WO2001008139A1

WO2001008139A1 - Repeatable runout compensation using a learning algorithm with scheduled parameters

Info

Publication number: WO2001008139A1
Application number: PCT/US2000/001735
Authority: WO
Inventors: Yangquan Chen; Leeling Tan; Kiankeong Ooi; Qiang Bi; Kokhiang Cheong
Original assignee: Seagate Technology Llc
Priority date: 1999-07-23
Filing date: 2000-01-21
Publication date: 2001-02-01
Also published as: CN1363087A; JP2003505818A; GB2366660A; DE10084854T1; KR20020025197A; US6437936B1; GB2366660B

Abstract

A method and apparatus for compensating for written-in repeatable runout in a disc drive (100) is provided. Compensation values are determined through an iterative learning process in which parameters of the learning process such as learning gain, servo loop gain, etc. are functions of the iteration number. The learning process also employs a nominal double integrator model of an actuator of the disc storage system (100). The learning process is also a function of a zero-phase low-pass filter.

Description

REPEATABLE RUNOUT COMPENSATION USING A LEARNING ALGORITHM WITH SCHEDULED PARAMETERS

FIELD OF THE INVENTION The present invention relates generally to disc dπve data storage systems More particularly, the present invention relates to compensation for errors in servo systems

BACKGROUND OF THE INVENTION Disc drives read and write information along concentπc tracks formed on discs To locate a particular track on a disc, disc drives typically use embedded servo fields on the disc These embedded fields are utilized by a servo subsystem to position a head over a particular track The servo fields are written onto the disc when the disc dπve is manufactured and are thereafter simply read by the disc drive to determine position A multi-rate servo system samples the position of the head relative to a particular track at a particular sampling rate and adjusts the position of the head at a rate that is a multiple of the sampling rate by estimating the position of the head between the measured position samples

Ideally, a head following the center of a track moves along a perfectly circular path around the disc However, two types of errors prevent heads from following this ideal path The first type of error is a wπtten-in error that aπses during the creation of the servo fields Wπtten-in errors occur because the wπte head used to produce the servo fields does not always follow a perfectly circular path due to unpredictable pressure effects on the write head from the aerodynamics of its flight over the disc, and from vibrations in the gimbal used to support the head Because of these wntten-in errors, a head that perfectly tracks the path followed by the servo wπte head will not follow a circular path

The second type of error that prevents circular paths is known as a track following eπor Track following errors aπse as a head attempts to follow the path defined by the servo fields The track following eσors can be caused bv the same aerodynamic and vibrational effects that create wπtten-in errors In addition, track following errors can arise because the servo system is unable to respond fast enough to high frequency changes in the path defined by the servo fields

Wπtten-in eπors are often referred to as repeatable runout errors because they cause the same errors each time the head moves along a track As track densities increase, these repeatable runout errors begin to limit the track pitch Specifically, variations between the ideal track path and the actual track path created by the servo fields can result in an inner track path that interferes with an outer track path This is especially acute when a first wntten-in error causes a head to be outside of an inner track's ideal circular path and a second wπtten-in error causes the head to be inside of an outer track's ideal circular path To avoid limitations on the track pitch, a system is needed to compensate for repeatable runout errors

The present invention provides a solution to this and other problems and offers othei advantages over t e prior art SUMMARY OF THE INVENTION

The present invention offers a method and apparatus for compensating for wntten-in repeatable runout in a disc drive which soh es the aforementioned problems In one aspect, repeatable runout (RRO) errors in a disc drive having a servo loop for positioning a head relative to a track on a disc surface of a rotating disc using compensation values Compensation values can be determined through a learning process which uses a nominal value (P_n) of an actuator of the disc drive In another aspect, the learning process is an iterative process and the learning gain is a function of a learning iteration number In another aspect, a gain of the servo loop is a function of a learning iteration number In yet another aspect, the learning process includes a zero-phase low- pass filter

