Disk drive generating feed-forward compensation value based on two points of a sinusoidal control signal

A disk drive is disclosed comprising a disk comprising tracks defined by servo sectors, a head, and control circuitry comprising a servo control system operable to actuate the head over the disk in response to the servo sectors. After seeking the head to a first track, a position error signal (PES) is generated representing a difference between a target location for the head and a measured location for the head. A sinusoidal control signal is generated in response to the servo sectors, and a third point of the sinusoidal control signal is generated based on a first point and second point of the sinusoidal control signal and independent of the PES, wherein the first, second and third points correspond to respective servo sectors. A feed-forward compensation value is generated based on the third point of the sinusoidal control signal using a feed-forward compensator.

BACKGROUND

FIG. 1shows a prior art disk format2as comprising a number of servo tracks4defined by servo sectors60-6Nrecorded around the circumference of each servo track. Each servo sector6icomprises a preamble8for storing a periodic pattern, which allows proper gain adjustment and timing synchronization of the read signal, and a sync mark10for storing a special pattern used to symbol synchronize to a servo data field12. The servo data field12stores 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 sector6ifurther comprises groups of servo bursts14(A, B, C, D in the example shown), which are recorded with precise intervals and offsets relative to the servo track centerlines. The servo bursts14provide fine head position information used for centerline tracking while accessing a data track during write/read operations.

DETAILED DESCRIPTION

FIG. 2Ashows a disk drive according to an embodiment of the present invention comprising a disk16comprising tracks20defined by servo sectors220-22N, a head24, and control circuitry26comprising a servo control system (e.g.,FIG. 2B) operable to actuate the head24over the disk16in response to the servo sectors220-22N. The control circuitry26is operable to execute the flow diagram ofFIG. 2C, wherein after seeking the head to a first track (block28), a position error signal (PES)30is generated representing a difference between a target location32for the head and a measured location34for the head (block36). A sinusoidal control signal is generated in response to the servo sectors (block38), and a third point of the sinusoidal control signal is generated based on a first point and second point of the sinusoidal control signal and independent of the PES (block40), wherein the first, second and third points correspond to respective servo sectors. A feed-forward compensation value42is generated based on the third point of the sinusoidal control signal using a feed-forward compensator44(block46).

Any suitable servo control system may be employed in the embodiments of the present invention. In the embodiment ofFIG. 2B, a feedback compensator48processes the PES30to generate a control signal50that is modified by the feed-forward compensation value42to generate a control signal52applied to an actuator54for actuating the head24radially over the disk16. Any suitable actuator54may be employed, such as a voice coil motor56that rotates an actuator arm58about a pivot in order to actuate the head24radially over the disk16. In another embodiment, the actuator54may further comprise a suitable microactuator (e.g., piezoelectric actuator) for actuating a suspension relative to the actuator arm58, or actuating a slider relative to the suspension.

In one embodiment, the feed-forward compensator44compensates for one or more repeatable disturbances in the PES30due, for example, to a repeatable runout (RRO) of the disk16. The RRO of the disk16may be caused by a written-in error when writing the servo sectors220-22Nto the disk16, or an eccentricity due to a misalignment when clamping the disk16to a spindle motor that rotates the disk16. In one embodiment, the feed-forward compensator44may compensate for any suitable frequency of the repeatable disturbance, such as the fundamental frequency (disk rotation frequency) and/or harmonics of the fundamental frequency.

In one embodiment, the feed-forward compensator44generates the feed-forward compensation values42according to a z-domain transfer function:

τ⁢⁢z+γz2-2⁢cos⁡(ω⁢⁢T)⁢z+1Eq.⁢1
where T represents a sampling period of the servo sectors, ω represents a target frequency (e.g., the fundamental or harmonic of RRO), and τ and γ are learning coefficients. The above transfer function of Eq. 1 can be implemented in any suitable manner, including a Direct Form I or a Direct Form II difference equation as described in the embodiments below.

In one embodiment, the feed-forward compensator44generates the feed-forward compensation values y(k)42based on a Direct Form I difference equation that implements the above transfer function of Eq. 1 according to:
y(k)=2 cos(ωT)*y(k−1)−y(k−2)+τe(k−1)+γe(k−2)  Eq. 2
where T represents a sampling period of the servo sectors, ω represents a target frequency (e.g., the fundamental or harmonic of RRO), e represents an error signal of the servo control system (e.g., the PES30), and τ and γ are learning coefficients.

