The present invention relates to a position control system for allowing a data transducer to trace a data track in a disk storage device, and more particularly to a posi­tion control system for a disk storage drive system in which a data transducer can be moved to a selected data recording track at a high speed and controlled to keep its relative position to the data recording track.

As information record/playback apparatuses have re­markably been improved in performance recently, the data transducer position control system is desired to be more compact in size and more accurate in operation, which acts as a positioning drive device for allowing the record or playback transducer to trace a reference data track in a magnetic disk storage device or an optical disk storage device. The compactification is required for the purpose of increasing the recording capacity in a given size and the high accuracy is also needed for the increase of track den­sity for mass storage.

Deflection of a data track which occurs during track­ing, will be described. In an optical disk storage device, the amplitude of track deflection will be about several tens to some dozen tens of micro meters, considerably greater than the width (about 1.6 µm) of a track to be traced, due to the eccentricity of the center of rotation after re­placement of a disk medium and/or the deflection of a rotary shaft of spindle motor for rotation of the disk. In a floppy disk drive (FDD), another kind of track deflection will result from the expansion or shrinkage of a base film of disk medium caused by heatup in addition to the same track deflection as of an optical disk storage device. In this case, the amplitude of track deflection is rather smaller than in the optical disk storage device. Although the deflection is some dozen to several tens of micro meters in operation, it will not be negligible when the track is reduced in width for mass storage at high density.

For the purpose of minimizing such a deflection of track, known data transducer position control systems for disk storage drive system have employed respective methods which will then be described.

For first example, there is provided a method in which the deflection of a track is estimated by differentiating 2 times a signal which is the sum of a tracking error signal and an integration signal given by integrating 2 times an input signal to the driver unit for actuating a data trans­ducer for tracking movement. As the estimation signal cor­responding to one rotation of the disk is stored in a memo­ry, it is then read out at a tracking mode and added to the input signal to the driver unit. With the use of such a resulting signal, the traceability of the data transducer can be improved, for example, as disclosed by US Patent 4, 594, 622. However, it will be difficult to put this method into practice due to difficulty in suppressing a variation in the integration or a noise resulting from the differen­tiation.

For secondary example, there is another method in which by extracting a repeatable signal component from the track­ing error signal representing a deviation of the data transducer from the reference data track, a Fourier coeffi­cient of repeatable frequency is obtained and used to calculate a repeatable error compensation signal. The re­peatable error compensation signal is then added to a driver input signal of the data transducer. With the use of such a resulting signal, the traceability of the data transducer can be improved in reference to the track deflection at a disk rotation frequency, for example, as disclosed by US Patent 4, 616, 276. However, the disadvantages of this method are that the arithmetic operation of Fourier analysis is troublesome and that the depression of a rotation non-­synchronous factor is yet unsatisfactory.

Accordingly, a prior art data transducer position con­trol system for disk storage drive system has such a setback as the control of a variation and a noise generated during the estimation of track deflection is too difficult to be executed in practice or as the arithmetic operation of a repeatable error compensation signal is troublesome.

It is an object of the present invention to provide a position control system for disk storage drive system in which the tracking error between a data transducer and a data track is minimized and the traceability is thus improved, and more particularly, to provide a data trans­ducer position control system capable of controlling the deflection of a data track which is remarkably common with an interchangeable medium.

It is another object of the present invention to pro­vide a practically improved data transducer position control system for disk storage drive system in which during the estimation of track deflection, no problem arises in sup­pression of a variation and a noise and also, the process of calculation is facilitated.

A position control system for a disk storage drive system according to the present invention, which includes a data transducer for record and playback of information stored in a desired data track of an information storage disk having a plurality of data storage tracks thereon, comprises a driver unit for actuating the data transducer in accordance with a reference position command signal, a po­sition encoder for detecting a variation in movement of the data transducer and producing a current position signal representing a current position of the data transducer, a tracking error detector for producing a tracking error sig­nal upon detecting a positional difference of the data transducer from the desired data track, a track deflection estimator for estimating a deflection of track resulting from either eccentricity or undulation of the data track and generating a feed-forward signal on the estimation, and a discrete-time control loop for controlling the driver unit in accordance with the tracking error signal, the loop hav­ing a compensating position calculator for calculating a compensating position command signal from the tracking error signal and an interpolation calculator for generating an interpolation signal which is applied to the driver unit through interpolation with the feed-forward signal and the compensating position command signal.

