Apparatus and Method for Displacing Movable System With Respect to a Data Carrier

The present invention relates to apparatus for and a method of displacing a movable system with respect to a data carrier and, more particularly, to displacing a head for a data carrier in response to acceleration instructions derived from addresses read by the head from the carrier and a measured head acceleration value.

In data processing systems, magnetic disc memories are very frequently used because they have high storage capacity and require a relatively short time for magnetic read/write heads to access a data item contained at any point on a disc from the moment an order is derived to access the data item. Magnetic discs used in such memories carry coded data in concentric circular recording tracks having a width no greater than a few hundredths of a millimeter. The recording tracks are situated on both faces of the discs. Data recorded in the tracks are usually coded in binary form.

Each individual track on a disc is assigned a serial number j, where j is an integer between zero and (N-1), where N is the total number of recorded tracks on a face of a disc. A binary coded expression of a serial number j for a particular track is referred to as the track address. Each track includes magnetic variations, representing binary values for the track addresses and for data recorded between the space provided for the addresses.

Data are read from or written into the tracks by magnetic heads that are positioned on each side of the discs, at a distance of a few tenths of a micron from the disc. To position the heads at a particular track address, the heads are driven radially relative to the disc, while the discs are driven at constant rotational speed by an electric motor.

In currently available magnetic disc memory systems, and, more particularly, in the case of disc memories including a limited number of discs, generally fewer than four or five, the data are arranged on the disc faces as follows. A large amount of space is reserved for data or information to be processed by the data processing system of which the memory is a part; for simplication, these data are referred to as "data to be processed". A relatively small amount of space is reserved for track addresses and for data used to control the position of the magnetic head or heads relative to the tracks. Hereafter, the track addresses and data for servo-controlling the position of the head are referred to as "track identifying data".

In the following discussion, for simplification, only one face of a disc is considered in combination with only one magnetic head. The magnetic head reads and/or writes both the data to be processed and the track identifying data. It is to be understood, however, that the principles of the invention are applicable to a system including multiple discs, each having two faces.

It is the present practice, as described, for example, in U.S. Pat. No. 4,151,571, for the data contained on each face of a disc to be distributed over equal and adjacent circular sectors S.sub.0, S.sub.1 . . . S.sub.i . . . S.sub.n-1. Generally, a disc face is divided into several tens of sectors, most often forty to fifty. As the face of a magnetic disc passes in front of or beneath a magnetic head associated with it, sector S.sub.0 is read by the head before sector S.sub.1, the sector S.sub.1 before the sector S.sub.2, etcetera. Thus, the nomenclature is that sector S.sub.0 precedes sector S.sub.1, which in turn precedes sector S.sub.2, etcetera. Thus, if two data items I.sub.k-1 and I.sub.k follow one another on the same track, having serial number j on the same face, data item I.sub.k-1 precedes data item I.sub.k because data item I.sub.k-1 is read by the head before data item I.sub.k ; conversely, data item I.sub.k is said to follow data item I.sub.k-1. The same reasoning is applicable for several data groups G.sub.k and G.sub.k-1.

Each sector S.sub.i is divided into a relatively large area and a relatively small area. The large area of each sector S.sub.i includes the data to be processed, while the smaller area includes the track identification data. The smaller area of each sector is divided into several zones, referred to as "reference zones"; the number of reference zones on each disc is equal to the number of tracks on the disc, such that each track is associated with one and the same zone.

Binary ones and zeros are designated as "bits". Binary bits can be represented as magnetic variations in a track or as analog or binary electric signals. Binary or logic signals are capable of assuming only one of two values, while an analog signal is defined as a signal that can vary continuously between two positive and/or negative limit values. For simplification, any data item contained on a magnetic disc is designated in the present specification and claims as a bit. In particular, data items for identifying tracks are referred to as "track reference bits", while data items to be processed are referred to as "processed data bits".

