Disk drive generating a disk locked clock using radial dependent timing feed-forward compensation

Description

BACKGROUND

Disk drives comprise a disk and a head connected to a distal end of an actuator arm which is rotated about a pivot by a voice coil motor (VCM) to position the head radially over the disk. The disk comprises a plurality of radially spaced, concentric tracks for recording user data sectors and servo sectors. The servo sectors comprise head positioning information (e.g., a track address) which is read by the head and processed by a servo control system to control the actuator arm as it seeks from track to track.

FIG. 1 shows a prior art disk format 2 as comprising a number of servo tracks 4 defined by servo sectors 6₀-6_N recorded around the circumference of each servo track. Each servo sector 6₁ comprises a preamble 8 for storing a periodic pattern, which allows proper gain adjustment and timing synchronization of the read signal, and a sync mark 10 for storing a special pattern used to symbol synchronize to a servo data field 12. The servo data field 12 stores coarse head positioning information, such as a servo track address, used to position the head over a target data track during a seek operation. Each servo sector 6₁ further comprises groups of servo bursts 14 (e.g., N and Q servo bursts), which are recorded with a predetermined phase relative to one another and relative to the servo track centerlines. The phase based servo bursts 14 provide fine head position information used for centerline tracking while accessing a data track during write/read operations. A position error signal (PES) is generated by reading the servo bursts 14, wherein the PES represents a measured position of the head relative to a centerline of a target servo track. A servo controller processes the PES to generate a control signal applied to a head actuator (e.g., a voice coil motor) in order to actuate the head radially over the disk in a direction that reduces the PES.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a prior art disk format comprising a plurality of radially spaced, concentric tracks defined by a plurality of product servo sectors.

FIGS. 2A and 2B illustrate an embodiment of the present invention wherein an external spiral servo writer is used to write a plurality of spiral tracks to the disk for use in writing product servo sectors to the disk.

FIG. 3 illustrates an embodiment of the present invention wherein each spiral track is written over multiple revolutions of the disk.

FIG. 4A shows an embodiment of the present invention wherein a servo write clock is synchronized by clocking a modulo-N counter relative to when the sync marks in the spiral tracks are detected.

FIG. 4B shows an eye pattern generated by reading the spiral track, including the sync marks in the spiral track.

FIG. 5 illustrates writing of product servo sectors using a servo write clock generated from reading the spiral tracks.

FIGS. 6A and 6B illustrate a radial dependent repeatable phase error relative to the spiral tracks due to an offset r₀ representing a difference between an axial rotation of the disk and an axial rotation of the spiral tracks.

FIG. 7A shows timing control circuitry according to an embodiment of the present invention that cancels the repeatable phase error using radial dependent timing compensation values in order to generate a servo write clock substantially synchronized to the rotation of the disk.

FIG. 7B shows timing control circuitry according to an embodiment of the present invention including feed-forward compensation values that compensate for a residual repeatable phase error.

FIG. 8 shows position control circuitry according to an embodiment of the present invention that servos the head over the disk by generating a position error signal (PES), wherein the offset r₀ is estimated by estimating a repeatable runout in the PES.

FIG. 9 is a flow diagram according to an embodiment of the present invention wherein a frequency of an oscillator is adjusted using the radial dependent timing compensation values in order to write evenly spaced product servo sectors.

FIGS. 10A and 10B illustrate an embodiment of the present invention wherein repeatable runout (RRO) of a phase error at two radial locations is used to estimate the offset r₀.

FIG. 11 shows an equation for computing the offset r₀.

FIGS. 12A and 12B show a timing control loop according to an embodiment of the present invention wherein coefficients of a sinusoid are adapted to learn the RRO of the phase error.

FIG. 13A shows an embodiment wherein the servo data comprises servo wedges having a non-radial shape.

FIG. 13B shows an embodiment wherein a phase of the radial dependent timing compensation values varies across the radius of the disk due to the non-radial shape of the servo wedges.

FIG. 14 shows timing control circuitry wherein the radial dependent timing compensation values are generated using a phase offset based on the radial location of the head.

DETAILED DESCRIPTION

In an embodiment of the present invention, a disk drive comprises a disk comprising servo data, and a head actuated over the disk. An offset r₀ representing a difference between an axial rotation of the disk and an axial rotation of the servo data is estimated, and radial dependent timing compensation values are generated in response to the estimated r₀. A phase error is generated in response to the servo data, and a control signal is generated in response to the phase error and the radial dependent timing compensation values. A frequency of an oscillator is adjusted in response to the control signal.

