Disk drive recursively estimating repeatable runout

1. A disk drive comprising:

(a) a disk comprising a plurality of data tracks, wherein each data track comprises a plurality of data sectors and a plurality of embedded servo sectors;

(b) an actuator arm;

(c) a head coupled to a distal end of the actuator arm;

(d) a voice coil motor (VCM) for rotating the actuator arm about a pivot in order to actuate the head over the disk; and

(e) control circuitry for generating a control signal applied to the VCM in response to a position error signal (PES) generated from reading the embedded servo sectors and a feed-forward compensation value that compensates for a repeatable runout (RRO) disturbance, the feed-forward compensation value generated for each servo sector in response to an RRO estimate Ŝ computed recursively for each servo sector according to:

S

^

n

+

1

=

S

^

n

-

λ

⁡

[

S

^

n

-

1

n

⁢

∑

i

=

1

n

⁢

⁢

PES

i

]

 wherein:

λ is a predetermined fraction;

PES i is the position error signal generated for a selected servo sector during an ith revolution of the disk; and

n represents a number of disk revolutions.

2. The disk drive as recited in claim 1 , wherein the RRO estimate Ŝ is computed recursively over a predetermined number of disk revolutions.

3. The disk drive as recited in claim 1 , wherein the RRO estimate Ŝ is computed recursively over a number of disk revolutions until the change in the RRO estimate Ŝ falls below a predetermined threshold.

4. The disk drive as recited in claim 1 , wherein:

(a) the disk comprises a plurality of zones, wherein each zone comprises a plurality of the data tracks; and

(b) the RRO estimate Ŝ is computed for each data track in each zone using a λ corresponding to each zone.

5. The disk drive as recited in claim 1 , wherein the RRO estimate Ŝ is computed recursively for each data track during a manufacturing process.

6. The disk drive as recited in claim 1 , wherein the RRO estimate Ŝ is computed recursively for a selected data track if the PES generated for the selected data track exceeds a predetermined threshold during normal operation of the disk drive.

7. A method of operating a disk drive, the disk drive comprising a disk having a plurality of data tracks, wherein each data track comprises a plurality of data sectors and a plurality of embedded servo sectors, an actuator arm, a head coupled to a distal end of the actuator arm, and a voice coil motor (VCM) for rotating the actuator arm about a pivot in order to actuate the head over the disk, the method comprising the steps of:

(a) generating a control signal applied to the VCM in response to a position error signal (PES) generated from reading the embedded servo sectors and a feed-forward compensation value that compensates for a repeatable runout (RRO) disturbance; and

(b) generating the feed-forward compensation value for each servo sector in response to an RRO estimate Ŝ computed recursively for each servo sector according to:

S

^

n

+

1

=

S

^

n

-

λ

⁡

[

S

^

n

-

1

n

⁢

∑

i

=

1

n

⁢

⁢

PES

i

]

 wherein:

λ is a predetermined fraction;

PES i is the position error signal generated for a selected servo sector during an ith revolution of the disk; and

n represents a number of disk revolutions.

8. The method as recited in claim 7 , wherein the RRO estimate Ŝ is computed recursively over a predetermined number of disk revolutions.

9. The method as recited in claim 7 , wherein the RRO estimate Ŝ is computed recursively over a number of disk revolutions until the change in the RRO estimate Ŝ falls below a predetermined threshold.

10. The method as recited in claim 7 , wherein:

(a) the disk comprises a plurality of zones, wherein each zone comprises a plurality of the data tracks; and

(b) the RRO estimate Ŝ is computed for each data track in each zone using a λ corresponding to each zone.

11. The method as recited in claim 7 , wherein the RRO estimate Ŝ is computed recursively for each data track during a manufacturing process.

12. The method as recited in claim 7 , wherein the RRO estimate Ŝ is computed recursively for a selected data track if the PES generated for the selected data track exceeds a predetermined threshold during normal operation of the disk drive.