Method for preventing radial error propagation during self-servowriting of tracks in a magnetic disk drive
View Patent ↗The present invention may be embodied in a method for preventing radial error propagation during self-servowriting of concentric tracks on a magnetic disk in a disk drive. Each written track comprises a plurality of embedded servo sectors that define a circumferential path and that eventually form corresponding servo wedges extending radially across the magnetic disk such that each servo sector t of a track corresponds to a particular servo wedge. In the method comprising, track following is performed along a previously written track and a position error signal is determined for each servo sector. A correction value is recursively estimated for each servo sector of an adjacent track. The correction value is for use in correcting a position error signal determined using the corresponding servo sector of the adjacent track to prevent radial error propagation from previously written track to the adjacent track.
1. A method for preventing radial error propagation during self-servowriting of concentric tracks on a magnetic disk in a disk drive, wherein each written track comprises a plurality of embedded servo sectors that define a circumferential path and that eventually form corresponding servo wedges extending radially across the magnetic disk such that each servo sector t of a track corresponds to a particular servo wedge, the method comprising:
track following along a previously written track k and determining a position error signal e for each servo sector t;
recursively estimating a correction value u for each servo sector t of an adjacent track k+1 based on the equation:
u k+1 ( t )=α 0 e k ( t )+α 1 e k ( t+ 1)+α 2 e k ( t+ 2)+α 3 e k ( t+ 3)
where
k is the track number,
t is the sector number for a sector corresponding to a particular wedge, and
α 0 , α 1 , α 2 , and α 3 are learning gain coefficients; and
wherein the correction value u k+1 (t) is for use in correcting a position error signal e k+1 (t) determined using the corresponding servo sector t of the adjacent track k+1 to prevent radial error propagation from track k to track k+1.
2. A method for preventing radial error propagation during self-servowriting of concentric tracks as defined in claim 1 , wherein α 0 is equal to about 0.65, α 1 is equal to about 0.25, α 2 is equal to about 0.25, and α 3 is equal to about 0.25.
3. A method for preventing radial error propagation during self-servowriting of concentric tracks on a magnetic disk in a disk drive, wherein each written track comprises a plurality of embedded servo sectors that define a circumferential path and that eventually form corresponding servo wedges extending radially across the magnetic disk such that each servo sector t of a track corresponds to a particular servo wedge, the method comprising:
track following along a previously written track k and determining a position error signal e for each servo sector t;
recursively estimating a correction value u for each servo sector t of an adjacent track k+1 based on the equation:
u k+1 =Ke k
where
u k+1 is a vector of dimension N,
N is the total number of servo sectors per track;
k is the track number, and
K is a stabilizing square matrix of learning coefficients having dimensions N×N; and
wherein the correction value u k+1 is for use in correcting a position error signal e k+1 determined using the corresponding servo sector t of the adjacent track k+1 to prevent radial error propagation from track k to track k+1.
4. A method for preventing radial error propagation during self-servowriting of concentric tracks as defined in claim 3 , wherein the stabilizing square matrix K is defined as follows:
K
=
[
α
0
α
1
α
2
α
3
0
L
0
0
α
0
α
1
α
2
α
3
O
M
0
0
α
0
α
1
α
2
O
0
0
0
0
α
0
α
1
O
α
3
M
O
O
O
O
O
α
2
0
0
0
0
0
O
α
1
α
1
α
2
α
3
0
L
0
α
0
]
where α 0 , α 1 , α 2 , and α 3 are learning gain coefficients.
5. A method for preventing radial error propagation during self-servowriting of concentric tracks as defined in claim 4 , wherein α 0 is equal to about 0.65, α 1 is equal to about 0.25, α 2 is equal to about 0.25, and α 3 is equal to about 0.25.