To minimize the time required by the magnetic head to access any item of data to be processed, it is necessary for the head to move from one track to another in the shortest possible time. It is also necessary for the head to be positioned precisely with respect to the track. One type of system having a relatively short accessing time employs a voice coil type, electro-dynamic motor which is operated in a "bang-bang" mode of operation. The voice coil motor includes a coil that is linearly displaced within a cylindrically shaped permanent magnet. The coil is mechanically connected by a suspension arm to a carriage for the magnetic head. The magnetic head is driven through an acceleration phase, followed by a deceleration phase, whereby the head is displaced and accurately positioned at a desired track. During the acceleration phase, a constant current of one polarity is applied to the voice coil. The constant current causes the speed of the carriage and of the heads to increase as a linear function of displacement time. Because of the linear increase in speed of the carriage and head, the position of the carriage and head, as a function of time, is represented as an ascending arc of a parabola.

During the deceleration phase, a constant current of the opposite polarity is applied to the voice coil. The speed of the carriage therefore decreases as a linear function of time, while the position of the carriage and head, as a function of time, is represented as a descending arc of a parabola. Upon the completion of the deceleration phase, the carriage speed and the distance which remains for it to traverse to the desired location on the track should be sufficiently small for the head to be stopped above the selected track. A preferred configuration for traversing the heads in the described manner is disclosed in commonly assigned, U.S. Pat. No. 4,166,970.

In the apparatus and method disclosed in U.S. Pat. No. 4,166,970, the address of a track is the only data controlling the magnitude of the current supplied to the voice coil which drives the read/write head. The read/write head is displaced from an initial track A to a desired track B, the addresses of which are derived by a circuit for controlling addresses of the disc associated with the particular head. During the acceleration phase, the motor is supplied by a constant current as the head traverses from track A to track C, between tracks A and B. When the head arrives at track C, the current is reversed and the deceleration phase occurs.

In the method of U.S. Pat. No. 4,166,970, the track addresses are recorded on the discs in reflected binary, i.e., Gray, code. The address of track C is calculated as a function of the addresses of tracks A and B, with all three addresses being expressed in weighted binary or standard code. As the magnetic head is displaced, it reads track addresses which are stored and converted into weighted binary code. During the acceleration phase, the converted addresses are compared with the calculated address of track C. In response to track address C being read by the magnetic head, the deceleration phase is entered. The deceleration phase subsists until the speed of the head and carriage, i.e., movable system, is less than a minimum threshold V.sub.0, as calculated from the read and converted addresses. In response to the speed of the movable system being less than the minimum threshold V.sub.0, addresses of the tracks read by the magnetic head are read and compared with track address B. In response to the read track address being equal to track address B, the movable system is immobilized. A new displacement takes place if the read address differs from the address of track B.

The prior art system disclosed in U.S. Pat. No. 4,166,970 performs both the acceleration and deceleration phases in an open loop manner, i.e., without servo-control. Because of the open loop manner of operation, certain disadvantages occur. In particular, the distance which the head must travel from the moment when the head speed has dropped below the threshold V.sub.0 is quite variable, even in situations wherein the same starting track A and the same final track B are involved. The variable travel distance is due to various internal and external parameters. Exemplary of the internal parameters are displacement direction, temperature, motor characteristics, such as coil inductance and resistance, and force coefficient, while exemplary of the external parameters are dry and viscous friction, effects of weight due to the relatively large disc memory inclination, and external vibrations. It has been found that the variable distance which must be traveled by the head after the head speed has dropped below the threshold V.sub.0 necessitates several successive operations to reach the desired, final track B. Thereby, the time required by the head to access the data to be processed is relatively long. A second disadvantage which has been found through experimentation is that the prior art method does not function properly if there is a small separation between the starting track A and the final track B. In one particular situation, it was found that if the separation between the starting and final tracks was less than six, the method would not function properly. A further disadvantage is that is is difficult of obtain short access times with the prior art method.