BRIEF DESCRIPTION OF THE DRAWINGS FIG 1 is a plan view of a disc drive of the present invention FIG 2 is a top view of a section of a disc showing an ideal track and a realized wntten-in track

FIG 3 is a block diagram of a learning process for a servo loop in accordance with the present invention DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

FIG 1 is a plan view of a disc dπve 100 that includes a housing with a base plate 102 and a top cover 104 (sections of top cover 104 are removed for claπty) Disc drive 100 further includes a disc pack 106, which is mounted on a spindle motor (not shown) Disc pack 106 can include a plurality of individual discs which are mounted for co-rotation about a central axis Each disc surface has an associated head gimbal assembly (HGA) 1 12 which is mounted to disc dπve 100 for communication with the disc surface Each HGA 112 includes a gimbal and a slider, which cames one or more read and write heads Each HGA 112 is supported by a suspension 118 which is in turn attached to a track accessing arm 20 known generally as a fixture, of an actuator assembly 122

Actuator assembly 122 is rotated about a shaft 126 by a voice coil motor 124, which is controlled by servo control circuitry within internal circuit 128 HGA 112 travels in an arcuate path 130 between a disc inner diameter 132 and a disc outer diameter 134 When the head is properly positioned, wπte circuitry within internal circuitry 128 encodes data for storage on the disc and sends an encoded signal to the head in HGA 112, which writes the information to the disc At other times, the read head in HGA 1 12 reads stored information from the disc and provides a recovered signal to detector circuitry and decoder circuitry within internal circuitry 128 to produce a recovered data signal FIG 2 is a top view of a section 198 of a disc showing an ideal, perfectly circular track 200 and an actual track 202 Section 198 includes a plurality of radially extending servo fields such as servo fields 204 and 206 The servo fields include servo information that identifies the location of actual track 202 along disc section 198

SUBSTTT Any vaπation in the position of a head away from circular track 200 is considered a position error The portions of track 202 that do not follow circular track 200 create wπtten-in repeatable runout position eπors A position error is considered a repeatable runout eπor if the same eπor occurs each time the head passes a particular circumferential location on the disc Track 202 creates a repeatable runout eπor because each time a head follows the servo fields that define track 202, it produces the same position error relative to ideal track 200 Under the present invention, a head attempting to wπte to or read from track 202 will not follow track 202 but instead will more closely follow perfectly circular track 200 This is accomplished using a compensation signal that prevents the servo system from tracking repeatable runout eπors resulting from the lπegular shape of track 202

As described in the Background section, one of the major head positioning eπor sources is the repeatable disturbance caused by spindle motor and wntten-in eπor duπng servo writing (WI-RRO , l e , the Repeatable Runout (RRO) wπtten in by the Servo Track Writer) Another eπor source is the non- repeatable disturbance caused by sources such as spindle ball bearing defects, rocking modes, disk vibration and so on A number of methods have been proposed to address repeatable disturbances These methods can be categoπzed into two groups In the first group, such as AFC (adaptive feedforward compensation), eπors are rejected by feedforward terms generated outside the main feedback loop A disadvantage of these methods is their intensive computational load, especially when the rejection of multiple disturbances is required In the second group, eπor rejection signals are generated inside the feedback loop One method is internal-model-based repetitive control This has been demonstrated to be effective in rejecting repeatable disturbances in hard disk drives However, this approach tends to amplify non-repeatable disturbances which are at frequencies between those of the repeatable disturbances

SUBSTTT To address WI-RRO, a possible approach is referred to as the Zero Acceleration Path (ZAP) concept which is often referred to as Repeatable Runout Compensation It is a non-adaptive feedforward technique to compensate the WI-RRO in front of the feedback controller C(s) This is different with AFC (adaptive feedforward compensation) technique for rejecting RRO induced by the spindle motor In AFC the compensation occurs after the feedback controller C(s)