Such an arrangement as described above offers the fol­lowing functions and effects.

The eccentricity or undulation of a data track is es­timated by the track deflection estimator and with its re­sultant information data, the feed-forward control is then executed, whereby the traceability can be improved in accu­racy and consistency.

As the estimation of track deflection is reckoned by the sum of the tracking error signal and the current posi­tion signal supplied from the position encoder, no problem arises in the suppression of a variation or a noise during the estimation and thus, the procedure of calculation will be facilitated.

The feed-forward signal applied to the driver unit is positively delayed in phase so as to improve the traceabil­ity.

The current position of the driver unit is identified with high accuracy and resolution by the position encoder so that the minimal positioning is possible and the impact from vibration is lessened through increasing the stiffness. As a result, the high density of data tracks can be obtained.

The interpolation signal is generated by the interpo­lation calculator through interpolating process of a feed-­forward signal and an output from the compensating position calculator and then, added to the reference position command signal, whereby the traceability can be improved.

Consequently, it will be possible to provide an im­proved data transducer position control system for disk storage drive system.

• Fig. 1 is a schematic view showing the arrangement of an embodiment of the present invention in the form of a position control system for disk storage drive system;
• Fig. 2 is a schematic view of a track deflection esti­mator according to the embodiment of the present invention;
• Fig. 3 is a waveform chart of signals in the track deflection estimator;
• Fig. 4 is a block diagram showing the procedure of estimation of track deflection in the track deflection es­timator;
• Fig. 5 is a block diagram showing the position control system for disk storage drive system in a track seek mode;
• Fig. 6 is a block diagram of an interpolation calcula­tor according to the embodiment of the present invention;
• Fig. 7 is a waveform chart of signals produced without interpolative calculation in the position control system for disk storage drive system;
• Fig. 8 is a block diagram showing the substantial ar­rangement of an interpolator for execution of a first in­terpolation process;
• Fig. 9 is a waveform chart of signals obtained through interpolation with the first interpolation process;
• Fig. 10 is a block diagram showing the substantial arrangement of an interpolator for execution of a second interpolation process;
• Fig. 11 is a waveform chart of signals obtained through interpolation with the second interpolation process;
• Fig. 12 is a block diagram showing the substantial arrangement of an interpolator for execution of a third interpolation process;
• Fig. 13 is a waveform chart of signals obtained through interpolation with the third interpolation process;
• Fig. 14(a) is a block diagram of a compensating posi­tion calculator according to the embodiment of the present invention; and
• Fig. 14(b) is a chart of frequency properties showing a transfer function from the tracking error e1 to the compen­sating position command signal rd.

One preferred embodiment of the present invention will be described in the form of a data transducer position con­trol system for disk storage drive system with reference to the drawings.

Fig. 1 is a block diagram of a position control system for a disk storage drive system according to the present invention. As shown in Fig. 1, the numeral 12 is a driver unit having a function for actuating a data transducer 2 to move about on the disk. The driver unit 12 includes an actuator 1 for movement of the data transducer 2, a position encoder 3 connected mechanically with the moving part of the actuator 1 for producing a current position signal ya upon detecting the position of the actuator 1 constantly, a com­pensator 5, a power supply circuit 4 for energizing the actuator 1 in accordance with an output from the compensator 5, a sample holder 15 for continuous conversion of discrete-time signals ya derived from the position encoder 3, and a comparator 6 for calculating a difference e2 be­tween the reference position command signal rs and the out­put of the sample holder 15. The compensator 5 calculates a control measure of the actuator 1 with reference to the difference e2. A servo-loop extending from the output of the position encoder 3 via the comparator 6, the compensator 5, and the power supply circuit 4 to the actuator 1, con­stitutes a position control loop. Particularly, the posi­tion encoder 3 is adapted to detect the action of a moving part constantly and its current position output signal is a linear representation of displacement of the data transducer 2 from a specific reference position within the movable range. The compensator 5 is also arranged for following the reference position command signal rs quickly with less er­ror. This servo-loop is substantially an absolute posi­tioning system and thus, will fail to provide the precise tracking along a data track which may deflect as the disk rotates.