In embodiments of the present invention, it may be desirable to disable the learning mode of Eq. 2 such as while the head is tracking on a first track during certain modes, or while the head is seeking to a second track. For example, when the head is seeking to a second track the error signal (e.g., the PES30) may not represent the repeatable disturbance in a form useful for adapting the feed-forward compensation values42; however, it may still be desirable to generate the feed-forward compensation values42while the learning mode of Eq. 2 is disabled. The learning mode may be disabled in Eq. 2 by setting the learning coefficients τ and γ to zero, or by setting the error signal e to zero. However, due to a quantization error inherent in computing the cosine in Eq. 2, the equation may eventually become unstable if the learning mode is disabled for an extended number of servo sectors.

To overcome the instability problem of Eq. 2, in one embodiment the control circuitry is operable to generate a third point of the sinusoidal control signal according to:
y(k+n)=θ(yjsin(ωT(i+n))−yisin(ωT(j+n)))  Eq. 3
where y(k+n) represents the third point, θ=csc((i−j)ωT) where (i−j)ωT does not equal mπ and m is an integer, yirepresents the first point, yjrepresents the second point, represents a phase of the first point, and j represents a phase of the second point. The above Eq. 3 generates the third point independent of the error signal (e.g., independent of the PES) and does not exhibit the instability problem of Eq. 2. Accordingly, the above Eq. 3 can be used to generate the feed-forward compensation values42when Eq. 2 may otherwise become unstable due to disabling the learning mode.

FIG. 3illustrates operation of Eq. 2 with the learning mode enabled, as well as Eq. 3 for generating the third points during a seek operation. The x-axis inFIG. 3represents one revolution of the disk where each hash mark represents a servo sample (a servo sector). The y-axis inFIG. 3represents the magnitude of the sinusoidal control signal relative to the servo sectors, and the phase of the sinusoidal control signal is represented by both the x-axis and the y-axis. In the example ofFIG. 3, the sinusoidal control signal represents the fundamental frequency of the repeatable disturbance (i.e., the period of the sinusoidal control signal equals the period of a disk revolution).

During a normal tracking operation while tracking the first track, the above Eq. 2 is used to generate the points of the sinusoidal control signal shown inFIG. 3, wherein the feed-forward compensation values42are generated based on the sinusoidal control signal (and in this embodiment the feed-forward compensation values42equal the points of the sinusoidal control signal). The above Eq. 2 adapts the feed-forward compensation values42so as to reduce the corresponding frequency component in the error signal e (e.g., the PES30). When the servo control system transitions into a seek mode in order to seek the head to a second track, two points of the sinusoidal control signal are used to generate the third points y(k+n) of the sinusoidal control signal using Eq. 3 as the head seeks from the first track to the second track. In the example shown inFIG. 3, the first and second points yiand yjcorrespond to the points generated at servo sectors k−1 and k−2 when the head is at servo sector k just prior to the seek. The phase i and j of the two points yiand yjis represented by the phase of the corresponding servo sectors relative to the rotation phase of the disk. Although the example ofFIG. 3uses first and second points at time k−1 and k−2, any two points of the sinusoidal control signal may be used in the above Eq. 3 to generate the third points.

As shown inFIG. 3, the third points of the sinusoidal control signal are generated using Eq. 3 during the seek until the head reaches the second track. When the head reaches the second track (at arbitrary servo sector k), the previous two points at times k−1 and k−2 (generated using Eq. 3) are used to initialize Eq. 2 (i.e., used to initialize the feed-forward compensator44). The feed-forward compensation values42are then generated using Eq. 2 including to adapt the feed-forward compensation values42while tracking the second track based on the error signal e.

In one embodiment, it may be desirable to measure an amplitude and/or phase of the sinusoidal control signal (e.g., the sinusoidal control signal shown inFIG. 3).

FIG. 4is a flow diagram according to an embodiment of the present invention which extends on the flow diagram ofFIG. 2B, wherein an amplitude and/or phase of the sinusoidal control signal is measured based on first and second points of the sinusoidal control signal (block60). In one embodiment, the amplitude of the sinusoidal control signal is generated based on the Direct Form I difference equation of Eq. 2 according to:

θ⁢yi2+yj2-2⁢yi⁢yj⁢cos⁡((i-j)⁢ω⁢⁢T)Eq.⁢4
where θ=csc((i−j)ωT) where (i−j)ωT does not equal mπ and m is an integer, yirepresents the first point, yirepresents the second point, represents a phase of the first point, and j represents a phase of the second point. In one embodiment, the phase of the sinusoidal control signal (at time k) is generated based on the Direct Form I difference equation of Eq. 2 according to:

In another embodiment, the feed-forward compensator44generates the feed-forward compensation values y(k)42based on a Direct Form II difference equation that implements the above transfer function of Eq. 1 according to:
w(k)=e(k)+2 cos(ωT)w(k−1)−w(k−2)
y(k)=τw(k−1)+γw(k−2)  Eq. 6
where T represents a sampling period of the servo sectors, ω represents a target frequency, e represents an error signal of the servo control system, and τ and γ are learning coefficients. In the above Eq. 6, the sinusoidal control signal represents an interim signal w(k) used to generate the feed-forward compensation values y(k)42. The above Eq. 6 may exhibit the same instability problem as the above Eq. 2, and therefore an alternative equation is used to generate the third points of the sinusoidal control signal when the learning mode of Eq. 6 is disabled (e.g., during a seek as shown inFIG. 3).

In one embodiment, the control circuitry is operable to generate the third points of the sinusoidal control signal according to:
w(k+n)=θ(wjsin(ωT(i+n))−wisin(ωT(j+n)))  Eq. 7
where w(k+n) represents the third point, θ=csc((i−j)ωT) where (i−j)ωT does not equal mπ and m is an integer, wirepresents the first point, wjrepresents the second point, i represents a phase of the first point, and j represents a phase of the second point. The above Eq. 7 generates the third point independent of the error signal (e.g., independent of the PES) and does not exhibit the instability problem of Eq. 6. Accordingly, the above Eq. 7 can be used to generate the feed-forward compensation values42when Eq. 6 may otherwise become unstable due to disabling the learning mode.

In one embodiment, the amplitude of the sinusoidal control signal is generated based on the Direct Form II difference equation of Eq. 6 according to:

v⁢θ⁢wi2+wj2-2⁢wi⁢wj⁢cos⁡((ⅈ-j)⁢ω⁢⁢T)Eq.⁢8
where θ=csc((i−j)ωT) where (i−j)ωT does not equal mπ and m is an integer,

v=τ2+γ2+2⁢τγ⁢⁢cos⁡(ω⁢⁢T)⁢,
wirepresents the first point, wjrepresents the second point, represents a phase of the first point, and j represents a phase of the second point. In one embodiment, the phase of the sinusoidal control signal (at time k) is generated based on the Direct Form II difference equation of Eq. 6 according to:

arctan⁡(θ⁡(wj⁢ξi,0s-wi⁢ξj,0s)θ⁡(wj⁢ξi,0c-wi⁢ξj,0c))Eq.⁢9
where θ=csc((i−j)ωT) where (i−j)ωT does not equal mπ and m is an integer,

[ξq,rsξq,rc]=[τ⁢⁢sin⁡(ω⁢⁢T⁡(q-1)+r)+γ⁢⁢sin⁡(ω⁢⁢T⁡(q-2)+r)τ⁢⁢cos⁡(ω⁢⁢T⁡(q-1)+r)+γ⁢⁢cos⁡(ω⁢⁢T⁡(q-2)+r)],
withe first point, wjrepresents the second point, i represents a phase of the first point, and j represents a phase of the second point.

Embodiments of the present invention may implement the transfer function of Eq. 1 using equations other than the Direct Form I or Direct Form II difference equations described above. In addition, the above equations that are based on the Direct Form I and Direct Form II difference equations may be implemented in any suitable manner, including using any suitable transformation that may simplify the implementation. In one embodiment, the above Eq. 3 and Eq. 7 may be implemented according to:
y(k+n)=vssin(nωT)+vccos(nωT)  Eq. 10
where for the Direct Form I of Eq. 3:
vc=θ(yjsin(iωT)−yisin(jωT))
vs=θ(yjcos(iωT)−yicos(jωT))  Eq. 11
and for the Direct Form II of Eq. 7:
(vc,vs)=θ(wjξi,0s−wiξj,0s,wjξi,0c−wiξj,0c)  Eq. 12
The magnitude of the sinusoidal control signal may be generated at any k+n according to

