PES linearization scheme for disk drive servo using small excitation bode measurements

[0002] This invention generally relates to methods of determining positions of the head element in a storage medium assembly to maximize the accuracy of a read or write operation of that head element, more particularly the invention relates to methods of measuring the non-linear relationship between measured servo burst amplitudes and head position to improve the accuracy of the servo positioning system.

[0003] In a typical disk drive assembly, methods of determining head element positions to enable accurate read and write operations include having a servo writer write track and burst data information into each of various spoke regions distributed at radial intervals across each track of a disk medium. The track and burst information at each spoke region is then used to identify a corresponding radial position on that track. As illustrated in FIG. 1, a prior technique to determine a radial position of the head element on a particular track is to measure the read-back amplitude, or servo burst amplitude, and determine the amount of overlap of that measured head position (i.e., x_m) to a pair of servo bursts, such as burst amplitude A 14 and burst amplitude C 16. When head element 12 overlaps equally both burst amplitudes A and C, i.e., amplitude measured for burst A equals amplitude measured for burst C (A=C), head element 12 is then considered centered over that track for an accurate write operation. However, with greater use of magneto-resistive (MR) heads in disk drives, typical servo burst amplitudes no longer vary linearly with cross-track position as was more common with inductive heads. The amount of non-linearity can vary with skew angle.

[0004] Thus, if the relationship between the head position to burst amplitudes is non-linear, then error in the perceived position occurs unless the disk drive assembly accounts for that non-linearity. Correspondingly, unless this non-linearity is taken into account in calculating the head position, an increased likelihood of errors in write and read operations can occur.

[0005] Various schemes have been proposed to address the problem raised by this non-linearity including methods of determining head element positions to enable accurate read and write operations. One technique provides a three pass track servo write to use smaller, more linear regions of the cross track profile. Yet another method would be to increase the number of burst combinations used so that each combination is used across only a quarter track instead of half track to provide another approach to use a smaller, more linear region of the head profile While these methods reduce the effect of the head non-linearities, they make no attempt to compensate for them directly.

[0006] There is therefore a need for an improved method of calculating the effect of the non-linearity of head element to provide more accurately measured head position for read and write operations in disk drives.

[0007] A PES linearization scheme using small excitation bode measurements is provided to account for non-linearity characteristics during measurements of head element positions so to generate a more accurate read and write operation by a head element of a disk drive assembly. The PES linearization scheme of this invention provides making gain measurements as the head element moves across the track, and then integrating the result to get a relative PES profile. By then finding two points on the profile a known distance apart, we can multiply the profile by the appropriate gain factor to get an actual PES profile. This profile can be then be used as a look up table to convert raw PES numbers into actual position.

[0008] FIG. 1 illustrates prior art head element positions relative to a previously written and stored burst pattern;

[0009] FIG. 2A illustrates prior art graphical representation of a linear relationship from measured burst amplitude difference (A−C) to head position x;

[0010] FIG. 2B illustrates a prior art graphical representation of a non-linear relationship from measured burst amplitude difference (A−C) to head position

[0011] FIG. 3 illustrates a PES linearization system provided in accordance with the principles of this invention;

[0012] FIG. 4 illustrates a flowchart of a PES linearization method for positional data in accordance with the principles of this invention

[0013] FIG. 5 illustrates a graphical representation of measurements made by a head element assembly of FIG. 3 relative to measured head position x_m; and

[0014] FIG. 6 illustrates a graphical representation of an integration of function illustrated in FIG. 5.

[0015] FIG. 3 illustrates a PES linearization system provided in accordance with the principles of this invention. FIG. 4. illustrates a flow diagram of a PES linearization method 100 for operating PES linarization system 10 of FIG. 3 in accordance with the principles of this invention. In step 101, a sinusoidal electrical current I_excis injected into a rotator coil 11 of head element 12 at a frequency 𝑓 and at a sufficient amplitude to cause a corresponding small movement x of head element 12 at preferably about 2-3% of track distance. Head element 12 is thus moved across a track of a storage device (not shown), such as a disk drive, in small increments while measuring the transfer function from excitation current to measured burst amplitude difference at frequency f using a Discrete Fourier Transform (DFT), wherein $\begin{array}{cc}\frac{\Delta \left(A-C\right)}{\Delta I_{\mathrm{exc}}}=\frac{\partial \left(A\left(k\right)-C\left(k\right)\right)}{\partial I_{\mathrm{exc}}\left(k\right)}{|}_{k=\mathrm{NfT}}& \text{Eqn. 1}\end{array}$