Represented by r is a measure of eccentricity or un­dulation of a selected data track 13 on the disk 14 situated just beneath the data transducer 2, also referred to as a deflection of track, while ys is an absolute position of the data transducer 2. A tracking error detector 7 detects a relative position error e1 between the data track 13 and the data transducer 2. A compensating position calculator 8 produces a compensating position command signal rd through control calculation with the tracking error e1. A track deflection estimator 9 estimates the amplitude of track deflection upon receiving both the tracking error signal e1 and current position signal ya and producing a feed-forward signal rc. The compensating position command signal rd and the feed-forward signal rc are then applied to an interpo­lation calculator 10 where a specific interpolation process is executed. The output from the interpolation calculator 10 is a reference position command signal rs.

The substantial operation in the position control sys­tem for a disk storage drive system according to the present invention will then be described in principle.

The embodiment shown in Fig. 1 employs a tracking servo-system also termed as a sector servo-system or a sam­pling servo-system. The system is adapted in which on the basis of each particular servo information which is essen­tial for tracking and embedded in the border area between fan-shaped sectors formed on the disk, a relative position signal (a tracking error signal) of the data transducer 2 to the target data track is detected in discrete-time base and then, applied in feedback for positioning in a closed loop. As shown in Fig. 1, the system is mainly constituted by a discrete-time control loop for allowing the data transducer 2 to trace the data track 13 with the tracking error signal e1 kept minimum. The discrete-time control loop represents a servo-loop from the data transducer 2 via the tracking error detector 7, the compensating position calculator 8, and the interpolation calculator 10 to the driver unit 12. While a deviation of the data transducer 2 from the selected data track 13 varies in time sequence, the position of the data track 13 is identified only intermittently in the sec­tor servo-system and thus, the tracking error signal e1 will be outputted as a discrete-time signal from the tracking error detector 7. The tracking error signal e1 is then processed by specific control calculation in the compensat­ing position calculator 8 to generate the compensating po­sition command signal rd. The compensating position calcu­lator 8 has a time discrete processing system containing a deviation compensating factor or if needed, a stability compensating factor and acts primarily for control of the offset.

The operation in the tracking deflection estimator 9 of Fig. 1 according to the present invention will be described. The tracking error detector 7 is arranged to detect the relative tracking error signal e1 of the data transducer 2 to the data track 13. When the absolute position of the data transducer 2 is ys and the position (track deflection) of the data track is r, the tracking error signal e1 is obtained from:

e1 = r - ys      (1)

Then, the position encoder 3 detects the position of the actuator 1 and produces a current position signal ya. The absolute position ys of the data transducer 2 is indirectly represented by the current position signal ya, which is expressed as:

ys ≈ ya      (2)

Therefore, from the statements (1) and (2), the value r is determined by:

r ≈ e1 + ya      (3)

The approximate equation (3) means that the track de­flection of a data track can be estimated from the tracking error signal e1 and the current position signal ya. The track deflection estimator 9 includes an adder for summing the tracking error signal e1 and the current position signal ya and calculates an estimate of track deflection from the equation (3). The resultant estimation rc of a track deflection r is then designated as a feed-forward signal. The feed-forward control is a procedure of applying an ex­ternal signal to the servo-loop, in which the controllability thereof can be increased without reducing the stability when an external signal has been supplied thereto. It is hence understood that the estimation rc of the track deflection r in the position control system of the present invention is an external signal outside the servo-­loop or the discrete-time control loop. More particularly, the input of this signal to the interpolatlon calculator 10 stands for an application to the servo-loop. Accordingly, the stability in the servo-loop remains no doubt unchanged in the event.