To understand the ZAP concept, consider FIG 2 The track 202 represents the track center after the servo write process Because of the various disturbances which occurred duπng the servo writing process, the track center is not ideally smooth and is difficult to follow by the actuator This will result in a repeatable Position Error Signal (PES) However, if an appropπate coπection amount is subtracted from the position measurement signal at each servo sector/sample, the original zigzag path becomes smooth, l e the track center becomes a perfect circle such as track 200 If the non-repeatable position disturbances are ignored, this perfectly circular track center can be followed with "zero actuator acceleration" (ZAP) technique

The improvement achieved by the ZAP concept depends on the accuracy of the coπection values that are subtracted from the position measurement samples at respective sectors The ZAP coπection value versus sector for each track is a deterministic profile which can also be regarded as a deterministic time function when the spindle motor velocity is kept constant Determining this profile is actually a curve identification problem in a dynamic system, which in turn can be regarded as an optimal control Or dynamic optimization problem Several different techniques can be used to extract the deterministic WI-

RRO profiles, or to compute the coπection values However, typical procedures involve complicated calculations, and require many revolutions for each track Therefore, a practical and inexpensive implementation of the ZAP concept has been difficult The challenge is to find a practically implementable method to determine the ZAP profile The computations should be easily implementable in a cheaper processor, and satisfactory accuracy should be achieved within 10 revolutions

FIG 3 is a simplified block diagram of a servo control system 300 in accordance with one embodiment of the invention Control system 300 includes a servo controller 302 identified as C(z) Actuator 304 is modeled as P(s) and a nominal model of the actuator 306 is modeled as P_n(s) ZAP compensation values are determined in accordance with a learning updating law 308 The simplified block diagram of FIG 3 shows servo controller system 300 One difference comparison to other techniques is the use of the nominal model P_n(s) of the voice coil motor (actuator) VCM for ZAP profile learning In FIG 3, the position disturbance signal which is superimposed on the actual head position > _{head '} ^{nas a} repeatable (d_w ) component and a non-repeatable (d_n ) component The updating law for ZAP profile learning is given by d£' _P (t) = d₂ ^k _AP (t) + γ_kZPF(ω_k, z, z- )[PES_k + /^>„ (*)"*] ^EQ ) where d_u" _p(t) is the ZAP profile at the k- learning iteration for sector number t, γ_k is the learning gain at the Ar-th learning iteration, ZPF(ω_k ,z,z^~λ ) is a zerophase low-pass filter with a cut-off frequency o_k scheduled for the k-_\ learning iteration, PES_k is the positional error signal at the k-th learning iteration, P_n (s) is the nominal VCM (actuator) model which is a double- integrator with a nominal gain available from measurement and u _lh is the control signal sent to actuator 304

In order to minimize the effect of non-repeatable runout (NRRO) on the ZAP learning performance when the SNR (signal to noise ratio I e , variance ratio of RRO over NRRO) is small, it is preferable to use the averaged PES_k and u of several revolutions in EQ (1) However, when servo controller is well designed and the SNR is high, such an averaging process is not required When the NRRO component is dominant, the temperal trend in it _ft, should be removed using de-mean, de-trend block 310 Also, the mean in

PES_k should be removed with block 310 before it is sent to block 306

One aspect of the present invention includes the recognition that improved learning can be achieved using EQ (1) in which various parameters are '"scheduled", that is, the parameters change the values as a function of a learmng iteration number For example, the cutoff frequency of the zero-phase low pass filter (ZPF) can change as a function of k, the learning iteration number For example, the cutoff frequency can change from low values (for example, several multiples of the bandwidth frequency of the servo loop) to a value of approximately the Nyquist frequency of the system In another aspect, the gain, γ_k , of the servo loop can change as a function of the learning iteration number For example, the gain of the servo loop can change from a smaller value to a larger value for subsequent iterations These are referred to as "scheduled parameters " Preferably, the learning gain of EQ (1) changes as a function of the learning iteration number For example, the learning gain can be adjusted such that EQ (1) initially learns the low frequency content of the wntten-in repeatable runout