It is, accordingly, an object of the present invention to provide a new and improved method of and apparatus for displacing a movable system with respect to a data carrier.

Another object of the present invention is to provide a new and improved apparatus for and method of controlling the movement of a magnetic read/write head of a magnetic disc memory system so that the head is very accurately and quickly driven from a starting track A to a desired final track B.

Another object of the present invention is to provide a new and improved apparatus for and method of driving a magnetic read/write head between track A and track B of a magnetic disc wherein internal and external parameters tending to increase the time required to drive the head between the tracks are circumvented.

A further object of the present invention is to provide a new and improved system for and method of driving a magnetic read/write head starting track A and a desired final track B of a magnetic disc wherein the same method and apparatus can be utilized for closely spaced and relatively distant tracks.

In accordance with the present invention, the prior art system is modified to circumvent the above mentioned disadvantages by providing a servo-control system responsive to acceleration of the movable system including the magnetic head. The servo-control system involves calculating at predetermined sampling instants an acceleration instruction function .gamma..sub.c of the track address over which the head is located. The calculated acceleration instruction function .gamma..sub.c is considered as the acceleration instruction function .gamma..sub.c for the movable system including the head and carriage. The calculated value of .gamma..sub.c is compared with a measured value .gamma. for the system acceleration. In response to the aforesaid comparison between the values of .gamma..sub.c and .gamma., a voltage is derived and applied to the terminals of the voice coil which displaces the head and arm.

The servo or feedback system of the present invention provides a significant reduction in the time required for the read/write head to access any data item recorded on the face of a disc, compared to the apparatus and method disclosed in U.S. Pat. No. 4,166,970. A further advantage of the present invention over the prior art is that the read/write head is driven to the final track B in a single movement, without several successive movements, as has been found frequently to be the case with the prior art.

In a more specific aspect, the present invention involves displacing a movable system with respect to a data carrier on which are recorded a plurality of tracks having addresses written on the carrier in a plurality of reference zones. The number of reference zones is at least equal to the number of tracks, whereby each track is associated with at least one zone. The movable system is actuated by an electric motor which drives at least one data read head from a starting track A to an arrival or final track B, having an address designated as AD.sub.f. As the head is traversed between tracks A and B, the addresses of the tracks are read by the head as addresses ADL.sub.j.

In the invention, one acceleration instruction .gamma..sub.c is calculated as a function of address ADL.sub.j at predetermined sampling instants. At each of the predetermined sampling instants, the system acceleration .gamma. is measured. The values of .gamma..sub.c and .gamma. are compared for each sampling instant. In response to the comparison between .gamma..sub.c and .gamma., the motor is controlled.

In a preferred embodiment of the invention, the method and apparatus involve calculating the separation .epsilon..sub.1, between the final track address and the track address where the head is located, as .epsilon..sub.1 =AD.sub.f -ADL.sub.j. From the calculated value of .epsilon..sub.1, a non-linear f(.epsilon..sub.1) is determined. The speed of the movable system is calculated as a function of the difference between the addresses read by the head at adjacent sampling instants. The acceleration instruction .gamma..sub.c is calculated as directly proportional to the sum of (f(.epsilon..sub.1)-v).

The above and still further objects, features and advantages of the present invention will become apparent upon consideration of the following detailed description of several specific embodiments thereof, especially when taken in conjunction with the accompanying drawings.

FIGS. 1a-1e are topological diagrams including schematic illustrations of the manner in which data are arranged in a preferred embodiment of the present invention on a magnetic disc;

FIGS. 2a-2c are schematic diagrams indicating the manner in which data are recorded in cells in accordance with the invention and of a waveform derived from a head reading a cell;

FIG. 3 is a block diagram of a device for displacing a movable system with respect to a magnetic disc data carrier, in accordance with the invention;

FIG. 4 is a curve of function f(.epsilon..sub.1) as a function of address separation .epsilon..sub.1 ;

FIG. 5 is a curve of the manner in which the speed of the movable system varies as a function of time;

FIG. 6 is a curve of supply voltage for a voice coil for the movable system, as a function of time;

FIG. 7 is a more detailed block diagram of a displacement device in accordance with a preferred embodiment of the invention;

FIG. 8 is a schematic illustration of the accurate manner in which the address ADL.sub.j of a track having serial number j is determined; and

FIG. 9 is a diagram of estimated average measured speed, with an estimation delay .theta., with respect to actual speed of the movable system.