The reason why the traceability is improved by applying the feed-forward signal rc to the servo-loop, is as follows. As the positioning control loop constituting the driver unit 12 is a closed servo-loop system governed by the reference position command signal rs, we have:

rs ≈ ya      (4)

Meanwhile, referring to (2), the formula (4) becomes:

ys ≈ rs      (5)

This means that the position ys of the data transducer 2 approximately follows the reference position command signal rs. Then, if a corresponding signal to the track deflection r is added to the reference position command signal rs, the data transducer 2 will comply with the command signal. Particularly, when rs ≈ r, we have:

ys ≈ rs ≈ r      (6)

This means that the data transducer 2 can comply with the track deflection r of the data track 13 with fair precision. At the time, the tracking error signal e1 becomes a minimum.

However, the driver unit 12 cannot respond instantly in practice when the reference position command signal rs is inputted and thus, a delay of time will occur. More specif­ically, the transfer properties of the driver unit 12 in­clude a phase delay within the basic and harmonic frequency band of a disk revolution frequency contained primarily in the track deflection r of data track. Also, another phase delay which is derived from a sample hold procedure of the discrete-time control loop, is applied. As a result, the data transducer 2 fails to trace a desired data track with the accuracy of more than a specific degree. The track deflection estimator 9 in the position control system for disk storage drive system of the present invention is thus arranged as described below.

Fig. 2 is a block diagram of the track deflection es­timator 9 according to the embodiment of the present inven­tion. As shown in Fig. 2, the track deflection estimator 9 comprises a memory section 21, digital compensators K1, K2, ... Kn-1, and Kn, and an adder 22. Represented by Z⁻¹ is a unit memory for holding an estimation signal of track de­flection ra for a time T equal to a sampling period in the discrete-time control loop. The memory section 21 is thus constituted for holding the track deflection estimation signals ra corresponding to one rotation of disk by con­necting in series n number (n is a positive integer) of unit memories which number corresponds to the number of sectors. The output from the final stage of the memory section 21 is connected to the input of the same so that the track de­flection estimation signals ra held therein can pass each unit memory recursively as synchronized with the rotation of the disk. The memory section 21 may also be formed of shift registers or the like.

Each of the digital compensators K1, K2, ... Kn-1, and Kn comprises adders and/or multipliers for amplifying or digital filtering the output signal of a unit memory of the memory section 21. The adder 22 is arranged to sum up the outputs of the digital compensators for producing the feed-forward signal rc.

The operation of the track deflection estimator 9 of Fig. 2 will be described in principle. As shown in Fig. 2, the track deflection estimation signals ra corresponding to one rotation of the disk are stored in the n number of the unit memories and during tracking, retrieved from their respective unit memories. The estimation signals are then applied to their respective digital compensators and summed up by the adder 22 to produce a track deflection estimation signal rc which is equal to or in a bit advance of the ac­tual track deflection r in phase measure. Then, the track deflection estimation signal rc is applied to the interpo­lation calculator 10 together with the output signal rd of the compensating position calculator 8 shown in Fig. 1. When the output from the interpolation calculator 10 is inputted to the driver unit 12, the actuator 1 moves to eliminate a delay in the tracking motion of the data trans­ducer 2.

The track deflection estimator 9 may be formed of such a hard ware as described above or a microprocessor contain­ing a software for execution of a similar procedure.

Fig. 3 is a waveform chart showing the track deflection estimation signal ra of the track deflection estimator of Fig. 2 and respective output signals of the digital compen­sator Ki and the adder 22. The digital compensator Ki is a multiplier for multiplying the signal by 0.1. The letter i represents the number of a unit memory as numbered from the front to i-th and is designated as i ≈ n·3/4. While the digital compensators K1 to Kn-1 except Ki are removed, the Kn is an amplifier of gain 1.

Assuming that the memory section 21 of Fig. 2 has a track deflection estimation signal corresponding to one rotation of the disk, which is a periodical signal including frequency components proportional to the rotation frequency of the disk, the output signal of a unit memory numbered with i is advanced 360°x(1-3/4) = 90° in the phase as com­pared to the output of another unit memory numbered with m in respect of the frequency in one rotation of the disk. As shown in Fig. 3, represented by (a) is the track deflection estimation signal ra, (b) is a signal given by multiplying the output signal of the i numbered unit memory by a coef­ficient 0.1 in the multiplier, and (c) is the output signal rc given by summing the former signals in the adder 22. If the track deflection contains only a basic frequency, the signal waveforms of Fig. 3 are respectively described as, in which the disk rotation angular frequency is ω.