With the present invention, the ZAP profile can be learned in accordance with a learning update law Preferably, the unknown but deterministic repeatable (WI-RRO) can be regarded as a virtual control input By trying different virtual control inputs, different tracking eπors, l e , PES's are recorded For a present trial input, l e , d_Z ^k _4P(t) , the learned value is composed of previous control effort d_ZiP(t) and the resulting tracking eπor PES_k In general, the learning updating law can be written as d_z:_p(t) =

, EQ (2) where f(») is a learning operator in a general form The following linear form can be used d_ _>(t) = d_ZiP(t) + f(PES^k (/)) EQ (3)

In runout compensation, it can be shown that

where r is set point which can be considered as 0 (see FIG 3) without loss of generality

By iterating EQ (4), the following is obtained

PES^k [r-d^-d_^-d_Z ^k _4P(t)-f(PES^k(t))} +P(s)C(z)

EQ (5) f 1

= 0- )PES^k

\ + PC \ + PC ⁽ '-

Next, denote p(ω) by i p{3)_^\~--—- fω),

^PC EQ (6) where p(ω) represents the learning rate as shown below By iterating EQ (4), one obtains

where d_n is an upper bound of d^k'] -d_n", l e , d_n > d_n ^k' -d^k, /t,k The

convergence condition is obtained with

where ω_s is the sampling frequency Similarly, starting from EQ (3), it can be shown

SUBSTTTUTE SHEET (RULE 26) = P'"W (\ - p(ω))∑p^> {ω)d^k ' (^l - ^⁺'⁽ω) * -^ =0 EQ (9)

From EQ (9), it can be shown d_ZiP converges to - d_w , the WI-RRO, as long as p_u < 1 Without any priori information, d__iP should be normally set to 0

With the ZAP concept, it is preferable to find an iterative learning operator ((•) such that PES can be reduced to a desirable level in only a few learning iterations When p_ω in EQ (8) is zero, the learning converges in only one iteration This implies that the ideal learning operator should be chosen as

f(jω) = \ + P(s)C(z), ft)

EQ (10)

However, this is not realistic since there are always uncertainties in a disc drive system Through the use of scheduled parameters of the invention, improved learning can be achieved Preferably, the learning gain of the present invention is scheduled to initially learn low frequency RRO In the present invention, refeπing to FIG 3, the learning operator is written as f(_*) = _rkZPF(ω_k , z, z-^] )[\ + P_n(s)C(z)] EQ (11)

In one aspect, the open loop gain of the servo loop is "scheduled" during learning Using scheduling parameters during ZAP profile learning can give additional benefits in improving the learning performance The following provides an in-depth discussion on servo-loop-gain scheduling

By adjusting K _a , the servo loop gain, duπng the ZAP learning process, the learning performance can be improved Suppose at the

iteration, (K )_k - a_kK_a ^* where K is the nominal K_a obtained from a system K_a -table (from outer to inner diameter) According to the learning updating law of EQ (1), the learning rate is given by

As discussed above, from EQ (12) r_k and ω_λ are used for conditioning the learning rate p(co) over a frequency range of interest Now, define the sensitivity functions

S^k(jω) = \l(\ + a PC){jω), EQ (13)

S_n ^k(jω) = \l(\ + a_kP_πC)(jω) EQ (14)

Suppose that the ZAP learning process is started with a smaller a_^ and then increased cc_k as the number of learning iterations increases, I e , a^k > a^k~l EQ (15)

For servo control systems S_n ^k(jω) < S^^k (jω)^, EQ (16)

S^k(jω) <S^k-^l(j ) EQ (17) It is true that at a low frequency band

This is an significant feature, which can be used to condition the learning rate Here, the learning rate is given by

The loop gain scheduling is achieved by setting the loop gain before PES/u _β data collecting Too aggressive a reduction ιn£^ may not bring the expected improvement However, using a = -3dB and α, = -2dB typically provides improved learning

Phase advance scheduling can be used to address mismatch between P_nC(jω) and PC(jω) , I e ,