Any suitable servo data may be read from the disk in order to adjust the frequency of the oscillator. In one embodiment, the servo data may comprise servo sectors such as shown in FIG. 1. In another embodiment, the servo data may comprise a plurality of spiral tracks, where each spiral track comprises a high frequency signal interrupted at a predetermined interval by a sync mark. However, the spiral tracks may comprise any suitable pattern and may be written to the disk using any suitable technique, such as using a media writer or an external writer for writing the spiral tracks to the disk, or stamping the spiral tracks on the disk using magnetic printing techniques. In another embodiment, the control circuitry internal to each production disk drive may be used to self-servo write the spiral tracks to the disk.

FIGS. 2A and 2B show an embodiment wherein a plurality of spiral tracks 20₀-20_N are written to a disk 18 of a disk drive 16 using an external spiral servo writer 36. The disk drive 16 comprises control circuitry 34 and a head disk assembly (HDA) 32 comprising the disk 18, an actuator arm 26, a head 28 coupled to a distal end of the actuator arm 26, and a voice coil motor 30 for rotating the actuator arm 26 about a pivot to position the head 28 radially over the disk 18. A write clock is synchronized to the rotation of the disk 18, and the plurality of spiral tracks 20₀-20_N are written on the disk 18 at a predetermined circular location determined from the write clock. Each spiral track 20₁ comprises a high frequency signal 22 (FIG. 4B) interrupted at a predetermined interval by a sync mark 24.

The external spiral servo writer 36 comprises a head positioner 38 for actuating a head positioning pin 40 using sensitive positioning circuitry, such as a laser interferometer. Pattern circuitry 42 generates the data sequence written to the disk 18 for the spiral tracks 20₀-20_N. The external spiral servo writer 36 inserts a clock head 46 into the HDA 32 for writing a clock track 44 (FIG. 2B) at an outer diameter of the disk 18. The clock head 46 then reads the clock track 44 to generate a clock signal 48 processed by timing recovery circuitry 50 to synchronize the write clock 51 for writing the spiral tracks 20₀-20_N to the disk 18. The timing recovery circuitry 50 enables the pattern circuitry 42 at the appropriate time relative to the write clock 51 so that the spiral tracks 20₀-20_N are written at the appropriate circular location. The timing recovery circuitry 50 also enables the pattern circuitry 42 relative to the write clock 51 to write the sync marks 24 (FIG. 4B) within the spiral tracks 20₀-20_N at the same circular location from the outer diameter to the inner diameter of the disk 18. As described below with reference to FIG. 5, the constant interval between sync marks 24 (independent of the radial location of the head 28) enables a servo write clock to maintain synchronization while writing the product servo sectors to the disk.

In the embodiment of FIG. 2B, each spiral track 20₁ is written over a partial revolution of the disk 18. In an alternative embodiment, each spiral track 20₁ is written over one or more revolutions of the disk 18. FIG. 3 shows an embodiment wherein each spiral track 20₁ is written over multiple revolutions of the disk 18. In the embodiment of FIG. 2A, the entire disk drive 16 is shown as being inserted into the external spiral servo writer 36. In an alternative embodiment, only the HDA 32 is inserted into the external spiral servo writer 36. In yet another embodiment, an external media writer is used to write the spiral tracks 20₀-20_N to a number of disks 18, and one or more of the disks 18 are then inserted into an HDA 32.

Referring again to the embodiment of FIG. 2A, after the external spiral servo writer 36 writes the spiral tracks 20₀-20_N to the disk 18, the head positioning pin 40 and clock head 46 are removed from the HDA 32 and the product servo sectors are written to the disk 18. In one embodiment, the control circuitry 34 within the disk drive 16 is used to process the spiral tracks 20₀-20_N in order to write the product servo sectors to the disk 18. In an alternative embodiment, an external product servo writer may be used to process the spiral tracks 20₀-20_N in order to write the product servo sectors to the disk 18 during a “fill operation”.