• (a) : A·sin(_ωt)
• (b) : B·cos(_ωt)
• (c) : C·sin(_ωt+φ)

C·sin(_ωt+φ) = A·sin(_ωt) + B·cos(_ω t)      (7)

When the coefficients are compared to each other, we have:

• A = C·cos(φ)      (8) and
• B = C·sin(φ)      (9)

tan(φ) = B/A      (10)

When B = 0.1·A, we have from the equation (10):

φ = 5.7° and C = 1.005·A

That is to say, the output signal rc from the adder 22 is advanced 5.7° in phase and approximately equal in amplitude as compared with the signal ra. Although the signal (b) is in 90° advance of the signal (a) in Fig. 3, variations will be possible. The waveforms of Fig. 3 are represented by smooth curved lines only provided that n is a quite large number. However, if n is a small number, the waveform is shown in a step form.

Fig. 4 is a block diagram showing a procedure of esti­mating the track deflection at the track deflection estima­tor 9 in the embodiment of the present invention, in which the track deflection estimation signal ra is generated by an adder 41 and expressed by:

ra = e1 + ya      (11)

A multiplier 42 multiplies the track deflection estimation signal ra by α (α is a real number and α < 1). Another multiplier 43 multiplies the output signal rb from the final stage of the memory section 21 by (1 - α). An adder for 44 adds the outputs of the multipliers 42 and 43.

The operation of the track deflection estimating pro­cedure of Fig. 4 will be described in principle. As shown in Fig. 4, the initial setting of a track deflection esti­mation signal is inputted to the memory section 21 in syn­chronization with a rotation of the disk while α is desig­nated as 1 at the first rotation of the disk. If α is 0.5 at the second rotation of the disk, the track deflection estimation signal ra is multiplied by 0.5 in the multiplier 42 and also, the track deflection estimation signal rb from the memory section 21 is multiplied by 0.5 in the multiplier 43. Then, the outputs from the multipliers 42 and 43 are summed up by the adder 44 and stored again in the memory section 21. As the disk rotates continuously, this process is repeated and the track deflection estimation signal will be calculated in sequence. The coefficient in the multi­plier 43 is 1 - α while the same in the multiplier 42 is α, so that the signals stored in the memory section 21 can be constantly normalized in amplitude.

This track deflection estimating procedure features in which the track deflection estimation signal ra stored in the memory section 21 at a particular moment of time, will decrease at a specific rate of 0.25 times the original amount in the second rotation and 0.125 times in the third rotation as the time passes. Accordingly, the remaining percentage of estimation signals which were stored in the past rotation in the memory section 21 will increase as the value of α becomes close to zero.

A primary object of the estimation procedure according to the present invention is to smooth amplitude variations of the track deflection estimation signal and level random noise factors contained in the same through repeating the above mentioned operation.

The track deflection estimator may be formed of such a hard ware as described or a microprocessor having a software for execution of a similar procedure.

The procedure of track deflection estimation will fur­ther be described in respect of various particulars.

In a first case, the estimation is effected with the data transducer 2 kept movable for tracing a given track. More specifically, the track deflection estimation procedure of Fig. 4 is carried out with the discrete-time control loop 11 kept activated in the arrangement of Fig. 1.

In a second case, the estimation is carried out with the discrete-time control loop 11 kept unactivated in the arrangement of Fig. 1 while the absolute position of the data transducer 2 remains unchanged by applying a specified instruction to the drive unit 12. Particularly, the track­ing error detector 7 produces a corresponding signal to the track deflection and the output of the position encoder 3 is a direct current.

Preferred locations on the disk for track deflection estimation will then be described.

In a first case, similar to the above cases, the esti­mation is carried out with the data transducer 2 either kept movable for tracing an unspecified track or kept fast adja­cent to the track.