To provide a better understanding of the principles of the present device, relating to an apparatus for and method of displacing a movable system with respect to a recording carrier in the form of a magnetic disc, it is useful to review the manner in which data are recorded on a magnetic disc in the prior art. To this end, reference is made to FIGS. 1a-1e wherein the layout of the data is illustrated. A preferred manner of writing data within reference zones of the magnetic disc illustrated in FIGS. 1a-1e is indicated by the illustrations in FIGS. 2a-2c.

In FIG. 1a, a magnetic disc D is assumed to be turning about its center, in the direction of arrow F. Disc D includes a useful recording surface between concentric circles d.sub.1 and d.sub.2, from which data are read by a single magnetic read/write head TEL, FIG. 1d. On disc D there are defined n.sub.0 equal and adjacent circular sectors S.sub.0, S.sub.1 . . . S.sub.i . . . S.sub.n.sbsb.0.sub.-1. Each sector S.sub.i is divided into a relatively large region SDO.sub.i and a relatively small region SAD.sub.i, on which are respectively recorded the data to be processed and track addresses. As illustrated in FIGS. 1c and 1d, address segments SAD.sub.i of sectors S.sub.i are divided into N zones ZRP.sub.i0 . . . ZRP.sub.ij . . . ZRP.sub.i(N-1), where N is the number of magnetic tracks on disc D. While only five zones ZRP.sub.i0 -ZRP.sub.i4 are illustrated in FIGS. 1c and 1d for simplification, it is to be understood that there are several tens of zones on a particular disc. The boundaries between different zones ZRP.sub.ij are circular axes Ax.sub.j of adjacent magnetic recording tracks. Zone ZRP.sub.ij is associated with magnetic tracks having serial number j on axis Ax.sub.j. Thus, reference zone ZRP.sub.i0 is associated with the track having serial number 0, while reference zone ZRP.sub.i1 is associated with the track having serial number 1, etcetera.

The magnetic read and/or write heads which cooperate with disc D include a magnetic circuit including a magnetic core on which is disposed a winding that extends across an air gap. To read and write the data to be processed from a track of serial number j of magnetic axis Ax.sub.j, magnetic head TEL remains stationary with respect to the track while data are read from the track. It is necessary for the air gap to be perfectly centered on magnetic axis Ax.sub.j, the boundary between reference zones ZRP.sub.ij and ZRP.sub.i(j+1). Thus, when disc D has been rotated so that head TEL is above a reference zone, the head straddles reference zones ZRP.sub.ij and ZRP.sub.i(j+1).

To simplify FIG. 1d, reference zones ZRP.sub.ij are represented as rectangles instead of arcuate regions. Each of reference zones ZRP.sub.ij contains the address of the track with which it is associated. Zone ZRP.sub.i0 contains the address of the track having serial number 0, zone ZRP.sub.i1 contains the address of the track having serial number 1, zone ZRP.sub.i2 contains the address of the track having serial number 2, etcetera. The track addresses are written in reference zones ZRP.sub.ij in reflected binary code, frequently referred to as Gray code. The Gray code is well known and a description thereof appears, for example, in a book written by H. Soubies-Camy, published by Editions Dunod, 1961, pages 253 and 254. The Gray code for two successive addresses, those associated with tracks 124 and 125, are illustrated in FIG. 1e as 001000010 and 001000011, respectively. Thus, the Gray code for tracks 124 and 125 differ from each other by only one bit, namely the last bit, which is equal to zero for track 124 and equal to one for track 125.