SUBSTTTUTE SHEET (RULE 26) \ + P c ^{^}ZPF(ω_k , z, z^'' )—^-(jω)

" ^{= | =} ! ₊ i^>C ^{" ' ■} EQ (20) where the phase advance step

another scheduled parameter This is particularly useful when total number of iterations is large However, scheduling this parameter may not be particularly advantageous in ZAP profile learning because it is normally desirable to use as few as possible iterations during learning process

In order to address high frequency noise problems, signal averaging and parameter scheduling are used The convergence bound of PES in EQ (4) can be reexamined EQ (6) can be written as

PES^k'^l = p^ ω)PES - -^—{d^ - p^k (ω)d_n ⁰ - (\ - p(ω)) _ip^J (ω)d^ }

^{1 +} -PC ^ EQ (21)

Note that 1 /(l + PC) , the sensitivity transfer function, is actually a high-pass

A -l filter which means that </*^"' - p^k (ω)d_n ^ϋ -(\ ~ p(ω))∑p^J (ω)d_n ^k-^] _m EQ (21)

can be amplified at very high frequencies This problem exists in all iterative learning methods Frequency domain trade-off is required and suitable filtering is essential However, better result is still achievable when d_n has some special characteristics along the time (sector) axis as well as iteration number (revolution number) axis For example, if α^ has some repetitiveness or near zero-mean over multiple iterations (revolutions), the effect of d_n can be reduced to an acceptable level using an algebraic averaging method over a number of revolutions High-frequencv amplification still exists but may not be very significant duπng just a number of initial iterations The number of revolutions required in ZAP profile learning depends on SNR (the ratio of variance of RRO over NRRO) If the SNR is high, one revolution per iteration may be sufficient for the initial learning ιteratιon(s) Typically, due to SNR and the high- frequency amplification considerations, the scheduling of parameters in the

SUBSTTTUTE SHEET (RULE 26) learmng process can be successfully employed such that the practical constraints are met and improved compromises are made between learning rate and accuracy

The present invention includes an apparatus and method for compensating for repeatable runout (RRO) eπors in a disc drive 100 having a servo loop 300 for positioning a head 112 relative to a track 200 on disc surface of a rotating disc 198 In the invention, a servo position value is retπeved from the disc 198 which is indicative of head 112 position relative to track 200 Compensation ZAP values are retπeved from a table of compensation values and the servo position value is compensated based upon the retπeved compensation value In one aspect, the compensation values are determined through a learning process which uses a nominal P_n of an actuator of the disc drive 100 In an iterative learning process, the learmng gain γ_k is a function of a learning iteration number Similarly, the iterative learning process is a function of a servo loop gain which is a function of an iteration number The learning process can also include a zero-phase low-pass filter in which the cut-off frequency can be a function of an iteration number

It is to be understood that even though numerous characteristics and advantages of various embodiments of the present invention have been set forth in the foregoing description, together with details of the structure and function of various embodiments of the invention, this disclosure is illustrative only, and changes may be made in details, especially in matters of structure and aπangement of parts within the principles of the present invention to the full extent indicated by the broad general meaning of the terms in which the appended claims are expressed For example, other learning algorithms or techniques can be used that implement the present invention without departing from the scope and spirit of the present invention

