Patent Publication Number: US-7224543-B1

Title: Method and apparatus for reducing off-track writes in data storage devices

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     Priority is claimed from U.S. Provisional Patent Application Ser. No. 60/476,128 filed Jun. 5, 2003, which is incorporated herein by reference in its entirety. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates generally to data storage devices, such as disk drives. More particularly, the present invention relates to a method and apparatus for reducing or preventing occurrences of off-track writes in data storage devices. 
     BACKGROUND OF THE INVENTION 
     Computer disk drives store information on magnetic disks. Typically, the information is stored on each disk in concentric tracks that are divided into sectors. Information is written to and read from a disk by a transducer that is mounted on an actuator arm capable of moving the transducer radially over the disk. Accordingly, the movement of the actuator arm allows the transducer to access different tracks. The disk is rotated by a spindle motor at high speed which allows the transducer to access different sectors on the disk. 
     A conventional disk drive, generally designated  10 , is illustrated in  FIG. 1 . The disk drive comprises a disk  12  that is rotated by a spin motor  14 . The spin motor  14  is mounted to a base plate  16 . 
     The disk drive  10  also includes an actuator arm assembly  18 , which includes a transducer  20  (wherein the transducer has both a write head and a read head) mounted to a flexure arm  22 . The actuator arm assembly  18  is attached to an actuator arm  24  that can rotate about a bearing assembly  26 . A voice coil motor  28  cooperates with the actuator arm  24  and, hence, the actuator arm assembly  18 , to move the transducer  20  relative to the disk  12 . The spin motor  14 , voice coil motor  28  and transducer  20  are coupled to a number of electronic circuits  30  mounted to a printed circuit board  32 . The electronic circuits  30  typically include a read channel chip, a microprocessor-based controller and a random access memory (RAM) device. 
     The disk drive  10  typically includes a plurality of disks  12  and, therefore, a plurality of corresponding actuator arm assemblies  18 . However, it is also possible for the disk drive  10  to include a single disk  12  as shown in  FIG. 1 . 
       FIG. 2  is a functional block diagram which illustrates a conventional disk drive  10  that is coupled to a host computer  33  via an input/output port  34 . The disk drive  10  is used by the host computer  33  as a data storage device. The host  33  delivers data access requests to the disk drive  10  via port  34 . The port  34  is also used to transfer customer data between the disk drive  10  and the host  33  during read and write operations. 
     In addition to the components of the disk drive  10  shown and labeled in  FIG. 1 ,  FIG. 2  illustrates (in block diagram form) the disk drive&#39;s controller  36 , read/write channel  38  and interface  40 . Conventionally, data is stored on the disk  12  in substantially concentric data storage tracks on its surface. In a disk drive  10 , for example, data is stored in the form of magnetic polarity transitions within each track. Data is “read” from the disk  12  by positioning the transducer  20  (i.e., the transducer&#39;s read head) above a desired track of the disk  12  and sensing the magnetic polarity transitions stored within the track, as the track moves below the transducer  20 . Similarly, data is “written” to the disk  12  by positioning the transducer  20  (i.e., the transducer&#39;s write head) above a desired track and delivering a write current representative of the desired data to the transducer  20  at an appropriate time. 
     The actuator arm assembly  18  is a semi-rigid member that acts as a support structure for the transducer  20 , holding it above the surface of the disk  12 . The actuator arm assembly  18  is coupled at one end to the transducer  20  and at another end to the VCM  28 . The VCM  28  is operative for imparting controlled motion to the actuator arm  18  to appropriately position the transducer  20  with respect to the disk  12 . The VCM  28  operates in response to a control signal i control  generated by the controller  36 . The controller  36  generates the control signal i control  in response to, among other things, an access command received from the host computer  33  via the interface  40 . 
     The read/write channel  38  is operative for appropriately processing the data being read from/written to the disk  12 . For example, during a read operation, the read/write channel  38  converts an analog read signal generated by the transducer  20  into a digital data signal that can be recognized by the controller  36 . The channel  38  is also generally capable of recovering timing information from the analog read signal. During a write operation, the read/write channel  38  converts customer data received from the host  32  into a write current signal that is delivered to the transducer  20  to “write” the customer data to an appropriate portion of the disk  12 . The read/write channel  38  is also operative for continually processing data read from servo information stored on the disk  12  and delivering the processed data to the controller  36  for use in, for example, transducer positioning. 