Reference is now made to FIG. 2a wherein there are schematically illustrated individual cells forming a reference zone ZRP.sub.ij of a sector S.sub.i. It is assumed that the disc containing the cells illustrated in FIG. 2a is moving from right to left relative to a magnetic head, as indicated by arrow F. As described in copending, commonly assigned, U.S. application, Ser. No. 076,332, filed Sept. 17, 1979, (Lowe, King, Price and Becker Docket 037-058), entitled "Method Of Writing Information On A Magnetic Recording Medium", the track address is contained in part PAD of zone ZRP.sub.ij. The rest of zone ZRP.sub.ij principally contains data for servo-controlling the position of head TEL on axis Ax.sub.j of the track having serial number j. Reference zone ZRP.sub.ij is preceded by zone ZB.sub.ij, referred to as a "wide zone" which separates the reference zone from segment SDO.sub.i of sector S.sub.i, containing data to be processed. In zone ZB.sub.ij, the magnetic induction is constant, for example, at a negative value, as indicated in FIG. 2a. In response to relative movement between zone ZB.sub.ij and head TEL, while the head is positioned above reference zone ZRP.sub.ij, the head derives a zero output signal.

To record data on a magnetic disc, a succession of small magnetic barriers, having dimensions on the order of a few microns, referred to as "elementary areas" are created on each disc track. These areas are of variable length and are distributed over the entire track length and include alternate magnetic inductions of the same value, but of opposite polarity, in a direction parallel to the disc surface.

The start of reference zone ZRP.sub.ij is indicated by line DZ.sub.ij, that defines a change in magnetic induction polarity between negative induction zone ZB.sub.ij and a positive magnetic induction area DM.sub.1 of zone ZRP.sub.ij. In the remainder of the specification and claims of the present application, a change in magnetic induction direction is refered to as a "magnetic transition".

A magnetic transition can be of two different types. A first type of magnetic transition occurs when the face of the magnetic disc travels beneath the magnetic head TEL, whereby the head is exposed to successive elementary magnetic areas of negative and positive induction; the corresponding magnetic transition is referred to as positive. A magnetic transition is defined as being negative if head TEL is exposed to successive elementary positive and negative induction areas.

Segment PAD of zone ZRP.sub.ij, where the address of the zone is located, includes m identical elementary cells, each having an identical length L; in the embodiment illustrated in FIG. 2a, twelve such cells are illustrated and denominated as C.sub.0, C.sub.1 . . . C.sub.k . . . C.sub.11. Each cell of segment PAD contains one address bit. Any address B.sub.k contained in a cell is defined by the presence or absence of a double magnetic transition. The first magnetic transition T.sub.1k is of an opposite polarity to the second transition T.sub.2k. For example, the first transition T.sub.1k is positive, while the second transition T.sub.2k is negative, as illustrated in FIG. 2b. The address bits ADE.sub.j of a track having serial number j of reference zone ZRP.sub.ij are coded, for example, such that bit B.sub.k is equal to a binary one, in the case of the presence of a double magnetic transition. If bit B.sub.k has a value equal to zero, the double magnetic transition is missing and there is a uniform magnetic induction across the length of the cell. For simplification, in the following description and claims, the absence and presence of a double magnetic transition are designated by the term "dibits".

In FIG. 2c are illustrated the analog signals derived by magnetic head TEL in response to cell C.sub.k having binary one and zero values. In response to cell C.sub.k having a binary one value, as indicated by the dibit on the left side, which includes two transitions, head TEL derives two analog pulses of opposite polarities and equal magnitudes, +AMP and -AMP, respectively. In response to the value of cell C.sub.k indicating a binary bit value of zero, as indicated by the right portion of FIG. 2b, head TEL derives a zero value, as indicated in the right portion of FIG. 2c.