Claims

-ι:WHAT IS CLAIMED IS1 A method for compensating for repeatable runout (RRO) eπors in a disc drive having a servo loop for positioning a head relative to a track on a disc surface of a rotating disc, comprising (a)retπevιng a servo position value from the disc surface indication of head position relative to the track, (b)retπevιng a compensation value dzAP from a table of compensation values, and (c)compensatιng the servo position value with the compensation value dZAp,(d)whereιn the compensation values are determined through an iterative learning process which uses a nominal Pn of an actuator of the disc drive2 The method of claim 1 wherein Pn is a nominal VCM transfer function, a double integrator with a lumped gain3 The method of claim 1 wherein the learning process is further a function of a servo loop gain which is a function of an iteration number4 The method of claim 3 wherein the servo loop gain increases with each iteration from a value lower than the nominal value 5 The method of claim 1 wherein the learning process is a function of a zero-phase low-pass filter6 The method of claim 5 wherein a cutoff frequency of the zero-phase low- pass filter is a function of an iteration number7 The method of claim 6 wherein the cutoff frequency of the zero-phase low-pass filter increases with each iteration number8 The method of claim 1 wherein the learning process is an iterative learning process and the learning process is a function of a learning gain which is a function of iteration number 9 The method of claim 8 wherein the learning gain is selected such that low frequency values are initially learned10 The method of claim 1 wherein the learning process includes a step of mean removing 11 The method of claim 1 wherein the learning process includes removing a trend12 A disc storage system implementing the method of claim 113 A disc storage system, comprising a disc configured to rotate and including a disc surface having a track thereon, a transducing element configured to read and write information on the disc, an actuator configured to move the transducing element radially across the disc surface, a servo loop configured to control movement of the actuator in response to an error signal and a compensation value, the compensation value derived through an iterative learning process which uses a nominal Pn of the actuator14 The disc storage system of claim 13 wherein Pn ιs a nominal voice coil motor (VCM) transfer function comprising a double integrator with a lumped15 The disc storage s stem of claim 13 wherein the learning process is further a function of a servo loop gain which is a function of an iteration number 16 The disc storage system of claim 15 wherein the servo loop gain increases with each iteration from a value lower than the nominal value 17 The disc storage svstem of claim 13 wherein the learning process is a function of a zero-phase lo -pass filterSUBSTT 18 The disc storage system of claim 17 wherein a cutoff frequency of the zero-phase low-pass filter is a function of an iteration number19 The disc storage system of claim 13 wherein the learning process is an iterative learning process and the learning process is a function of a learning gain which is a function of iteration number20 A disc storage system, comprising a transducer configured to read and write information on a disc, and servo control means for controlling movement of the transducer based upon an iterative learning process AMENDED CLAIMS[received by the International Bureau on 11 August 2000 (11.08.00); original claims 1-20 replaced by new claims 1-10 (2 pages)]WHAT IS CLAIMED IS:

1. A method for compensating for repeatable runout (RRO) errors in a disc drive having a servo loop for positioning a head relative to a track on a disc surface of a rotating disc, comprising: (a)retrieving a servo position value from the disc surface indication of head position relative to the track; (b)retrieving a compensation value dzApfrom a table of compensation values; and (c)compensating the servo position value with the compensation value dzAp;

(d)wherein the compensation values are determined through an iterative learning process which uses a nominal P„ of an actuator of the disc drive.

2. A disc storage system, comprising: a disc configured to rotate and including a disc surface having a track thereon; a transducing element configured to read and write information on the disc; an actuator configured to move the transducing element radially across the disc surface; a servo loop configured to control movement of the actuator in response to an error signal and a compensation value, the compensation value derived through an iterative learning process which uses a nominal P_n of the actuator.

3. The invention of claims 1 or 2 wherein P„ is a nominal voice coil motor

(VCM) transfer function comprising a double integrator with a lumped gain.

4. The invention of claims 1 or 2 wherein the learning process is further a function of a servo loop gain which is a function of an iteration number.

5. The invention of claim 4 wherein the servo loop gain increases with each iteration from a value lower than the nominal value.

6. The invention of claims 1 or 2 wherein the learning process is a function of a zero-phase low-pass filter.

7. The invention of claim 6 wherein a cutoff frequency of the zero-phase low-pass filter is a function of an iteration number.

8. The invention of claim 1 or 2 wherein the learning process is an iterative learning process and the learning process is a function of a learning gain which is a function of iteration number.

9. The invention of claim 8 wherein the learning gain is selected such that low frequency values are initially learned.

10. The invention of claim 1 wherein the learning process includes a step of mean removing.