Repeatable runout (RRO) compensation methods and apparatus for data storage devices
View Patent ↗In one illustrative example, a method for use in reducing Repeatable Run Out (RRO) error in a data storage device involves obtaining an RRO measurement for each track of a limited number of N disk tracks; characterizing the RRO measurement for each track with real and imaginary values by performing a discrete Fourier transform (DFT) calculation on each RRO measurement; performing a least-squares fit on all of the real values to identify a first set of (n+1) coefficients of an nth-order polynomial function which is a function of disk track r and representable in the form A i (r)=a n r n +a (n−1) r (n−1) + . . . +a 1 r+a 0 ; and performing a least-squares fit on all of the imaginary values to identify a second set of (n+1) coefficients of an nth-order polynomial function which is a function of disk track r and representable in the form B i (r)=b n r n +b (n−1) r (n−1) + . . . +b 1 r+b 0 . RRO compensation is performed based on the relation D RRO (r, s)=Σ i for all H {A i (r)cos(i(s2π/total_sectors))+B i (r)sin(i(s2π/total_sectors))} where D RRO is the estimated RRO error; r is a track number; s is a sector number at track number r; i is an RRO harmonic number; H is a set of harmonics to be compensated; and total_sectors is a total number of sectors along track number r. Advantageously, RRO variations across the disk can be accurately compensated for with use of a small amount of memory.
1. In a data storage device, a method of reducing repeatable runout (RRO) error comprising:
receiving a plurality of RRO measurements for a plurality of disk tracks;
for each one of one or more RRO harmonics to be compensated:
performing a discrete Fourier transform (DFT) on each RRO measurement for the RRO harmonic to identify a real value and an imaginary value associated with each disk track;
identifying, from the real values, a first set of (n+1) polynomial coefficients of a first nth-order polynomial function as a function of disk track;
identifying, from the imaginary values, a second set of (n+1) polynomial coefficients of a second nth-order polynomial function as a function of disk track; and
storing the first and the second sets of (n+1) polynomial coefficients for use in RRO compensation.
2. The method of claim 1 , wherein the first set of polynomial coefficients are identified by performing a least-squares fit on the real values and the second set of polynomial coefficients are identified by performing a least-squares fit on the imaginary values.
3. The method of claim 1 , wherein the plurality of disk tracks comprises a limited number of disk tracks on the disk.
4. The method of claim 1 , wherein the first nth-order polynomial function comprises a best fit curve for the real values and wherein the second nth-order polynomial function comprises a best fit curve for the imaginary values.
5. The method of claim 1 , wherein performing RRO compensation comprises:
providing an RRO function which is a function of current disk track and a current sector number;
identifying a current disk track and a current sector number;
selecting polynomial coefficients from the first and the second sets which correspond to the current disk track;
executing the RRO function based on the current disk track, the current sector number, and the selected polynomial coefficients, to thereby estimate a current RRO error; and
performing RRO compensation based on the current RRO error.
6. The method of claim 1 , wherein RRO compensation is based on a predetermined function which is expressible as:
D RRO ( r,s )=Σ i for all H {A i ( r )cos( i ( s 2π/total_sectors))+ B i ( r )sin( i ( s 2π/total_sectors))}
where r is a track number; s is a sector number at track number r; i is an RRO harmonic number; H is a set of harmonics to be compensated; total_sectors is a total number of sectors along track number r;
where A i (r)=a n r n +a (n−1) r (n−1) + . . . +a 1 r+a 0 is the first nth-order polynomial function which is a best fit curve of the real values determined from the DFTs; and
where B i (r) is b n r n +b (n−1) r (n−1) + . . . +b 1 r+b 0 is the second nth-order polynomial function which is a best fit curve of the imaginary values determined from the DFTs.
7. An apparatus for use in reducing a repeatable runout (RRO) error for a data storage device, the apparatus comprising:
memory;
processor instructions stored in the memory;
the processor instructions executable by a processor for:
receiving a plurality of RRO measurements associated with a plurality of disk tracks;
for each one of one or more RRO harmonics to be compensated:
performing a discrete Fourier transform (DFT) on each RRO measurement for the RRO harmonic to identify a real value and an imaginary value associated with each disk track;
identifying, from the real values, a first set of (n+1) polynomial coefficients of a first nth-order polynomial function as a function of disk track;
identifying, from the imaginary values, a second set of (n+1) polynomial coefficients of a second nth-order polynomial function as a function of disk track; and
storing the first and the second sets of (n+1) polynomial coefficients for use in RRO compensation.