In a second case, the track deflection estimation is carried out intermediate the track seek operations. More specifically, the estimation procedure is carried out for a period of time with the data transducer 2 kept movable for tracing an unspecified track or fixed adjacent to the track and after shifting to another track, the same procedure will be repeated again.

Between the continuous estimation procedures, another procedure such as writing of data into or reading of data from the disk may be inserted.

The timing of the track deflection estimation will then be described. Such a procedure as the track deflection estimation is repeated at each of the plural tracks, can be employed when the track deflection is constant regardless of the diameter of the disk. Accordingly, the procedure will be inapplicable if the disk, e.g. a floppy disk, has elliptical eccentricity due to changes in the temperature or the moisture. This is because each floppy disk is distinct in elliptical eccentricity as depending on the diameter of a track and also, the writing and reading of data involves frequent seek operations throughout the tracks having re­spective diameters. Hence, the estimation has to be carried out at each particular data track and within a specific period of time.

In a floppy disk drive system, the spindle motor will stop when the access to a disk is interrupted for a certain period of time and the track deflection estimation should thus be carried out intermittently between access opera­tions. The track deflection estimation requires at least a duration corresponding to one rotation of the disk and more particularly, a smoothing period taken for improved estima­tion with less noise while the disk is rotated 2 or 3 more times along a desired track. The track deflection estima­tion is preferably carried out just after the spindle motor starts rotating with the disk loaded in the floppy disk drive system and before the spindle motor stops. If the track deflection is varied during a considerable length of time when the spindle remains ceased, the estimation can be carried out when it is detected that the ceasing period between stop and restart of the spindle exceeds a predeter­mined time.

The operation of the track deflection estimator 9 in a track seek mode will be described.

Fig. 5 is a block diagram showing the position control system for disk storage drive system of the present inven­tion in the track seek mode.

As shown in Fig. 5, the driver unit 12 acts as a main operator in the track seek mode. A track seek instruction rk and an output rc from the track deflection estimator 9 are applied to an adder 51 which in turn sends its output to the driver unit 12.

The memory section 21 (not shown) in the track deflec­tion estimator 9 is formed in the same recursive arrangement as of Fig. 2 and its final stage output is supplied out­wardly through no digital compensator. The driver unit 12 is actuated according to the output signal of the adder 51. When the track seek instruction rk as a position signal is entered without any output of the track deflection estimator 9 applied to the adder 51, the data transducer 2 moves from a track to another track in response to the instruction. As the rotation of the disk causes a track deflection during the track seeking, the track to which the data transducer 2 advances is displaced by a distance of deflection after the track seeking. As shown in Fig. 5, the output rc of the track deflection estimator 9 is applied to the adder 51 together with the track seek instruction rk thus to correct the deflection of the target track caused after the track seeking.

The arrangement and operation of the interpolation calculator 10 in the embodiment of the present invention, shown in Fig. 1, will then be described.

The embodiment of Fig. 1 employs a sector servo-system for which a trade-off of design is established in respect of the number of sectors.

If the number of sectors is great, the sampling fre­quency in discrete-time control system increases and will be available in a wide band for the control. On the contrary, a servo-area portion of the recording surface of the disk increases in size and the capacity of storage will be re­duced when the formatting on the disk is completed. Hence, the number of the sectors should be kept minimum to increase the availability on the disk recording surface.

When the number of the sectors is small, the sampling frequency in control system decreases and will be available only in a narrow band. This allows the traceability to be increased with much difficulty. As the controllable range is commonly adjusted so as to equal several to ten times the basic frequency of the track deflection, a control gain on the discrete-time compensator can be increased for control of the track deflection. However, if the controllable range is limited due to the above described respects, the control gain will hardly increase. Also, if the number of the sec­tors is small, the length of a sampling interval will in­crease while a certain command signal only is applied to the actuator for drive of the data transducer. As the track changes position continuously due to track deflection, an off-track will result from a considerable degree of track deflection even if the control gain is increased.

There is provided a method of increasing the trace­ability with the sectors of a small number, in which the reference position command signal supplied to the driver unit 12 at discrete-time intervals is interpolated between the preceding and following signals in time measure. This method allows the reference position command signal to be interpolated, thus providing the same effect as the number of sectors is increased.

