick? Slip Vibration by Sliding Mode Control: Numerical and Experimental Studies
,”
Eur. J. Appl. Math.
,
29
(
5
), pp.
805
825
. 10.1017/S0956792518000232
5.
Zhang
,
X.
,
Sun
,
L.
,
Zhao
,
K.
, and
Sun
,
L.
,
2013
, “
Nonlinear Speed Control for PMSM System Using Sliding-Mode Control and Disturbance Compensation Techniques
,”
IEEE Trans. Power Electron.
,
28
(
3
), pp.
1358
1365
. 10.1109/TPEL.2012.2206610
6.
Wadoo
,
S. A.
,
2013
, “
Sliding Mode Control of Crowd Dynamics
,”
IEEE Trans. Control Syst. Technol.
,
21
(
3
), pp.
1008
1015
. 10.1109/TCST.2012.2196700
7.
Kurode
,
S.
,
Spurgeon
,
S. K.
,
Bandyopadhyay
,
B.
, and
Gandhi
,
P. S.
,
2013
, “
Sliding Mode Control for Slosh-Free Motion Using a Nonlinear Sliding Surface
,”
IEEE/ASME Trans. Mechatronics
,
18
(
2
), pp.
714
724
. 10.1109/TMECH.2011.2182056
8.
Zhang
,
B. L.
,
Han
,
Q.-L.
,
Zhang
,
X. M.
, and
Yu
,
X.
,
2014
, “
Sliding Mode Control With Mixed Current and Delayed States for Offshore Steel Jacket Platforms
,”
IEEE Trans. Control Syst. Technol.
,
22
(
5
), pp.
1769
1783
. 10.1109/TCST.2013.2293401
9.
Zhang
,
Q. Z.
,
He
,
Y. Y
,
Li
,
L.
, Nurzat
,
2010
, “
Sliding Mode Control of Rotary Drilling System With Stick Slip Oscillation
,”
Proceedings of Intelligent Systems and Applications (ISA)
,
Wuhan, China
,
May 22–23
, pp.
1
4
.
10.
Pupadubsin
,
R.
,
Chayopitak
,
N.
,
Taylor
,
D. G.
,
Nulek
,
N.
,
Kachapornkul
,
S.
,
Jitkreeyarn
,
P.
,
Somsiri
,
P.
, and
Tungpimolrut
,
K.
,
2012
, “
Adaptive Integral Sliding-Mode Position Control of a Coupled-Phase Linear Variable Reluctance Motor for High-Precision Applications
,”
IEEE Trans. Ind. Appl.
,
48
(
4
), pp.
1353
1363
. 10.1109/TIA.2012.2199455
11.
Xi
,
Z.
,
Feng
,
G.
, and
Hesketh
,
T.
,
2011
, “
Piecewise Integral Sliding-Mode Control for T-S Fuzzy Systems
,”
IEEE Trans. Fuzzy Syst.
,
19
(
1
), pp.
65
74
. 10.1109/TFUZZ.2010.2082553
12.
Navarro-Lopez
,
E. M.
, and
Cortes
,
D.
,
2011
, “
Sliding-Mode Control of a Multi-DOF Oilwell Drill-String With Stick-Slip Oscillations
,”
American Control Conference (ACC)
,
New York
,
July 9–13
, pp.
3837
3842
.
13.
Yigit
,
A. S.
, and
Christoforou
,
A. P.
,
2006
, “
Stick-Slip and Bit-Bounce Interaction in Oil-Well Drill-Stringss
,”
ASME J. Energy Resour. Technol.
,
128
(
4
), pp.
268
274
. 10.1115/1.2358141
14.
Zou
,
A. M.
,
Kumar
,
K. D.
,
Hou
,
Z. G.
, and
Liu
,
X.
,
2011
, “
Finite-Time Attitude Tracking Control for Spacecraft Using Terminal Sliding Mode and Chebyshev Neural Network
,”
IEEE Trans. Syst., Man, Cybern. B, Cybern.
,
41
(
4
), pp.
950
963
. 10.1109/TSMCB.2010.2101592
15.
Li
,
S.
,
Zhou
,
M.
, and
Xinghuo
,
Y.
,
2013
, “
Design and Implementation of Terminal Sliding Mode Control Method for PMSM Speed Regulation System
,”
IEEE Trans. Ind. Informat.
,
9
(
4
), pp.
1879
1891
. 10.1109/TII.2012.2226896
16.
Yu
,
W. S.
, and
Weng
,
C. C.
,
2014
, “
Neural-Based Adaptive Integral Sliding Mode Tracking Control for Nonlinear Interconnected Systems
,”
Proceedings of the 2014 International Joint Conference on Neural Networks (IJCNN)
,
Beijing, China
,
July 6–11
, pp.
1314
1351
.
17.
Sastry
,
S. S.
, and
Bodson
,
M.
,
1989
,
Adaptive Control: Stability, Convergence, and Robustness
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
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