FIG. 4B illustrates an “eye” pattern in the read signal that is generated when the head 28 crosses over a spiral track 20. The read signal representing the spiral track crossing comprises high frequency transitions 22 interrupted by sync marks 24 at a predetermined interval. When the head 28 moves in the radial direction, the eye pattern will shift (left or right) while the sync marks 24 remain fixed (ideally). The shift in the eye pattern (detected from the high frequency signal 22) relative to the sync marks 24 provides the off-track information (spiral position error signal (PES)) for servoing the head 28.

FIG. 4A shows an embodiment of the present invention wherein a saw-tooth waveform 52 is generated by clocking a modulo-N counter with the servo write clock, wherein the frequency of the servo write clock is adjusted until the sync marks 24 in the spiral tracks 20₀-20_N are detected at a target modulo-N count value. The servo write clock may be generated using any suitable circuitry, such as a phase locked loop (PLL). As each sync mark 24 in the spiral tracks 20₀-20_N is detected, the value of the modulo-N counter represents the phase error for adjusting the PLL.

The sync marks 24 in the spiral tracks 20₀-20_N may comprise any suitable pattern, and in one embodiment, a pattern that is substantially shorter than the sync mark 10 in the conventional product servo sectors 2 of FIG. 1. A shorter sync mark 24 allows the spiral tracks 20₀-20_N to be written to the disk 18 using a steeper slope (by moving the head faster from the outer diameter to the inner diameter of the disk 18) which reduces the time required to write each spiral track 20₀-20_N.

In one embodiment, the servo write clock is further synchronized by generating a timing recovery measurement from the high frequency signal 22 between the sync marks 24 in the spiral tracks 20₀-20_N. Synchronizing the servo write clock to the high frequency signal 22 helps maintain proper radial alignment (phase coherency) of the Gray coded track addresses in the product servo sectors. The timing recovery measurement may be generated in any suitable manner. In one embodiment, the servo write clock is used to sample the high frequency signal 22 and the signal sample values are processed to generate the timing recovery measurement. The timing recovery measurement adjusts the phase of the servo write clock (PLL) so that the high frequency signal 22 is sampled synchronously. In this manner, the sync marks 24 provide a coarse timing recovery measurement and the high frequency signal 22 provides a fine timing recovery measurement for maintaining synchronization of the servo write clock.

FIG. 5 illustrates how the product servo sectors 56₀-56_N are written to the disk 18 after synchronizing the servo write clock in response to at least the sync marks 24 in the spiral tracks 20₀-20_N. In the embodiment of FIG. 5, the dashed lines represent the centerlines of the data tracks. The sync marks in the spiral tracks 20₀-20_N are written so that there is a shift of two sync marks 24 in the eye pattern (FIG. 4B) between data tracks. In an alternative embodiment, the sync marks 24 in the spiral tracks 20₀-20_N are written so that there is a shift of N sync marks in the eye pattern between data tracks. In the embodiment of FIG. 5, each spiral track 20₀-20_N is wider than a data track, however, in an alternative embodiment the width of each spiral track 20₀-20_N is less than or proximate the width of a data track.

The spiral PES for maintaining the head 28 along a servo track (tracking) may be generated from the spiral tracks 20₀-20_N in any suitable manner. In one embodiment, the PES is generated by detecting the eye pattern in FIG. 4B using an envelope detector and detecting a shift in the envelope relative to the sync marks 24. In one embodiment, the envelope is detected by integrating the high frequency signal 22 and detecting a shift in the resulting ramp signal. In an alternative embodiment, the high frequency signal 22 between the sync marks 24 in the spiral tracks are demodulated as servo bursts and the PES generated by comparing the servo bursts in a similar manner as the servo bursts 14 in the product servo sectors (FIG. 1).

Once the head 28 is tracking on a servo track, the product servo sectors 56₀-56_N are written to the disk using the servo write clock. Write circuitry is enabled when the modulo-N counter reaches a predetermined value, wherein the servo write clock clocks the write circuitry to write the product servo sector 56 to the disk. The spiral tracks 20₀-20_N on the disk are processed in an interleaved manner to account for the product servo sectors 56₀-56_N overwriting a spiral track. For example, when writing the product servo sectors 56₁ to the disk, spiral track 20₀ is processed initially to generate the spiral PES tracking error and the servo write clock timing recovery measurement. When the product servo sectors 56₁ begin to overwrite spiral track 20₁, spiral track 20₀ is processed to generate the spiral PES tracking error and the servo write clock timing recovery measurement.