vc2+vs2
and the phase according to arctan

(vcvs)
with

y⁡(k+n)=vc2+vs2⁢sin⁡(n⁢⁢ω⁢⁢T+arctan⁡(vcvs))Eq.⁢13
With j=0 the equivalent of the above Eq. 3 may be computed with:
(vc,vs)=(y(k),csc(iωT)(y(k)cos(iωT)−y(k−i)))  Eq. 14
With i=2 and j=1, the equivalent of the above Eq. 7 may be computed with:
vc=γw2+τw1
vs=θ(γw1−τw2+(τw1−γw2)cos(ωT))  Eq. 15
Yet another transformation of Eq. 3 and Eq. 7 may be derived by considering arbitrary values of ρ and φ where for the Direct Form I, let y(k,φ)=ρ cos(kωT+φ) then:
(vc,vs)=ρ(cos(kωT+φ),−sin(kωT+φ))  Eq. 16
For the Direct Form II, let w(k,φ)=ρ cos(kωT+φ) then:
(vc,vs)=ρ(ξk,φc−ξk,φs)  Eq. 17
For both Direct Form I and Direct Form II, vcand vsare related to the sinusoidal feed-forward compensation values y(k) by:
(vc,vs)=(y(k,φ),y(k,φ+π/2))  Eq. 18

In one embodiment of the present invention, the magnitude and/or phase of the repeatable disturbance may vary based on the radial location of the head. To compensate for this variation, in one embodiment the tracks20ofFIG. 2Aare grouped together to define a plurality of zones, wherein a different sinusoidal control signal may be generated for each zone to compensate for the difference in the repeatable disturbance. In one embodiment, the control circuitry26saves two points of the sinusoidal control signal for each zone, wherein the two points of each zone are used to initialize the feed-forward compensator44when the head seeks into a different zone.

This embodiment is understood with reference to the flow diagram ofFIG. 5Aand as illustrated by the example ofFIG. 5B. After seeking the head to a first zone (block62) and initializing the feed-forward compensator with the two points saved for the first zone, the sinusoidal control signal is generated in response to the servo sectors (block64). The feed-forward compensation values are generated based on the sinusoidal control signal (block66), including to adapt the sinusoidal control signal and the corresponding feed-forward compensation values (e.g., using Eq. 2 or Eq. 6). Prior to the head seeking out of the first zone, two points of the adapted sinusoidal control signal are saved (block68) and used to initialize the feed-forward compensator when the head returns to the first zone. The control circuitry then seeks the head from the first zone to a second zone (block70), generates third points of the sinusoidal control signal based on the saved first and second points for the second zone (block72), and initializes the feed-forward compensator based on the third points (block74).

In one embodiment, while seeking the head from the first zone to the second zone the third points of the sinusoidal control signal are generated as described above with reference toFIG. 3(i.e., using Eq. 3 or Eq. 7). The sinusoidal control signal used to generate the third points ofFIG. 3may correspond to the first or second zone. For example, in one embodiment the sinusoidal control signal used to generate the third points ofFIG. 3may correspond to the first zone. The third points may be generated based on the first zone up until the head crosses the zone boundary, or until the head reaches the target track within the second zone. In yet another embodiment, the sinusoidal control signal used to generate the third points during the seek may correspond to the second zone. That is, the first and second points saved for the second zone may be used to generate the third points ofFIG. 3(e.g., using Eq. 3 or Eq. 7) throughout the entire seek operation from the first zone to the second zone.

The phase of the first and second points saved for each zone does not affect the ability to generate the third points during the seek, or to initialize the feed-forward compensator after the seek. As described above, in one embodiment the first and second points are saved when the head seeks away from a current zone, and therefore the saved first and second points may have any arbitrary phase. In the example shown inFIG. 5B, the first and second points saved for the second zone have an arbitrary phase with respect to the phase of the head after it reaches the target track within the second zone at the end of the seek. Regardless as to the phase of the first and second points, the third and fourth points of the sinusoidal control signal shown inFIG. 5Bcan be generated based on the first and second points (e.g., using Eq. 3 or Eq. 7), wherein the third and fourth points are used to initialize the feed-forward compensator at the end of the seek operation. If the sinusoidal control signal for the second zone is used to generate the third points ofFIG. 3during the seek to the second zone, then the third and fourth points shown inFIG. 5Bwill already have been generated at the end of the seek operation. If the sinusoidal control signal for the first zone is used to generate the third points ofFIG. 3during the seek to the second zone, then the third and fourth points shown inFIG. 5Bare generated using the first and second saved points for the second zone (independent of the seek operation). After initializing the feed-forward compensator, the sinusoidal control signal and feed-forward compensation values are adapted (e.g., using Eq. 2 or Eq. 6), and then two of the adapted points of the sinusoidal control signal are saved when the head seeks away from the second zone.