Directional drilling attitude hold controller
A drilling tool in accordance to one or more aspects includes a processor and a steering device. The processor determines a demand attitude and an instantaneous drilling tool attitude, evaluates a control law to derive a control law tool face, and converts the control law tool face to an equivalent tool face. The steering device applies the equivalent tool face to control a drill attitude of the drilling tool.
1. A wellbore drilling tool, comprising:
a controller to convert attitude reference data into a vector unit in vector space representing a drill attitude, to institute a control law to stabilize the drill attitude and to drive the drill attitude to a set point, to perform a coordinate transformation to implement an attitude hold controller, the coordinate transformation comprising evaluating one of a gravity and a magnetic tool face that is equivalent to a zero relative tool face, wherein an angular direction of an arbitrary globally referenced vector is projected onto a plane at right angles to a tool face; and
a steering device operationally connected to the controller in use to implement the attitude hold controller to control an instantaneous attitude of the drilling tool.
2. The wellbore drilling tool of claim 1 , wherein the attitude reference data comprises an inclination and an azimuth angle set point.
3. The wellbore drilling tool of claim 1 , wherein the control law is a time varying response of the drilling tool represented as:
{dot over (x)}=ω×x
where x is a unit vector representing the drill attitude and ω is an angular velocity vector parameter.
4. The wellbore drilling tool of claim 1 , wherein the control law is
ω= kx×x d
where ω is an angular velocity vector parameter, k is a variable build-rate of the drill attitude, x is a unit vector representing the drill attitude, and x d is a demand attitude.
5. The wellbore drilling tool of claim 1 , wherein the control law is
ω
=
{
K
x
×
x
d
x
×
x
d
for
x
≠
x
d
0
for
x
=
x
d
1
where ω is an angular velocity vector parameter, K is constant build-rate of the drill attitude, x is a unit vector representing the drill attitude, and x d is a demand attitude.
6. The wellbore drilling tool of claim 1 , wherein the control law is
ω
~
(
i
)
=
{
x
(
i
)
×
x
d
x
(
i
)
×
x
d
for
x
(
i
)
≠
x
d
w
~
(
i
-
1
)
f
for
x
(
i
)
=
x
d
,
i
≠
0
ω
~
l
for
x
(
i
)
=
-
x
d
or
x
d
and
i
=
0
where {tilde over (ω)} is an actuation velocity vector, x is a unit vector representing the drill attitude, and x d is a demand attitude.
7. The wellbore drilling tool of claim 1 , wherein the controller is one of a roll stabilized control unit and a strap down control unit.
8. The wellbore drilling tool of claim 7 , wherein the control law is one selected from the group of:
(a) a time varying response of the drilling tool represented as:
{dot over (x)}=ω×x
where x is a unit vector representing the drill attitude and ω is an angular velocity vector parameter;
(b)
ω= kx×x d
where ω is an angular velocity vector parameter, k is a variable build-rate of the drill attitude, x is a unit vector representing the drill attitude, and x d is a demand attitude;
(
c
)
ω
=
{
K
x
×
x
d
x
×
x
d
for
x
≠
x
d
0
for
x
=
x
d
1
where ω is an angular velocity vector parameter, K is constant build-rate of the drill attitude, x is a unit vector representing the drill attitude, and x d is a demand attitude; and
(
d
)
ω
~
(
i
)
=
{
x
(
i
)
×
x
d
x
(
i
)
×
x
d
for
x
(
i
)
≠
x
d
w
~
(
i
-
1
)
f
for
x
(
i
)
=
x
d
,
i
≠
0
ω
~
l
for
x
(
i
)
=
-
x
d
or
x
d
and
i
=
0
where {tilde over (ω)} is an actuation velocity vector, x is a unit vector representing the drill attitude, and x d is a demand attitude.