       FIG. 3  is a top view of a magnetic storage disk  12  illustrating a typical organization of data on the surface of the disk  12 . As shown, the disk  12  includes a plurality of concentric data storage tracks  42 , which are used for storing data on the disk  12 . The data storage tracks  42  are illustrated as center lines on the surface of the disk  12 ; however, it should be understood that the actual tracks will each occupy a finite width about a corresponding centerline. The data storage disk  12  also includes servo information in the form of a plurality of radially-aligned servo spokes  44  that each cross all of the tracks  42  on the disk  12 . The servo information in the servo spokes  44  (also known as servo sectors) is read by the transducer  20  during disk drive operation for use in positioning the transducer  20  above a desired track  42  of the disk  12 . Among other things, the servo information includes a plurality of servo bursts (e.g., A, B, C and D bursts or the like) that are used to generate a Position Error Signal (PES) to position the write head relative to a track&#39;s centerline during a track following operation. The portions of the track between servo spokes  44  have traditionally been used to store customer data received from, for example, the host computer  33  and are thus referred to herein as customer data regions  46 . 
     It should be understood that, for ease of illustration, only a small number of tracks  42  and servo spokes  44  have been shown on the surface of the disk  12  of  FIG. 3 . That is, conventional disk drives include one or more disk surfaces having a considerably larger number of tracks and servo spokes. 
     During operation, disk drives may be subjected to disturbances such as shocks and vibrations. Shocks may generally be due to external forces, while vibrations may generally be due to both external and internal forces. For example, a shock can occur when someone or something bumps the disk drive (or the housing containing the disk drive). External vibrations may be due to, for example, an attached cooling fan or nearby disk drives performing seek operations. Internal vibrations may be due to seek operations and/or movement of other components within the disk drive. 
     Because the transducer&#39;s position is only corrected when a servo sector is encountered, there is a risk that shocks and vibrations can cause off-track writes. That is, shocks and vibrations can cause data to be written: (1) at improper locations such that data in nearby tracks (usually adjacent tracks) is overwritten; or, (2) so far away from the data&#39;s intended location that it cannot be properly read (i.e., it is irrecoverable). 
     One prior method of reducing off-track writes uses a shock sensor comprising an accelerometer that is mounted on the printed circuit board  32 . However, using an accelerometer has a number of disadvantages (only some of which are mentioned herein). 
     Specifically, an accelerometer, since it is an off-the-shelf component, adds cost to the disk drive  10 . Accordingly, it would be beneficial to develop a method and apparatus for reducing off-track writes which does not require any additional components, such as an accelerometer. 
     It should be understood that disk drives are expected to withstand a certain level of shock or vibration without writing off-track. “Safe shocks” are shocks which would not result in an off-track write, while “unsafe” shocks are shocks which would result in an off-track write. Similarly, “safe vibrations” are vibrations which would not result in an off-track write, and “unsafe vibrations” are vibrations which would result in an off-track write. 
     When a shock or vibration occurs, an accelerometer outputs an analog signal which (after filtering) is compared to a predetermined threshold. If the threshold is exceeded (or, in another case, not met), an off-track event is likely to occur and any write operations are prohibited, generally, for one revolution. Next, the output of the accelerometer is again compared to the predetermined threshold. If the output of the accelerometer is less than (or, in another case, greater than) the predetermined threshold, the write operation is allowed to be performed. 
     Determination or “tuning” of the predetermined threshold is performed using an iterative technique. Because it is extremely time-consuming to determine individual predetermined thresholds for each drive, a predetermined threshold is determined for a group of drives (generally, on a product-line by product-line basis). 
     A “false trigger” can occur when the disk drive believes that a “safe shock” or “safe vibration” is an “unsafe shock” or “unsafe vibration.” For example, in the case of an accelerometer, a false trigger can occur when the output of the accelerometer is greater than the predetermined threshold, but an off-track write would not actually occur due to the shock or vibration that is being measured by the accelerometer. Because false triggers can reduce a disk drive&#39;s performance (due to, for example, write operations being prohibited for one revolution), it is important that false triggers are kept to a low level. 
     Accelerometers can cause an undesirable number of false triggers due to output variations between individual accelerometers. That is, a first accelerometer mounted to a printed circuit board that is subjected to a shock may output a signal that is different from the signal output by a second accelerometer (of the same brand, type and model as the first accelerometer) mounted identically to the printed circuit board when subjected to the same shock. This makes tuning of the predetermined threshold extremely difficult and, therefore, can cause a large number of false triggers, thereby negatively impacting drive performance. Accordingly, it would be desirable to develop a method and apparatus for reducing off-track writes which does not cause a large number of false triggers. 