Fig. 6 is a block diagram of the interpolation calcu­lator 10 in the embodiment of the present invention, in which represented by 61 is an adder for combining the com­pensating position command signal rd with the feed-foward signal rc, 62 is an interpolator for performing numerical interpolation upon receiving an output w from the adder 61, and 63 is a sample holder for converting a discrete-time signal v of the interpolator 62 into a continuation. When the sampling period T of the discrete-time control loop is further interpolated at a minimal degree, the hold time Th of the sample holder 63 is expressed as:

Th < T      (12)

The interpolation is an arithmetic operation in which if values of a function f(x) at m points x1, x2, ... and xm are known, a value of f(x) at a point x is obtained from the known values of f(x). More precisely, termed as interpola­tion is when the value of x is between the minimum and max­imum of the values of m points, but otherwise referred to as extrapolation. Lagrange's interpolation is one of the known similar procedures.

The function and operation of the interpolator 62 will specifically be described in reference to a simple example in which m is 2, that is to say, interpola-tion or extrapo­lation is made with the use of a couple of factors. For the purpose of facilitating the description, the relative pro­cedure is not distinguished between interpolation and ex­trapolation and will be referred to as "interpolation" hereinafter.

Fig. 7 is a waveform chart of signals showing the track deflection r with no interpolation procedure carried out, the output w from the adder 61, the reference position com­mand signal rs, the absolute position ys of the data trans­ducer, and the real tracking error es incorporated in the position control system for disk storage drive system of the present invention shown in Figs. 1 and 6. The real tracking error es is an existing tracking error between the data transducer 2 and the reference data track and is obtained from:

es = r - ys      (13)

Represented by (b) in Fig. 7 is a discrete-time signal designated on the abscissa axis kT (k is a positive integer) at sampling intervals of T.

As shown in Fig. 7, the reference position command signal rs which is given by sample holding the output w of the adder 61, is expressed in a wide step waveform. The data transducer position ys or a response of the driver unit 12 to the signal rs is also shown in a wide step waveform. Accordingly, the real tracking error es has an oscillatory waveform of great amplitude.

Fig. 8 is a block diagram showing a substantial ar­rangement of the interpolator for execution of a first in­terpolation procedure, in which 81 is a sampler for sampling at intervals of period T/m the input signal w which has been sampled at T period intervals while 82 is a digital filter H(z) provided in the form of an integral filter for smooth­ing an input signal. Both the sampler 81 and the digital filter 82 are actuated according to an interpolation pulse of T/m period. Represented by 83 and 84 are multipliers for multiplying the signal by a numeral a (a is a positive real number and a < 1) and by 1 - a respectively. Also repre­sented by Z⁻¹ is a register for holding data for the sam­pling period of T/m.

The interpolator may be formed of a hard ware as de­scribed or a microprocessor having a software for execution of a similar procedure.

Fig. 9 is a waveform chart of signals interpolated by the first interpolation procedure (where m = 2). As shown in (b) of Fig. 9, a sample signal denoted by the black dot is the input w (kT) uninterpolated. An interpolated signal is represented by the white dot. The sample signal w (k· T/m) is then applied to the digital filter 82 which actuates in reference to the T/m period interpolation pulse. The signal v smoothed by the digital filter 82 is held by the sampler holder 63 of Fig. 6 for output of a signal rs which has a small step waveform as compared with the signal rs of Fig. 7(c). Consequently, the real tracking error es will be small in the amplitude and moderate in the waveform. Addi­tionally by increasing the interpolation points m, the out­put es will be smooth in the response and further smaller in the amplitude. The output w from the discrete-time compen­sator is sampled to a considerable degree and passed through a digital integral filter, whereby the track traceability can be improved.

Fig. 10 is a block diagram showing another arrangement of the interpolator for execution of a second interpolation procedure, in which 101 is a register actuated on synchro­nizing with a sector detection pulse for holding the input signal w for a period of T. Represented by 102 is an adder for calculating a difference between the current input w(kT) and the register output w((k-1)T). Also, 103 is a multi­plier for multiplying the output of the adder 102 by 1/m (m = 2) and 104 is another adder actuated in response to an interpolation pulse for summing up the current input w(kT) and the output of the multiplier 103.

