LMI-based control of stick-slip oscillations in drilling
A control system for controlling stick-slip oscillations in a drilling system is disclosed. The control system includes a processor and a memory communicatively coupled to the processor with computer program instructions stored therein. The instructions are configured to, when executed by the processor, cause the processor to receive a communication including a value of a drilling system parameter, determine based on the value of the drilling system parameter, a value for a torque to be applied to a drill string to reduce the effect of stick-slip oscillations, and transmit to a drive system the value for the torque to be applied by the drive system. The value for the torque to be applied by the drive system is determined by solving a set of linear matrix inequalities including a disturbance minimization linear matrix inequality, a first magnitude constraint linear matrix inequality, and a second magnitude constraint linear matrix inequality.
1. A control system for controlling stick-slip oscillations in a drilling system, comprising:
a processor; and
a memory communicatively coupled to the processor with computer program instructions stored therein, the instructions configured to, when executed by the processor, cause the processor to:
receive a communication including a value of a drilling system parameter;
determine, based on the value of the drilling system parameter, a value for a torque to be applied to a drill string to reduce the effect of stick-slip oscillations, wherein the value for the torque is determined by solving a set of linear matrix inequalities including a disturbance minimization linear matrix inequality, a first magnitude constraint linear matrix inequality, and a second magnitude constraint linear matrix inequality; and
transmit to a drive system the value for the torque to be applied to the drill string by the drive system; wherein the disturbance minimization linear matrix inequality comprises:
[
A
i
Q
+
Q
T
A
i
T
+
B
i
Y
+
Y
T
B
i
T
+
E
i
E
i
T
Q
T
C
T
CQ
-
η
2
I
]
≤
0
∀
i
=
1
,
…
,
p
.
2. The system of claim 1 , wherein the drilling system parameter includes at least one of angular position of a drive system of the drilling system, the rotational speed of the drive system, angular position of the drill string, rotational speed of the drill string, angular position of a drill bit of the drilling system, or rotational speed of the drill bit.
3. The system of claim 1 , wherein the drilling system receives the communication including the value of the drilling system parameter from a drive system of the drilling system, sensors associated with the drill string, or sensors associated with a drill bit of the drilling system.
4. The system of claim 1 , wherein the computer program instructions are configured to, when executed by the processor, cause the processor to solve the set of linear matrix inequalities using interior point methods.
5. A control system for controlling stick-slip oscillations in a drilling system, comprising:
a processor; and
a memory communicatively coupled to the processor with computer program instructions stored therein, the instructions configured to, when executed by the processor, cause the processor to:
receive a communication including a value of a drilling system parameter;
determine, based on the value of the drilling system parameter, a value for a torque to be applied to a drill string to reduce the effect of stick-slip oscillations, wherein the value for the torque is determined by solving a set of linear matrix inequalities including a disturbance minimization linear matrix inequality, a first magnitude constraint linear matrix inequality, and a second magnitude constraint linear matrix inequality; and
transmit to a drive system the value for the torque to be applied to the drill string by the drive system; wherein the first magnitude constraint linear matrix inequality comprises:
[
1
e
(
0
)
T
e
(
0
)
Q
]
≥
0.
6. The system of claim 5 , wherein the drilling system parameter includes at least one of angular position of a drive system of the drilling system, the rotational speed of the drive system, angular position of the drill string, rotational speed of the drill string, angular position of a drill bit of the drilling system, or rotational speed of the drill bit.
7. The system of claim 5 , wherein the drilling system receives the communication including the value of the drilling system parameter from a drive system of the drilling system, sensors associated with the drill string, or sensors associated with a drill bit of the drilling system.
8. The system of claim 5 , wherein the computer program instructions are configured to, when executed by the processor, cause the processor to solve the set of linear matrix inequalities using interior point methods.
9. A control system for controlling stick-slip oscillations in a drilling system, comprising:
a processor; and
a memory communicatively coupled to the processor with computer program instructions stored therein, the instructions configured to, when executed by the processor, cause the processor to:
receive a communication including a value of a drilling system parameter;
determine, based on the value of the drilling system parameter, a value for a torque to be applied to a drill string to reduce the effect of stick-slip oscillations, wherein the value for the torque is determined by solving a set of linear matrix inequalities including a disturbance minimization linear matrix inequality, a first magnitude constraint linear matrix inequality, and a second magnitude constraint linear matrix inequality; and
transmit to a drive system the value for the torque to be applied to the drill string by the drive system; wherein the second magnitude constraint linear matrix inequality comprises:
[
Q
Y
T
Y
μ
2
I
]
≥
0.
10. The system of claim 9 , wherein the drilling system parameter includes at least one of angular position of a drive system of the drilling system, the rotational speed of the drive system, angular position of the drill string, rotational speed of the drill string, angular position of a drill bit of the drilling system, or rotational speed of the drill bit.
11. The system of claim 9 , wherein the drilling system receives the communication including the value of the drilling system parameter from a drive system of the drilling system, sensors associated with the drill string, or sensors associated with a drill bit of the drilling system.
12. The system of claim 9 , wherein the computer program instructions are configured to, when executed by the processor, cause the processor to solve the set of linear matrix inequalities using interior point methods.