     In order to ensure that disk drives are capable of properly handling shocks and vibrations, disk drives are subjected to a battery of qualification tests. If a drive fails to meet the shock and vibration qualification tests, the drive may be scrapped or a line of disk drives may be required to be redesigned, thereby increasing manufacturing costs and/or reducing manufacturing throughput. Accordingly, it would be desirable to design a method and apparatus for reducing off-track writes, which meets shock and vibration qualification tests more effectively than prior techniques. 
     SUMMARY OF THE INVENTION 
     The present invention is designed to meet some or all of the aforementioned, and other, needs. 
     A method and apparatus for reducing off-track writes in a data storage device is disclosed. In one embodiment, a command is received to perform a write operation using a write head at a first location on a disk surface. A determination is made as to whether to perform or inhibit the write operation using an equation having a tunable acceleration coefficient. The equation is used to predict a position error signal (PES) value for a write head at a servo sector that immediately circumferentially follows the first location. If the predicted PES value is outside of (e.g., greater than or less than) a predetermined threshold, an off-track write is likely to occur and the write operation is inhibited. 
     In one embodiment, when the predicted PES value is outside of the predetermined threshold, write operations are inhibited for at least one servo sector. In another embodiment, when the predicted PES value is outside of the predetermined threshold, write operations are inhibited for at least one revolution. 
     In one embodiment, the PES value is predicted for the write head using two equations. In the first equation, a first tunable acceleration coefficient is provided, wherein said first tunable acceleration coefficient has a positive value. In addition, a first threshold is associated with the first equation. In the second equation, a second tunable acceleration coefficient is provided, wherein said second tunable acceleration coefficient has a negative value. In addition, a second threshold is associated with the second equation. If the PES value predicted by the first equation is outside of the first threshold or if the PES value predicted by the second equation is outside of the second threshold, then an off-track write is likely to occur and write operations are inhibited. 
     By using a PES based safe-write algorithm, off-track writes are reduced. Furthermore, the need for providing an accelerometer to be used as a shock or vibration sensor is eliminated, thereby reducing the costs associated therewith. 
     Other embodiments, objects, features and advantages of the invention will be apparent from the following specification taken in conjunction with the following drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a diagrammatic representation illustrating a conventional disk drive with its top cover removed; 
         FIG. 2  is a functional block diagram which illustrates a conventional disk drive that is coupled to a host computer via an input/output port; 
         FIG. 3  is a diagrammatic representation of a top view of a magnetic storage disk illustrating a typical organization of data on a disk surface; 
         FIG. 4  is a flowchart which provides an overview of one embodiment of the present invention; 
         FIG. 5  illustrates exemplary predicted PES values using three techniques during a consistent acceleration situation; 
         FIG. 6  illustrates exemplary predicted PES values using three techniques during an inconsistent acceleration situation; and, 
         FIG. 7  is flowchart illustrating one embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     While this invention is susceptible of embodiments in many different forms, there are shown in the drawings and will herein be described in detail, preferred embodiments of the invention with the understanding that the present disclosure is to be considered as an exemplification of the principles of the invention and is not intended to limit the broad aspects of the invention to the embodiments illustrated. 
     The present invention is directed to a method and apparatus for reducing off-track writes in a data storage device, such as a disk drive. An overview of one embodiment of the present invention is shown in  FIG. 4 . 
     As shown in  FIG. 4 , a prediction is made of a PES value associated with a transducer position at a next servo sector  410 . A determination is made as to whether the predicted PES value is greater than (or, in other embodiments, is less than) a predetermined threshold  420 . If the predicted PES value is greater than the predetermined threshold, an off-track write is likely to occur and, therefore, write operations are inhibited  430 . If, on the other hand, the predicted PES value is less than the predetermined threshold, the write operation is allowed to be performed  440 . Techniques associated with both predicting the PES value associated with the next servo sector and the predetermined thresholds are discussed below. 
     One method of predicting the PES value associated with the next servo sector is to estimate it using the first three terms of the Taylor expansion. A second order expansion of any function is given by: 
                     f   ⁡     (     k   +   1     )       =       f   ⁡     (   k   )       +         f   ′     ⁡     (   k   )       ⁡     [       (     k   +   1     )     -   k     ]       +       1   2     ⁢           f   ″     ⁡     (   k   )       ⁡     [       (     k   +   1     )     -   k     ]       2                     =       f   ⁡     (   k   )       +       f   ′     ⁡     (   k   )       +       1   2     ⁢         f   ″     ⁡     (   k   )       .                     
where f′(k) and f″(k) denote the first and second derivatives, respectively.
 