In the embodiment of FIG. 2B, the spiral tracks 20₀-20_N are concentric with relative to a rotation axis of the disk, and therefore the spiral tracks define concentric servo tracks relative to the rotation axis of the disk. In reality the spiral tracks 20₀-20_N may be eccentric relative to the rotation axis of the disk due to a misalignment in clamping the disk to a spindle motor after writing the spiral tracks 20₀-20_N to the disk, or due to servo errors when self-writing the spiral tracks 20₀-20_N to the disk. The eccentricity of the spiral tracks 20₀-20_N results in an offset r₀ representing a difference between an axial rotation of the disk 18 and an axial rotation of the spiral tracks. This is illustrated in FIG. 6A which shows a center rotation of the disk (Cspin) relative to a center rotation of the spiral tracks (Cseed) and a corresponding offset r₀ between the two.

As the disk 18 rotates about Cspin, Cseed will rotate about Cspin along the dashed circle shown in FIG. 6A. As a result, a circumferential phase offset Ψ is induced (relative to the head 28) between the circumferential phase of the disk 18 and the circumferential phase of the spiral tracks 20₀-20_N. If the servo write clock is synchronized to the spiral tracks 20₀-20_N, the resulting product servo sectors 56₀-56_N will be written to the disk 18 with a circumferential phase offset Ψ relative to the disk, thereby resulting in unevenly spaced produce servo sectors. In one embodiment, the circumferential phase offset Ψ is estimated and used to compensate timing control circuitry that generates the servo write clock so that the product servo sectors 56₀-56_N are written with substantially even spacing.

The magnitude of the circumferential phase offset Ψ will vary based on the radial location of the head 28. This is illustrated in FIGS. 6A and 6B wherein the circumferential phase of the disk 18 is the same, but the magnitude of the circumferential phase offset Ψ decreases as the radial location increases toward the outer diameter of the disk 18. Since the circumferential phase offset Ψ varies in a sinusoid as the disk 18 rotates, the magnitude of the circumferential phase offset Ψ can be estimated in one embodiment according to:

r 0 r s ⁢ sin ⁢ ⁢ θ
where r_s represents the radial location of the head 28, and θ represents the rotation angle of the disk 18. In the embodiment of FIG. 6A, θ represents the rotation angle of the disk 18 relative to Cseed and Cspin. That is, θ is zero when Cseed is aligned with the head 28 and with Cspin as illustrated in FIG. 6A.

FIG. 7A shows timing control circuitry according to an embodiment of the present invention wherein an oscillator 58 generates an output frequency 60 (the servo write clock) used to clock a modulo-N counter 62. The output 64 of the modulo-N counter represents a measured phase of the output frequency 60 which is subtracted from a target phase 66 to generate a phase error (PE) 68. The PE comprises a repeatable runout (RRO) corresponding to the circumferential phase offset Ψ described above. Accordingly, in the embodiment of FIG. 7A the PE 68 is adjusted by radial dependent timing compensation values 70 to generate an adjusted PE 74 having the RRO canceled from the PE 68, wherein the radial dependent timing compensation values 70 are generated according the equation in block 72 described above. The adjusted PE 74 is filtered using a suitable compensator 76 to generate a control signal 78 applied to the oscillator 58. Cancelling the RRO from the PE 68 causes the output frequency 60 of the oscillator 58 (the servo write clock) to synchronize to the rotation of the disk 18 rather than to the rotation of the spiral tracks 20₀-20_N. Consequently, the product servo sectors 56₀-56_N are written on the disk 18 with a substantially even spacing.

FIG. 7B shows timing control circuitry according to another embodiment of the present invention including to generate feed-forward compensation values 80 in response to the adjusted PE 74, wherein the feed-forward compensation values 80 compensate for a residual RRO in the adjusted PE 74. The feed-forward compensation values 80 are used to adjust the control signal 78 to generate an adjusted control signal 82 applied to the oscillator 58 so as to force the output frequency 60 to follow the residual RRO while writing the product servo sectors 56₀-56_N to the disk, thereby improving the phase coherency of the product servo sectors 56₀-56_N.