Reference is now made to FIG. 3 of the drawing wherein there is illustrated a block diagram for performing the method of the invention wherein a movable system SYSMOB to be displaced includes magnetic read/write head TEL, mechanically coupled to carriage CHAR. The object of the apparatus illustrated in FIG. 3 is to displace, in a single motion, in the shortest possible time, magnetic read/write head TEL from a starting or initial track A to a final or arrival track B, having an address AD.sub.f. The movement of head TEL is controlled by a non-linear second order differential equation of the type:

where

.epsilon..sub.1 and f(.epsilon..sub.1) are respectively the non-linear variable and function defined supra;

f(.epsilon..sub.1) is assumed to be an increasing function;

by definition, .epsilon..sub.2 =d.epsilon..sub.1 /dt=-v, where v is the speed of head TEL; and

.epsilon..sub.3 equals

where .gamma. is the acceleration of head TEL. By substitution, Equation (1) can be written:

In a preferred embodiment of the invention, movable system SYSMOB is displaced with respect to the face of disc D by performing the following sequence of operations:

(1) at predetermined, equally spaced sampling instants spaced from each other by T seconds, an acceleration instruction .gamma..sub.c is calculated by:

(a) determing the address ADL.sub.j where head TEL is located and calculating the separation .epsilon..sub.1 ;

(b) determining the corresponding function f(.epsilon..sub.1), a predetermined function of .epsilon..sub.1, whereby f(.epsilon..sub.1) is also a function of address ADL.sub.j ;

(c) calculating the speed v of system SYSMOB as a function of the difference between addresses ADL(nT+k.sub.0 T) and ADL(nT), the addresses ADL.sub.j read by head TEL at sampling instants t.sub.n =nT and t.sub.k.sbsb.0 =nT+k.sub.0 T, where n and k are integers;

(d) calculating the acceleration instruction .gamma..sub.c such that .gamma..sub.c /C.sub.2 =(f(.epsilon..sub.1)-v), whereby .gamma..sub.c is a function of ADL.sub.j ;

(2) the acceleration .gamma. of system SYSMOB is measured and divided by the constant C.sub.2 ;

(3) the difference (.gamma..sub.c -.gamma.)/C.sub.2 =.DELTA.(.gamma./C.sub.2) is calculated;

(4) a coil of electro-dynamic motor ML is driven by a constant voltage having a polarity dependent upon the polarity of the calculated difference .DELTA.(.gamma./C.sub.2).

The apparatus of FIG. 3 for performing the stated method includes electro-dynamic motor ML having a voice coil which drives carriage CHAR of system SYSMOB. Motor ML is responsive to a network including circuit CIRCAD which determines the address ADL.sub.j read by head TEL from disc D. The address derived from circuit CIRCAD is combined with an address output signal for the final or desired address of head TEL, as derived from address control circuit GESTAD. The signals from circuits CIRCAD and GESTAD are combined in a calculating network ACCEL, which derives, by calculation, the acceleration instruction .gamma..sub.c. Calculating network ACCEL is also responsive to an output signal of acceleration measuring device MES, which is coupled to motor ML, whereby the measuring device derives a signal representing the acceleration .gamma. of system SYSMOB. The output signal of measuring device MES is also divided by a predetermined constant C.sub.2 in multiplier MUL, having an output signal which is supplied to one input of comparator COMP, having a second input responsive to the acceleration instruction signal .gamma..sub.c derived from calculating network ACCEL. Comparator COMP compares the acceleration instruction .gamma..sub. c with the measured acceleration .gamma., to derive an error signal which is coupled to voltage supply generator ALIM for the voice coil of electro-dynamic motor ML.