     Since we are interested in predicting the PES value, i.e. p(k), we set p(k)=f (k). Next, since the PES is a discrete time signal, we use the following approximations for its first two derivatives:
 
 f ′( k )≈ p ( k )− p ( k− 1)
 
and
 
     
       
         
           
             
               
                 
                   
                     
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     These approximations result in the following estimation equation for the predicted PES: 
     
       
         
           
             
               
                 
                   
                     
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     The above equations use crude approximations of velocity and, more importantly, of acceleration. Specifically, a constant acceleration is assumed. The inventors have determined that the above equations will provide an inaccurate estimation of the PES value associated with the next servo sector. This is because the equations fail to account for the tracking controller  36  (see  FIG. 2 ) which attempts to minimize the PES whenever it is nonzero. Accordingly, the above-described estimation is also affected by a force that acts to correct the position error. Therefore, the assumption of a constant acceleration is a poor assumption. 
     In order to provide a better estimation of the PES value associated with the next servo sector, a tunable acceleration coefficient, β, is introduced such that: 
                               p   ^     β     ⁡     (     k   +   1     )       =       ⁢       p   ⁡     (   k   )       +     v   ⁡     (   k   )       +     β   ⁢           ⁢     a   ⁡     (   k   )                       ≈       ⁢       p   ⁡     (   k   )       +     v   ⁡     (   k   )       +     β   ⁡     [       v   ⁡     (   k   )       -     v   ⁡     (     k   -   1     )         ]                     ≈       ⁢       p   ⁡     (   k   )       +     [       p   ⁡     (   k   )       -     p   ⁡     (     k   -   1     )         ]     +                     ⁢     β   ⁡     [       p   ⁡     (   k   )       -     2   ⁢           ⁢     p   ⁡     (     k   -   1     )         +     p   ⁡     (     k   -   2     )         ]                     =       ⁢         (     2   +   β     )     ⁢     p   ⁡     (   k   )         -       (     1   +     2   ⁢           ⁢   β       )     ⁢     p   ⁡     (     k   -   1     )         +     β   ⁢           ⁢     p   ⁡     (     k   -   2     )             ,                 (     Equation   ⁢           ⁢   1     )               
where p(k) denotes the measured PES of the actuator, v(k) the velocity and a(k) the acceleration. The coefficient β is a tunable weight on the acceleration, while {circumflex over (p)} β (k+1) is the predicted position (i.e., based upon a predicted PES value) at the next servo sector. The subscript denotes the dependence of the predicted PES on the selection of β.
 