The offset r₀ between Cspin and Cseed shown in FIG. 6A may be estimated using any suitable technique, and in one embodiment, the offset r₀ is estimated in response to a position error signal (PES) used to servo the head over the disk in response to the spiral tracks. This embodiment is understood with reference to FIG. 8 which shows position control circuitry according to an embodiment of the present invention. An actuator 82 (e.g., a voice coil motor) actuates the head over the disk, and a position 86 of the head is measured 84 in response to the spiral track crossings. The measured position 86 of the head is subtracted from a target position 88 to generate the PES 90. The eccentricity of the spiral tracks will generate an RRO in the PES 90 corresponding to the offset r₀. The PES 90 is processed 92 to adapt coefficients (a1,b1) of a sinusoid 94, wherein the sinusoid 94 generates compensation values 96 that are subtracted from the PES 90 to generate an adjusted PES 98. The instantaneous phase of the sinusoid 94 is determined by the kth spiral track crossing out of N spiral track crossings, as well as the ratio of the radial location r_s of the head to a partial radius of the disk r₁, where r₁ represents a part of the radius of the disk spanned by a complete revolution of the spiral tracks (as illustrated in FIG. 3).

The adjusted PES 98 is filtered using a suitable compensator 100 to generate a control signal 102 applied to the actuator 82. Eventually the coefficients (a1,b1) of the sinusoid 94 will adapt such that the RRO in the adjusted PES 98 is substantially canceled. Once the coefficients (a1,b1) have adapted, the amplitude of the resulting sinusoid 94 represents the amplitude of the offset r₀ in FIG. 6A. The phase of the sinusoid 94 may also be used to estimate the phase of the offset r₀ in FIG. 6A, thereby estimating when θ is zero in block 72 of FIG. 7A relative to the spiral track crossings.

In the embodiment of FIG. 8, the RRO is canceled from the PES 90 so that the product servo sectors 56₀-56_N written to the disk define substantially concentric servo tracks relative to Cspin. In an alternative embodiment, the RRO estimate in the PES 90 may be used to generate feed-forward compensation values which force the head to follow the RRO in the PES 90 while writing the product servo sectors 56₀-56_N to the disk so that the resulting servo tracks are concentric relative to Cseed, or a hybrid technique may be employed by adapting the coefficients of two sinusoids. In any event, the resulting sinusoid(s) that generates the position compensation values for the position control system may be used to estimate the magnitude and phase of the offset r₀ in FIG. 6A, which in turn is used in block 72 of FIG. 7A.

FIG. 9 shows a flow diagram according to an embodiment of the present invention for writing substantially evenly spaced product servo sectors to the disk by employing radially dependent timing compensation values in the timing control loop that generates the servo write clock. The spiral tracks are read (block 106), a corresponding PES is generated (block 108), and the head servoed over the disk in response to the PES (block 110). The offset r₀ is estimated (block 112), such as by estimating the RRO in the PES of the position control loop as described above with reference to FIG. 8. Radial dependent timing compensation values are generated based on the offset r₀ (block 114) as described above. A phase error (PE) is generated (block 116), and a control signal is generated based on the phase error and the radial dependent timing compensation values (block 118), wherein an output frequency (servo write clock) of an oscillator is adjusted using the control signal (block 120). The servo write clock is then used to write substantially evenly spaced product servo sectors on the disk (block 122).

The offset r₀ may be estimated in any suitable manner, and in one embodiment the offset r₀ is estimated in response to a repeatable runout (RRO) in the phase error of the PLL that generates the servo write clock. As the disk 18 rotates and Cseed rotates around Cspin as shown in FIG. 10A, a repeatable runout (RRO) is induced in the phase error of the PLL that generates the servo write clock. The instantaneous RRO in the phase error relative to the rotation angle of the disk is represented by the angle Ψ₁ in FIG. 10A. In addition, the angle Ψ₁ representing the RRO in the phase error will reach a peak when the distance R1 of the head 28 from Cseed forms a right angle with the offset r₀. Although the location of the head 28 can be determined relative to the spiral track 20₀-20_N, the distance R1 of the head 28 from Cseed is unknown (because r₀ is unknown).