The interpolator may be formed of a hard ware as de­scribed or a microprocessor having a software for execution of a similar procedure.

Fig. 11 is a waveform chart of signals interpolated by the second interpolation procedure. As shown in (b) of Fig. 11, a sample signal denoted by the black dot is the input w(kT) uninterpolated. The interpolation is carried out in which the signal values (represented by the white dots) are given by dividing the extension (represented by the broken line) which extends across the summit of the current sample signal w(kT) through the summit of the preceding sample signal w((k-1)T), by the number of m in the following sample period.

The interpolated output v (represented by both the black dots and the white dots) is held by the sample holder 63 of Fig. 6 for output of a signal rs, as shown in (c) of Fig. 11 where the hatching area represents the result of interpolation. Particularly, the signal rs has a small step waveform as compared with that of Fig. 7[c) and thus, the response ys of the driver unit 12 becomes moderate in the waveform as compared with that of Fig. 7(d). Consequently, the real tracking error es will be small in the amplitude and moderate in the waveform. Additionally by increasing the interpolation points m, the output es will be smooth in the response and further smaller in the amplitude. The track traceability can thus be improved by interpolation of the signal w.

A further arrangement of the interpolator will be de­scribed, in which the discrete-time signal w is preliminarily held through learning or in reference to a repeatable period for the purpose of an arithmetic operation of interpolation which is then carried out in the first and second interpolation procedures with either the current discrete-time output w or a discrete-time output produced before several sample periods.

Fig. 12 is a block diagram showing the substantial arrangement of the interpolator for execution of a third interpolation procedure, in which 121 is a memory section actuated in synchronizing with a sector detection pulse for holding a signal w corresponding to one rotation of the disk. Represented by 122 is an adder for calculating a difference between the output x(kT) and the output x((k+1)T). Also, 123 is a multiplier for multiplying the output of the adder 122 by 1/m (m = 2) and 124 is another adder actuated in response to an interpolation pulse for summing up the current input w(kT) and the output of the multiplier 123.

The interpolator may be formed of a hard ware as de­scribed or a microprocessor having a software for execution of a similar procedure.

Fig. 13 is waveform chart of signals interpolated by the third interpolation procedure. Shown in (a) of Fig. 13 is a discrete-time signal put into the memory section 121 through learning or in reference to a repeatable period. As shown in (b) of Fig. 13, a sample signal denoted by the black dot is the time-discrete signal w(kT) applied to the interpolator in a real time. The interpolation according to the sample signal stored in the memory section 121 is car­ried out in which a sloping portion (represented by the broken line) between the current sampling time and the fol­lowing sampling time is obtained from the sample signal stored in the memory section 121 and is used for interpola­tion of the following sample period (represented by the white dot). This procedure is made on each sample input for interpolation in correspondence to one rotation of the disk.

The interpolated signal v is then held by the sample holder 63 of Fig. 6 for output of a signal rs. The signal rs is applied to the driver unit 12 and thus, the track traceability can thus be improved as well as in the first or second interpolation procedure.

Fig. 14(a) is a block diagram of the compensating po­sition calculator 8 in the embodiment of the present inven­tion, in which represented by Z⁻¹ is a unit memory for holding a discrete-time signal of sample time T, Ha(z) is a low-band compensation digital filter, Hb(z) is a recursive digital filter, and LPF is a low-pass filter contained within the recursive digital filter for stabilization. There is also provided multipliers L1, L2, ... and L4 for multiplying the input signal by a coefficient. Fig. 14(b) shows the frequency characteristics of a transfer function from the tracking error e1 to the compensating position command signal rd. While f0 is a rotation frequency of the disk, a high gain is apparently given in the harmonic fre­quency component which is a multiplication of the basic frequency f0 by an integer.

The arrangement of the compensating position calculator is not limited to the above mentioned system and may be formed of a low-band compensator capable of substantially increasing the gain of a low frequency component included in the tracking error signal.