     The inventors have determined that the value of the predicted PES at the next servo sector is dependent upon whether the PES was consistently increasing (or decreasing) over the last few (e.g., three) servo sectors (defined as a “consistent acceleration” situation) or whether the PES was not consistently increasing (or decreasing) over the last few (e.g., three) servo sectors (defined as an “inconsistent acceleration” situation). In a consistent acceleration situation, when the tunable weight β is set to a positive number, the predicted PES at the next servo sector will yield a greater absolute value than if the tunable weight β was set to a negative number. Similarly, in an inconsistent acceleration situation, when the tunable weight β is set to a negative number, the predicted PES at the next servo sector will yield a greater absolute value than if the tunable weight β was set to a positive number. 
     In view of the above, the following two equations are provided for the “consistent acceleration” (CA) situation and the “inconsistent acceleration” (IA) situation, respectively:
 
 {circumflex over (p)}   CA ( k+ 1)=(2+β CA ) p ( k )−(1+2β CA ) p ( k− 1)+β CA   p ( k− 2) where β CA &gt;0
 
 {circumflex over (p)}   IA ( k+ 1)=(2+β IA ) p ( k )−(1+2β IA ) p ( k− 1)+β IA   p ( k− 2) where β IA &gt;0
 
     The values of β CA  and β IA  are selected for a group of disk drives (e.g., a product line of disk drives) based upon data collected from a sample of such group of disk drives. More specifically, the values of β CA  and β IA  are selected based upon data collected from the drives under prescribed conditions of shock, vibration and seek, as well as quiescent TMR. Although value of β CA  is positive and the value of β IA  is negative, their absolute values do not have to be equal to one another (e.g., β CA  may be set to 0.2, while β IA  may be set to −0.5). In one embodiment, 0&lt;β CA &lt;1 and −1&lt;β IA &lt;0. 
     It should be noted that the value of the PES at the next servo sector can also be predicted using a relatively simple position plus velocity predictor (P+V Predictor). Unfortunately, the PES predicted by the P+V predictor is relatively crude, unless the acceleration is zero. The predicted values of the PES using the consistent acceleration method and the inconsistent acceleration method provide results such that one of the values is greater than the value predicted by a conventional P+V predictor and one of the values is less than the value predicted by a conventional P+V predictor (except, of course, when the acceleration is zero where all three predictions will be the same). Subject to the narrow exception where the acceleration is zero, one of the two predicted PES values will be more conservative than the PES value predicted by a conventional P+V predictor. 
       FIG. 5  illustrates an example of predicted PES values using the consistent acceleration method, the P+V method and the inconsistent acceleration method when the PES values are consistently increasing over the last few servo sectors (i.e., during a consistent acceleration situation). The y-axis indicates the value of the PES in units of tracks, while the x-axis indicates the servo sector number. The track centerline is represented by dashed line  510 , while the high threshold and the low threshold are represented by dashed lines associated with reference numerals  520  and  530 , respectively. Furthermore, measured PES values are represented by small circles, while predicted values of the PES (according to the various methods) are each represented by a small “x”. 
     As illustrated in  FIG. 5 , the value of the PES is to be predicted for servo sector number  4  using the measured PES values for servo sector  3 , servo sector  2  and servo sector  1  (see Equation 1, above). Because the PES is consistently increasing (i.e., the value of the PES for spoke  2  is greater than the value of the PES for spoke  1 , and the value of the PES for spoke  3  is greater than the value of the PES for spoke  2 ), the prediction of the value of the PES using the consistent acceleration method should be greater than both the value of the PES predicted using the P+V method and the PES predicted using the inconsistent acceleration method. This is shown in  FIG. 5 . 
       FIG. 5  also shows that, using the consistent acceleration method, the predicted PES for servo sector  4  is greater than the high threshold  520  and, therefore, an off-track write is likely to occur. Accordingly, write operations are inhibited. 