In one embodiment in order to estimate the offset r₀, the head 28 is positioned at a first radial location R1 as shown in FIG. 10A and a first peak Ψ₁ in a first RRO of the phase error is measured. The head 28 is then positioned at a second radial location R2 as shown in FIG. 10B and a second peak Ψ₂ in a second RRO of the phase error is measured. The offset r₀ may then be estimated in one embodiment as follows:
R2−R1=r₀/tan ψ₂−r₀/tan ψ₁
then

r 0 = ( R ⁢ ⁢ 2 - R ⁢ ⁢ 1 ) ( 1 ⁢ / ⁢ tan ⁢ ⁢ ψ 2 - 1 ⁢ / ⁢ tan ⁢ ⁢ ψ 1 ) ( FIG . ⁢ 11 )
The phase of the offset r₀ relative to the rotation angle of the disk 18 may be determined relative to the angle of the disk 18 when the RRO in the phase error reaches its peak. In the example shown in FIGS. 10A and 10B, the rotation angle of the disk 18 is slightly different between the first peak Ψ₁ and the second peak Ψ₂. In one embodiment, the phase of the offset r₀ may be computed as the average of the rotation phase of the disk measured at the first peak Ψ₁ and the second peak Ψ₂.

Estimating the offset r₀ using the above equation assumes the head 28 follows the RRO in the position error while servoing on the spiral tracks 20₀-20_N (e.g., using feed-forward compensation). In this manner, the distance between R1 and R2 can be measured based on the corresponding tracks defined by the spiral tracks 20₀-20_N when Ψ₁ and Ψ₂ reach their peak. In another embodiment, the RRO may be canceled from the position error while servoing on the spiral tracks 20₀-20_N. In this embodiment, R1 and R2 may be measured along the axis aligned with Cspin based on the corresponding tracks defined by the spiral tracks 20₀-20_N when Ψ₁ and Ψ₂ reach their peak. Accordingly, the above equation in this embodiment is modified to derive the estimate for the offset r₀ based on the measured hypotenuse of the right triangles shown in FIGS. 10A and 10B.

FIG. 12A shows a timing control loop according to an embodiment of the present invention which is similar to the timing control loop described above with reference to FIG. 7A. The phase error 68 comprises a RRO due to the offset r₀ between Cspin and Cseed as described above. In this embodiment, the RRO in the phase error 68 may be learned by adapting coefficients a1,b1 (block 124) of a sinusoid 126 that generates feed-forward timing compensation values 128. The sinusoid is generated according to:

a ⁢ ⁢ 1 ⁢ ⁢ cos ⁡ ( ( 2 ⁢ ⁢ π · ( k N ) ) + ( 2 ⁢ ⁢ π · r r 1 ) ) + b ⁢ ⁢ 1 ⁢ ⁢ sin ⁡ ( ( 2 ⁢ π · ( k N ) ) + ( 2 ⁢ ⁢ π · r r 1 ) )
where a1 and b1 are the first coefficients, k is the kth spiral track out of N spiral tracks, r is the radial location of the head, and r₁ represents a part of the radius of the disk spanned by a complete revolution of the spiral tracks (as illustrated in FIG. 3).

The feed-forward timing compensation values 128 adjust the control signal 78 to generate an adjusted control signal 130 used to adjust the frequency of the oscillator 58. The coefficients a1,b1 are adapted 124 in order to drive the RRO in the phase error 68 toward zero. Once the coefficients a1,b1 have adapted, the resulting sinusoid 126 represents the RRO in the phase error 68, and the peak in the sinusoid 126 represents the peak in the RRO (Ψ₁ or Ψ₂ described above).

FIG. 12B shows an alternative embodiment of the present invention wherein coefficients a1,b1 of a sinusoid 132 may be adapted 134 in response to the phase error 68 to generate timing compensation values 136 that are subtracted from the phase error 68 in order to generate an adjusted phase error 138. The coefficients a1,b1 are adapted until the RRO is substantially canceled from the adjusted phase error 138, thereby generating a servo write clock 60 that is synchronized to the rotation of the disk 18 rather than to the rotation of the spiral tracks 20₀-20_N as in the embodiment of FIG. 12A. Similar to the embodiment of FIG. 12A, after the coefficients a1,b1 have adapted, the resulting sinusoid 132 represents the RRO in the phase error 68, and the peak in the sinusoid 132 represents the peak in the RRO (Ψ₁ or Ψ₂ described above).

The above described embodiments may be employed for any suitable servo data instead of, or in addition to, the spiral servo tracks shown in FIG. 2B and FIG. 3. For example, in one embodiment the above described embodiments may be employed when the servo data comprises servo sectors such as shown in FIG. 1. In one embodiment, the servo sectors form servo wedges due to the decreasing linear bit density form the outer diameter toward the inner diameter of the disk. The servo wedges may form a single wedge shape as shown in FIG. 1 due to writing the servo sectors using a single data rate, or the servo wedges may form multiple wedge shapes due to writing the servo sectors at a varying data rate across multiple zones over the radius of the disk.