9. A drilling tool, comprising a control unit to apply an equivalent tool face with the drilling tool to control a drill attitude, wherein the equivalent tool face is derived by the control unit evaluating a control law,
wherein the control law is one selected from the group of:
(a) a time varying of the drilling tool represented as:
{dot over (x)}=ω×x
where x is a unit vector representing the drill attitude and ω is an angular velocity vector parameter;
(b)
ω= kx×x d
where ω is an angular velocity vector parameter, k is a variable build-rate of the drill attitude, x is a unit vector representing the drill attitude, and x d is the demand attitude;
(
c
)
ω
=
{
K
x
×
x
d
x
×
x
d
for
x
≠
x
d
0
for
x
=
x
d
1
where ω is an angular velocity vector parameter, K is constant build-rate of the drill attitude, x is a unit vector representing the drill attitude, and x d is the demand attitude; and
(
d
)
ω
~
(
i
)
=
{
x
(
i
)
×
x
d
x
(
i
)
×
x
d
for
x
(
i
)
≠
x
d
w
~
(
i
-
1
)
f
for
x
(
i
)
=
x
d
,
i
≠
0
ω
~
l
for
x
(
i
)
=
-
x
d
or
x
d
and
i
=
0
where {tilde over (ω)} is an actuation velocity vector, x is a unit vector representing the drill attitude, and x d is the demand attitude.
10. The drilling tool of claim 9 , wherein the equivalent tool face is one of an equivalent gravity tool face and an equivalent magnetic tool face.
11. The drilling tool of claim 9 , wherein the control unit is one of a roll stabilized control unit and a strap down control unit.
12. The drilling tool of claim 9 , wherein the equivalent tool face is one of an equivalent gravity tool face and an equivalent magnetic tool face; and
the control unit is one of a roll stabilized control unit and a strap down control unit.
13. A drilling tool, comprising:
a processor to determine a demand attitude, determine an instantaneous drilling tool attitude, evaluate a control law using the instantaneous drilling tool attitude and the drilling tool demand attitude to derive a control law tool face, and to convert the control law tool face to an equivalent tool face; and
a steering device to apply the equivalent tool face to control a drill attitude of the drilling tool,
wherein the control law is one selected from the group of:
(a) a time varying of the drilling tool represented as:
{dot over (x)}=ω×x
where x is a unit vector representing the drill attitude and ω is an angular velocity vector parameter;
(b)
ω= kx×x d
where ω is an angular velocity vector parameter, k is a variable build-rate of the drill attitude, x is a unit vector representing the drill attitude, and x d is the demand attitude;
(
c
)
ω
=
{
K
x
×
x
d
x
×
x
d
for
x
≠
x
d
0
for
x
=
x
d
1
where ω is an angular velocity vector parameter, K is a variable build-rate of the drill attitude, x is a unit vector representing the drill attitude, and x d is the demand attitude; and
(
d
)
ω
~
(
i
)
=
{
x
(
i
)
×
x
d
x
(
i
)
×
x
d
for
x
(
i
)
≠
x
d
w
~
(
i
-
1
)
f
for
x
(
i
)
=
x
d
,
i
≠
0
ω
~
l
for
x
(
i
)
=
-
x
d
or
x
d
and
i
=
0
where {tilde over (ω)} is the actuation velocity vector, x is a unit vector representing the drill attitude, and x d is the demand attitude.
14. The drilling tool of claim 13 , wherein the control law is
ω
~
(
i
)
=
{
x
(
i
)
×
x
d
x
(
i
)
×
x
d
for
x
(
i
)
≠
x
d
w
~
(
i
-
1
)
f
for
x
(
i
)
=
x
d
,
i
≠
0
ω
~
l
for
x
(
i
)
=
-
x
d
or
x
d
and
i
=
0
where {tilde over (ω)} is an actuation velocity vector, x is a unit vector representing the drilling tool attitude, and x d is the demand attitude.
15. The drilling tool of claim 13 , wherein the instantaneous drilling tool attitude is one of a zone of exclusion and drilling vertically.
16. The drilling tool of claim 13 , wherein the equivalent tool face is one of an equivalent gravity tool face and an equivalent magnetic tool face.
17. The drilling tool of claim 13 , wherein the demand attitude is determined from a demand inclination and a demand azimuth with respect to a global coordinate system.
18. The drilling tool of claim 13 , wherein the demand attitude is determined from a demand inclination and a demand azimuth with respect to a global coordinate system; and
the instantaneous drilling tool attitude is one of a zone of exclusion and drilling vertically.