     On the other hand, the predicted values of the PES for servo sector  4  using both the P+V method and the inconsistent acceleration method are less than the high threshold. Accordingly, had such methods been used to predict the value of the PES for servo sector  4 , write operations would still have been permitted, which might have led to an off-track write. 
       FIG. 6  illustrates an example of predicted PES values using the inconsistent acceleration method, the P+V method and the consistent acceleration method when the PES values are not consistently increasing or decreasing over the last few servo sectors (i.e., during an inconsistent acceleration situation). The y-axis indicates the value of the PES in units of tracks, while the x-axis indicates the servo sector number. The track centerline is represented by dashed line  610 , while the high threshold and the low threshold are represented by the dashed lines associated with reference numerals  620  and  630 , respectively. Furthermore, measured PES values are represented by small circles, while predicted values of the PES (according to the various methods) are each represented by a small “x”. 
     As illustrated in  FIG. 6 , the value of the PES is to be predicted for servo sector number  4  using the measured PES values for servo sector  3 , servo sector  2  and servo sector  1  (see Equation 1, above). Because the PES is not consistently increasing (i.e., the value of the PES for spoke  2  is greater than the value of the PES for spoke  1 , but the value of the PES for spoke  3  is less than the value of the PES for spoke  2 ), the prediction of the value of the PES using the inconsistent acceleration method should be greater than both the value of the PES predicted using the P+V method and the value of the PES predicted using the consistent acceleration method. This is shown in  FIG. 6 . 
       FIG. 6  also shows that, using the inconsistent acceleration method, the predicted PES value for servo sector  4  is greater than the high threshold  620  and, therefore, an off-track write is likely to occur. Accordingly, write operations are inhibited. 
     On the other hand, the predicted values of the PES for servo sector  4  using both the P+V method and the consistent acceleration method are less than the high threshold. Accordingly, had the value of the PES for servo sector  4  been predicted using such methods, write operations would still have been permitted, which might have led to an off-track write. 
     It should be noted that the high threshold  520  and the low threshold  530  may be equal to one another (as shown in  FIG. 5 ) or each may be a different value. Similarly, the high threshold  620  and the low threshold  630  may also be equal to one another (as shown in  FIG. 6 ) or each may be a different value. Furthermore, the threshold(s) associated with the consistent acceleration situation ( FIG. 5 ) and the threshold(s) associated with the inconsistent acceleration situation ( FIG. 6 ) may be equal to, or different from, one another. 
     In order to reduce the likelihood of off-track writes, writes are inhibited when the predicted PES at the next servo sector, using either the consistent acceleration method or the inconsistent acceleration method, is outside of a threshold. That is, there is a Logical OR relationship between the two methods in deciding whether to inhibit at the write at a customer data location following the next servo sector. This is summarized in the Table I (below). 
     
       
         
           
               
               
               
             
               
                 TABLE I 
               
               
                   
               
               
                 CA Trigger 
                 IA Trigger 
                 Inhibit Write 
               
               
                   
               
             
            
               
                 No 
                 No 
                 No 
               
               
                 No 
                 Yes 
                 Yes 
               
               
                 Yes 
                 No 
                 Yes 
               
               
                 Yes 
                 Yes 
                 Yes 
               
               
                   
               
            
           
         
       
     