8. The apparatus of claim 7 , wherein the processor comprises a digital signal processor (DSP).
9. The apparatus of claim 7 , wherein the first set of polynomial coefficients are identified by performing a least-squares fit on the real values and the second set of polynomial coefficients are identified by performing a least-squares it on the imaginary values.
10. The apparatus of claim 7 , wherein the plurality of disk tracks comprises a limited number of disk tracks on the disk.
11. The apparatus of claim 7 , wherein the first nth-order polynomial function comprises a best fit curve for the real values and wherein the second nth-order polynomial function comprises a best fit curve for the imaginary values.
12. The apparatus of claim 7 , wherein RRO compensation is based on a predetermined function which is expressible as:
D RRO ( r,s )=Σ i for all H {A i ( r )cos( i ( s 2π/total_sectors))+ B i ( r )sin( i ( s 2π/total_sectors))}
where r is a track number; s is a sector number at track number r; i is an RRO harmonic number; H is a set of harmonics to be compensated; total_sectors is a total number of sectors along track number r;
where A i (r)=a n r n +a (n−1) r (n−1) + . . . +a 1 r+a 0 is the first nth-order polynomial function which is a best fit curve of the real values determined from the DFTs; and
where B i (r) is b n r n +b (n−1) r (n−1) + . . . +b 1 r+b 0 is the second nth-order polynomial function which is a best fit curve of the imaginary values determined from the DFTs.
13. A data storage device, comprising:
at least one rotatable magnetic disk;
a disk drive motor for use in rotating the at least one rotatable magnetic disk;
a magnetic head for use in reading and/or writing data to the at least one rotatable magnetic disk;
an actuator for use in positioning the magnetic head;
one or more processors of the data storage device for use in:
receiving a plurality of RRO measurements associated with a plurality of disk tracks of the disk;
for each one of one or more RRO harmonics to be compensated:
performing a discrete Fourier transform (DFT) on each RRO measurement for the RRO harmonic to identify a real value and an imaginary value associated with each disk track;
identifying, from the real values, a first set of (n+1) polynomial coefficients of a first nth-order polynomial function as a function of disk track;
identifying, from the imaginary values, a second set of (n+1) polynomial coefficients of a second nth-order polynomial function as a function of disk track; and
storing the first and the second sets of (n+1) polynomial coefficients for use in RRO compensation.
14. The data storage device of claim 13 , wherein the first set of polynomial coefficients are identified by performing a least-squares fit on the real values and the second set of polynomial coefficients are identified by performing a least-squares fit on the imaginary values.
15. The data storage device of claim 13 , wherein the plurality of disk tracks comprises a limited number of disk tracks on the disk.
16. The data storage device of claim 13 , wherein the first nth-order polynomial function comprises a best fit curve for the real values and wherein the second nth-order polynomial function comprises a best fit curve for the imaginary values.
17. The data storage device of claim 13 , wherein the processor is for use in performing RRO compensation which comprises:
providing an RRO function which is a function of current disk track and a current sector number;
identifying a current disk track and a current sector number;
selecting polynomial coefficients from the first and the second sets which correspond to the current disk track;
executing the RRO function based on the current disk track, the current sector number, and the selected polynomial coefficients, to thereby estimate a current RRO error; and
performing RRO compensation based on the current RRO error.
18. The data storage device of claim 13 , wherein RRO compensation is based on a predetermined function which is expressible as:
D RRO ( r,s )=Σ i for all H {A i ( r )cos( i ( s 2π/total_sectors))+ B i ( r )sin( i ( s 2π/total_sectors))}
where r is a track number; s is a sector number at track number r; i is an RRO harmonic number; H is a set of harmonics to be compensated; total_sectors is a total number of sectors along track number r;
where A i (r)=a n r n +a (n−1) r (n−1) + . . . +a 1 r+a 0 is the first nth-order polynomial function which is a best fit curve of the real values determined from the DFTs; and
where B i (r) is b n r n +b (n−1) r (n−1) + . . . +b 1 r+b 0 is the second nth-order polynomial function which is a best fit curve of the imaginary values determined from the DFTs.
