Disk drive compensating for radial phase change of repeatable position error due to servo writing from spiral tracks
View Patent ↗A disk drive is disclosed comprising a head actuated over a disk comprising a plurality of servo sectors defining a plurality of tracks, wherein the servo sectors are written to the disk by servoing off of spiral tracks. The head is positioned over a target track in response to the servo sectors, and coefficients of a first sinusoid are generated corresponding to the target track, wherein the first sinusoid corresponds a repeatable position error of the head relative to the target track. The coefficients of the first sinusoid comprise a coherent component due to a repeatable runout of the disk and a spiral component due to writing the servo sectors by servoing off of the spiral tracks, where the spiral component varies based on a radial location of the head. The head is servoed over the target track in response to the coefficients.
1. A disk drive comprising:
a disk comprising a plurality of servo sectors defining a plurality of tracks, wherein the servo sectors are written to the disk by servoing off of spiral tracks;
a head actuated over the disk; and
control circuitry operable to:
position the head over a target track in response to the servo sectors;
generate coefficients of a first sinusoid corresponding to the target track,
wherein:
the first sinusoid corresponds a repeatable position error of the head relative to the target track;
the coefficients of the first sinusoid comprise a coherent component due to a repeatable runout of the disk and a spiral component due to writing the servo sectors by servoing off of the spiral tracks; and
the spiral component varies based on a radial location of the head; and
servo the head over the target track in response to the coefficients.
2. The disk drive as recited in claim 1 , wherein the first sinusoid comprises:
a·cos(2πω j k/N)+b·sin(2πω j k/N)
where:
the coefficients comprise a and b;
ω j represents one of a fundamental frequency and a harmonic frequency of the repeatable position error; and
k represents one of N servo sectors written around the target track.
3. The disk drive as recited in claim 2 , wherein the coefficients comprise:
a=a coh +a sp
b=b coh +b sp
where a coh and b coh represent the coherent component and a sp and b sp represent the spiral component.
4. The disk drive as recited in claim 3 , wherein the control circuitry generates the spiral component according to:
[
a
1
sp
b
1
sp
]
=
[
-
c
1
c
2
·
cot
(
θ
/
2
)
-
c
3
·
cot
(
θ
/
2
)
-
c
4
]
[
δ
a
δ
b
]
where:
[
δ
a
δ
b
]
=
[
a
2
sp
-
a
1
sp
b
2
sp
-
b
1
sp
]
a 1 sp and b 1 sp represent the spiral component at the target track;
a 2 sp and b 2 sp represent the spiral component at a second track; and
θ represents a radial distance between the target track and the second track.
5. The disk drive as recited in claim 4 , wherein the control circuitry is further operable to:
position the head over a second track; and
generate the spiral component of the coefficients of the first sinusoid for the second track in response to a radial distance between the target track and the second track:
⌊
a
2
sp
b
2
sp
⌋
=
[
cos
(
θ
)
-
sin
(
θ
)
sin
(
θ
)
cos
(
θ
)
]
⌊
a
1
sp
b
1
sp
⌋
where:
a 1 sp and b 1 sp represent the spiral component at the target track;
a 2 sp and b 2 sp represent the spiral component at a second track; and
θ represents the radial distance between the target track and the second track.
6. The disk drive as recited in claim 1 , wherein the control circuitry is further operable to:
position the head over a second track; and
generate the coefficients of the first sinusoid for the second track in response to a radial distance between the target track and the second track.
7. The disk drive as recited in claim 1 , wherein the control circuitry is further operable to generate feedforward compensation values in response to the coefficients of the first sinusoid so that the head substantially follows the repeatable position error.
8. The disk drive as recited in claim 1 , wherein the control circuitry is further operable to generate feedback compensation values in response to the coefficients of the first sinusoid so that the head substantially ignores the repeatable position error.
9. The disk drive as recited in claim 1 , wherein the control circuitry is further operable to generate coefficients of a second sinusoid corresponding to the target track, wherein:
the first sinusoid corresponds to a fundamental frequency of the repeatable position error; and
the second sinusoid corresponds to a harmonic frequency of the repeatable position error.
10. A method of operating a disk drive, the disk drive comprising a head actuated over a disk comprising a plurality of servo sectors defining a plurality of tracks, wherein the servo sectors are written to the disk by servoing off of spiral tracks, the method comprising:
positioning the head over a target track in response to the servo sectors;
generating coefficients of a first sinusoid corresponding to the target track,
wherein:
the first sinusoid corresponds a repeatable position error of the head relative to the target track;
the coefficients of the first sinusoid comprise a coherent component due to a repeatable runout of the disk and a spiral component due to writing the servo sectors by servoing off of the spiral tracks; and
the spiral component varies based on a radial location of the head; and
servoing the head over the target track in response to the coefficients.
11. The method as recited in claim 10 , wherein the first sinusoid comprises:
a·cos(2πω j k/N)+b·sin(2πω j k/N)
where:
the coefficients comprise a and b;
ω j represents one of a fundamental frequency and a harmonic frequency of the repeatable position error; and
k represents one of N servo sectors written around the target track.
12. The method as recited in claim 11 , wherein the coefficients comprise:
a=a coh +a sp
b=b coh +b sp
where a coh and b coh represent the coherent component and a sp and b sp represent the spiral component.
13. The method as recited in claim 12 , further comprising generating the spiral component according to:
[
a
1
sp
b
1
sp
]
=
[
-
c
1
c
2
·
cot
(
θ
/
2
)
-
c
3
·
cot
(
θ
/
2
)
-
c
4
]
[
δ
a
δ
b
]
where:
[
δ
a
δ
b
]
=
[
a
2
sp
-
a
1
sp
b
2
sp
-
b
1
sp
]
a 1 sp and b 1 sp represent the spiral component at the target track;
a 2 sp and b 2 sp represent the spiral component at a second track; and
θ represents a radial distance between the target track and the second track.
14. The method as recited in claim 13 , further comprising:
positioning the head over a second track; and
generating the spiral component of the coefficients of the first sinusoid for the second track in response to a radial distance between the target track and the second track:
⌊
a
2
sp
b
2
sp
⌋
=
[
cos
(
θ
)
-
sin
(
θ
)
sin
(
θ
)
cos
(
θ
)
]
⌊
a
1
sp
b
1
sp
⌋
where:
a 1 sp and b 1 sp represent the spiral component at the target track;
a 2 sp and b 2 sp represent the spiral component at a second track; and
θ represents the radial distance between the target track and the second track.
15. The method as recited in claim 10 , further comprising:
positioning the head over a second track; and
generating the coefficients of the first sinusoid for the second track in response to a radial distance between the target track and the second track.
16. The method as recited in claim 10 , further comprising generating feedforward compensation values in response to the coefficients of the first sinusoid so that the head substantially follows the repeatable position error.
17. The method as recited in claim 10 , further comprising generating feedback compensation values in response to the coefficients of the first sinusoid so that the head substantially ignores the repeatable position error.
18. The method as recited in claim 10 , further comprising generating coefficients of a second sinusoid corresponding to the target track, wherein:
the first sinusoid corresponds to a fundamental frequency of the repeatable position error; and
the second sinusoid corresponds to a harmonic frequency of the repeatable position error.