[0016] where

[0017] f=frequency of excitation current

[0018] N=number of sample points

[0019] T=sample time

[0020] If $\frac{\Delta \left(A-C\right)}{\Delta I_{\mathrm{exc}}}$

[0021] from Eqn 1 is described as the gain, then the inverse gain is: $\begin{array}{cc}\mathrm{Inverse}\mathrm{gain}=\frac{\Delta I_{\mathrm{exc}}}{\Delta \left(A-C\right)}& \text{Eqn. 2}\end{array}$

[0022] Since the distance the head moves is proportional to the excitation current, substitute kΔx for ΔI_exc, then $\begin{array}{cc}\mathrm{Inverse}\mathrm{gain}=\frac{k\Delta x}{\Delta \left(A-C\right)}& \text{Eqn. 3}\end{array}$

[0023] with x equivalent to actual head position of head element 12.

[0024] Thus, head element 12 is repeatedly moved in small increment radially across a center point where bursts A equally overlaps C (i.e., track center 0 ) while a transfer function measurement (Eqn. 1) is made at each corresponding small incremental position. FIG. 5 illustrates a resulting graphical representation of a set of such resulting measurements. This set of measurements is referred to as the inverse gain profile. Then as illustrated in FIG. 6, an integration of the inverse gain profile generates a relative position profile. Since the function illustrated in FIG. 4 is a discrete series, use a summation to approximate the integration $\begin{array}{cc}\mathrm{kx}=\sum \left(\frac{k\Delta x}{\Delta \left(A-C\right)}*\Delta \left(A-C\right)\right)& \text{Eqn. 4}\end{array}$

[0025] Specifically, this summation can take the form of a trapezoidal approximation to the integral: $\begin{array}{cc}{\mathrm{kx}}_{n+1}={\mathrm{kx}}_n+\frac{1}{2}\left(\frac{k\Delta x_n}{\Delta {\left(A-C\right)}_n}+\frac{k\Delta x_{n+1}}{\Delta {\left(A-C\right)}_{n+1}}\right)*\left({\left(A-C\right)}_{n+1}-{\left(A-C\right)}_n\right)& \text{Eqn. 5}\end{array}$

[0026] To convert relative position to actual position, solve for k. Two reference points of known distance apart are selected. Because the bursts are written by the servo writer at exactly one half track intervals, the distance from where A equals B to where B equals C for the burst pattern as shown in FIG. 3 is known to be exactly one half track. This can be expressed as: $\begin{array}{cc}\mathrm{kx}\left(B=C\right)-\mathrm{kx}\left(A=B\right)=\frac{1}{2}& \text{Eqn. 6}\end{array}$

[0027] Solve for k to generate a table which translates from burst amplitude difference to actual position as shown in FIG. 2B. The profile measurements are preferably done during the manufacturing process. A table of actual positions vs. burst amplitude differences calculated for each head is then written into one or more lookup tables stored in the system cylinders of the drive. These lookup tables are then read back from the system cylinders during the power-up stage of the drive. To determine a position to move head element 12, the head element 12 senses the burst values, then the drive firmware looks up the result in the appropriate lookup table and interpolates between two consecutive entries.

[0028] One advantage of PES linearization scheme of this invention over schemes that do not linearize is unlike methods which use a smaller region of the head profile to reduce the amount of non-linearity, this scheme measures and accounts for the non-linearity. The, result is less error in position measurement, less error in the servo loop gain, and smaller discontinuities between quadrant boundaries. Being able to use servo bursts outside of their linear region makes it possible to consider a wider range of PES including schemes which use all four bursts to determine position.

[0029] Foregoing described embodiments of the invention are provided as illustrations and descriptions. They are not intended to limit the invention to precise form described. In particular, it is contemplate that functional implementation of invention described herein may be implemented equivalently in hardware, software, firmware, and/or other available functional components or building blocks. Other variations and embodiments are possible in light of above teachings, and it is thus intended that the scope of invention not be limited by this Detailed Description, but rather by claims following.