19. In a data storage device, a method for use in reducing repeatable runout (RRO) error comprising:
estimating RRO error based on a predetermined function;
performing RRO compensation with use of the estimated RRO error;
the predetermined function being expressible as:
D RRO ( r,s )=Σ i for all H {A i ( r )cos( i ( s 2π/total_sectors))+ B i ( r )sin( i ( s 2π/total_sectors))}
where r is a track number; s is a sector number at track number r; i is an RRO harmonic number; H is a set of one or more harmonics to be compensated; total_sectors is a total number of sectors along track number r;
where A i (r)=a n r n +a (n−1) r (n−1) + . . . +a 1 r+a 0 is a best fit curve of real values from a discrete Fourier transform (DFT) of a plurality of RRO measurements of a plurality of disk tracks; and
where B i (r) is b n r n +b (n−1) r (n−1) + . . . +b 1 r+b 0 is a best fit curve of imaginary values from a DFT of the RRO measurements of the plurality of disk tracks.
20. The method of claim 19 , wherein the polynomial coefficients for A i (r) are determined by a least-squares fit of the real values and the polynomial coefficients for B i (r) are determined by a least-squares fit of the imaginary values.
21. The method of claim 19 , wherein i≧2.
22. The method of claim 19 , wherein the polynomial coefficients a and b are determined during calibration.
23. A data storage device, comprising:
memory;
repeatable runout (RRO) data stored in the memory;
the RRO data comprising:
a first set of (n+1) polynomial coefficients of a first nth-order polynomial best fit function for real values derived from a discrete Fourier transform (DFT) of a plurality of RRO measurements of a plurality of disk tracks across a disk;
a second set of (n+1) polynomial coefficients of a second nth-order polynomial function which represents a best fit curve for imaginary values derived from the DFT of the RRO measurements; and
one or more processors for use in reducing RRO with use of the RRO data.
24. The data storage device of claim 23 , wherein the first nth-order polynomial function is representable in the form A i (r)=a n r n +a (n−1) r (n−1) + . . . +a 1 r+a 0 and the second nth-order polynomial is representable in the form B i (r) is b n r n +b (n−1) r (n−1) + . . . +b 1 r+b 0 , where i represents an RRO harmonic number.
25. The data storage device of claim 23 , wherein the first and the second sets of polynomial coefficients represent coefficients for a first RRO harmonic, and wherein the RRO data further comprises additional first and second sets of polynomial coefficients for a second RRO harmonic.
26. The data storage device of claim 23 , further comprising:
wherein the first set of (n+1) polynomial coefficients for the real values are derived from a least-squares fit of the real values; and
wherein the second set of (n+1) polynomial coefficients for the imaginary values are derived from a least-squares fit of the imaginary values.
27. The data storage device of claim 23 , wherein the one or more processors are for use in:
estimating RRO error with use of the RRO data and a predetermined function.
28. The data storage device of claim 23 , wherein the one or more processors are for use in:
estimating RRO error with use of the RRO data and a predetermined function; and
performing RRO compensation with use of the estimated RRO error.
29. The data storage device of claim 23 , wherein the first nth-order polynomial function is representable in the form A i (r)=a n r n +a (n−1) r (n−1) + . . . +a 1 r+a 0 and the second nth-order polynomial is representable in the form B i (r) is b n r n +b (n−1) r (n−1) + . . . +b 1 r+b 0 , where i represents an RRO harmonic number, and wherein the one or more processors are for:
estimating RRO error with use of the RRO data and a predetermined function;
performing RRO compensation with use of the estimated RRO error; and
the predetermined function being expressible as:
D RRO ( r,s )=Σ i for all H {A i ( r )cos( i ( s 2π/total_sectors))+ B i ( r )sin( i ( s 2π/total_sectors))}
where r is a track number; s is a sector number at track number r; i is an RRO harmonic number; H is a set of one or more harmonics to be compensated; and total_sectors is a total number of sectors along track number r.
30. The data storage device of claim 24 , wherein the one or more processors comprise a digital signal processor (DSP).