In one embodiment, the servo wedges may have a non-radial shape due, for example, to an arc trajectory of the head as a VCM rotates an actuator arm about a pivot when servo writing the servo sectors on the disk. In another embodiment, the servo wedges may have a non-radial shape due to imperfections in seed tracks (e.g., spiral tracks) used to self-servo write the servo sectors on the disk. An example of a non-radial servo wedge 140 is shown in FIG. 13A relative to an example radial servo wedge 142. FIG. 13A also shows the offset r₀ representing a difference between an axial rotation of the disk and an axial rotation of the servo wedge 140 which causes a radial dependent repeatable phase error in the timing control circuitry as described above. In addition, in one embodiment the non-radial shape of the servo wedge 140 may induce a radial dependent phase shift Ψ(r_s) of the repeatable phase error since the circumferential position of the servo wedge 140 changes across the radius of the disk as illustrated in FIG. 13A and FIG. 13B.

Accordingly, in one embodiment the control circuitry may generate the radial dependent timing compensation values according to:

r 0 r s ⁢ sin ⁢ ⁢ ( θ + φ ⁡ ( r s ) )
where r_s represents a radial location of the head, θ represents the rotation angle of the disk, and φ(r_s) represents a phase offset of the radial dependent timing compensation values based on the radial location of the head. Any suitable technique may be employed to generate the phase offset φ(r_s) as a function of the radial location of the head r_s. In one embodiment, coefficients a1,b1 of a sinusoid may be adapted similar to the embodiment described above with reference to FIG. 12A. In this embodiment the target θ is generated as if the servo wedges comprise a radial shape (i.e.,

θ = 2 ⁢ ⁢ π · ( k N )
where k is the kth servo wedge out of N servo wedges), and the term

( 2 ⁢ π · r r 1 )
is zero. The phase offset of the resulting sinusoid at different radial locations (relative to a reference radial location where θ+φ=θ) represents the phase offset φ(r_s) in the above equation. In one embodiment, the phase offset φ(r_s) may be measured at a plurality of different radial locations, and the resulting data points curve fitted to a suitable polynomial. During normal operation, the phase offset φ(r_s) may then be computed using the polynomial based on the current radial location of the head r_s.

FIG. 14 shows timing control circuitry according to an embodiment where block 144 generates the radial dependent timing compensation values 146 based on the current radial location of the head r_s using the above equation. In the embodiment of FIG. 14, the radial dependent timing compensation values 146 are added to adaptive feed-forward compensation values generated by block 148 to generate feed-forward compensation values 150 that adjust the control signal 78 output by the compensator 76, thereby generating the adjusted control signal 152 applied to the oscillator 58. In one embodiment, block 148 generates the adaptive feed-forward compensation values by adapting coefficients of a sinusoid similar to the embodiments described above with reference to FIG. 7B and FIG. 12B, where the adaptive feed-forward compensation values compensate for any residual RRO in the phase error not accounted for by the radial dependent timing compensation values 146.

Any suitable control circuitry may be employed to implement the flow diagrams in the embodiments of the present invention, such as any suitable integrated circuit or circuits. For example, the control circuitry may be implemented within a read channel integrated circuit, or in a component separate from the read channel, such as a disk controller, or certain operations described above may be performed by a read channel and others by a disk controller. In one embodiment, the read channel and disk controller are implemented as separate integrated circuits, and in an alternative embodiment they are fabricated into a single integrated circuit or system on a chip (SOC). In addition, the control circuitry may include a suitable preamp circuit implemented as a separate integrated circuit, integrated into the read channel or disk controller circuit, or integrated into an SOC.

In one embodiment, the control circuitry comprises a microprocessor executing instructions, the instructions being operable to cause the microprocessor to perform the flow diagrams described herein. The instructions may be stored in any computer-readable medium. In one embodiment, they may be stored on a non-volatile semiconductor memory external to the microprocessor, or integrated with the microprocessor in a SOC. In another embodiment, the instructions are stored on the disk and read into a volatile semiconductor memory when the disk drive is powered on. In yet another embodiment, the control circuitry comprises suitable logic circuitry, such as state machine circuitry.