     In one embodiment, the write is inhibited for one revolution. In another embodiment, the write is inhibited for one at least servo sector, wherein another prediction is made with respect to the value of the PES at the next servo sector (e.g., if a write is inhibited at servo sector  4 , then the next servo sector would be servo sector  5 ). Based upon the predicted PES at the next servo sector (e.g., servo sector  5 ), a write is either performed or inhibited at a data sector that follows the next servo sector (e.g., servo sector  5 ). 
     The present invention allows at least four parameters to be tuned based upon data collected from a sample of the drives under prescribed conditions of shock, vibration and seek, as well as quiescent TMR. Specifically, the parameters are β CA , β IA , the threshold for the consistent acceleration method (e.g., in % tracks), and the threshold for the inconsistent acceleration method (e.g., in % tracks). Additional parameters may also include high and low thresholds for both the CA method and the IA method. These parameters can be easily tuned off-line by post processing the PES data collected from a sufficient number of drives with the algorithm turned off. That is, the parameters can be tuned by studying many PES signals during certain conditions (e.g., shock events, vibrations and seeks) to characterize the drive&#39;s reactions to such conditions. 
       FIG. 7  is a flowchart which illustrates one embodiment of the present invention. However, prior to discussing  FIG. 7 , some prefatory comments are required. 
     A command (e.g., from the host computer) may be given to write data at a data sector using a write head. In such case, there is a servo sector that immediately circumferentially precedes the data sector (i.e., there are no intervening servo sectors between the data sector and the servo sector, although there may be intervening data sectors). That is, if the write operation is not inhibited, this servo sector will be used to position the write head immediately prior to writing the data on the disk surface. After reading this servo sector, a prediction is made of a PES value for the write head associated with the next servo sector to determine whether to allow or inhibit the write operation. 
     Referring now to  FIG. 7 , when a write operation is to be performed (step  710 ) to write data following sector k, PES values are measured at sector k−2, sector k−1, and sector k (steps  720 - 740 ). Next, the PES value for sector k+1 is predicted using both the consistent acceleration equation and the inconsistent acceleration equation (step  750 ). 
     Next, a determination is made as to whether both the predicted PES value for sector k+1 calculated according to the consistent acceleration equation is within its associated threshold and the predicted PES value for sector k+1 calculated according to the inconsistent acceleration equation is within its associated threshold (step  760 ). If so, the write is allowed to be performed at the data sector following sector k (i.e., data sectors that are encountered prior to encountering another servo sector) because an off-track write is not likely to occur (step  770 ). 
     On the other hand, if either (or both) the predicted PES for sector k+1 calculated according to the consistent acceleration equation is outside of its associated threshold or the predicted PES for sector k+1 calculated according to the inconsistent acceleration equation is outside of its associated threshold, then the write operation is inhibited (step  780 ). Specifically, the write operation is inhibited for at least one servo sector. Accordingly, the value of k is incremented by 1 (step  790 ). Then, measurements of the PES at new sector k−2, new sector k−1 and new sector k are used to predict the PES at new sector k+1 (steps  720 - 750 ). Of course, the measurements of the PES at new sector k− 2  and new sector k−1 are not required to be retaken since those measurements correspond with original sector k−1 and original sector k, respectively. 
     As an alternative, instead of running both the equations in parallel, a determination may first be made as to whether a consistent acceleration or inconsistent acceleration exists. Then, a calculation may be made using the appropriate equation. 
     As mentioned above, write operations may be inhibited for one servo sector or for one revolution when the predicted PES of a servo sector (i.e., servo sector k+1) is outside of a threshold. In another embodiment, a flag is set each time write operations are inhibited due to a predicted PES being outside of a threshold. Based upon the history of the flags, (e.g., if there have been at least two instances in a row which have raised a flag), another mode may be entered where more conditions must be satisfied before write operations are permitted. For example, a tightened threshold (e.g., a tighter position and/or velocity) must be satisfied before write operations are permitted. 
     The present invention may also be used to test track quality (e.g., in a self-test process). In the test, track quality may be deduced by using the present invention to determine whether a track (or portion of a track) has predicted PES values that are within a threshold (wherein the threshold is relatively tighter than the threshold used during normal operations). If a track (or portion of a track) has more than a predetermined number of predicted PES values that fall outside of the threshold, the track (or portion of the track) will be considered to be a “bad” track (or “bad” portion of a track). 
     While an effort has been made to describe some alternatives to the preferred embodiment, other alternatives will readily come to mind to those skilled in the art. Therefore, it should be understood that the invention may be embodied in other specific forms without departing from the spirit or central characteristics thereof. The present examples and embodiments, therefore, are to be considered in all respects as illustrative and not restrictive, and the invention is not intended to be limited to the details given herein.