Circuit CIRCAD, illustrated in detail in FIG. 7, responds to an analog signal ST derived by magnetic read/wirte head TEL when the data dibits contained in segment PAD of zone ZRP.sub.ij are beneath head TEL. Signal ST is composed of a set of analog pulses, as indicated in FIG. 2c. Circuit CIRCAD responds to signal ST, to transform it into a set of logic pulses representative of the address ADG.sub.j, in Gray code, of the serial number j of the track associated with reference zone ZRP.sub.ij which head TEL is over. Circuit CIRCAD converts the Gray code address ADG.sub.j into a weighted binary coded address ADL.sub.j ; weighted binary codes are described in the previously cited book by Soubies-Camy. Circuit CIRCAD derives the binary coded weighted address ADL.sub.j as a multibit, parallel signal that is supplied to calculation network ACCEL on a parallel bus. Address ADL.sub.j is supplied by circuit CIRCAD to calculating network ACCEL with a sampling frequency F=1/T, where T is a sampling period equal to the time required for disc D to travel between two segments PAD of two adjacent reference zones ZRP.sub.ij and ZRP.sub.(i+1)j associated with the same track having serial number j, whereby zone ZRP.sub.ij precedes zone ZRP.sub.(i+1)j. In other words, addresses ADL.sub.j are supplied by circuit CIRCAD to calculating network ACCEL every T seconds.

Calculating network ACCEL, which calculates the acceleration instruction .gamma..sub.c, is illustrated in FIGS. 3 and 7 as including a subtractor SOUS, which responds to the addresses ADL.sub.j and AD.sub.f, respectively derived from circuits CIRCAD and GESTAD. Subtractor SOUS responds to the output signals of circuits CIRCAD and GESTAD to derive an output signal proportional to the quantity .epsilon..sub.1 =ADF.sub.f -ADL.sub.j. The output of subtractor SOUS is expressed in the same weighted binary code as address ADL.sub.j because the final address of track B, as derived from circuit GESTAD, is expressed in the same weighted binary code as address ADL.sub.j. Subtractor SOUS calculates a new value of .epsilon..sub.1 every T seconds in response to the new address ADL.sub.j being derived from circuit CIRCAD every T seconds.

The .epsilon..sub.1 output signal of subtractor SOUS is supplied to function generator GF, which derives a binary output signal having a magnitude f(.epsilon..sub.1) every T seconds. Function generator GF derives the non-linear function f(.epsilon..sub.1) and supplies it to one input of binary adder ADDIT. The function f(.epsilon..sub.1) is a predetermined, known function, whereby the function generator can be in the form of a look-up table memory which derives the binary values of f(.epsilon..sub.1) in response to the values of .epsilon..sub.1 derived from subtractor SOUS.

FIG. 4 includes a curve representing an exemplary non-linear output function f(.epsilon..sub.1) of function generator GF in response to a set of input values .epsilon..sub.1. From FIG. 4, the slope of the function relating .epsilon..sub.1 to f(.epsilon..sub.1) is relatively large for small values of .epsilon..sub.1, and relatively small for large values of .epsilon..sub.1, i.e., the derivative df(.epsilon..sub.1)/d.epsilon..sub.1 is relatively large for small values of .epsilon..sub.1, but the derivative is small for large values of .epsilon..sub.1. It is also noted that the values of f(.epsilon..sub.1) and .epsilon..sub.1 are related to each other as a monotonic, approximately exponential, function.

Acceleration instruction calculating network ACCEL also includes a network CALVIT for deriving a binary signal representing the speed of head TEL relative to disc D. Network CALVIT responds every T seconds, i.e., once each sampling instant, to the multibit, parallel address ADL.sub.j output of circuit CIRCAD. Network CALVIT determines the speed v.sub.m of head TEL relative to disc D, in a radial direction, by calculating the number of addresses traversed by the head in a predetermined number of sampling intervals from the relationship: ADL(nT+k.sub.0 T)-ADL(nT)=1q, where 1 is an integer and q is a distance equal to a fraction of the width of the tracks on disc D. Because all of the tracks of disc D have approximately the same width lp, as indicated in FIGS. 1d and 8, the value of q=f.multidot.lp, where f is a constant between zero and one and q represents the accuracy with which an address is determined. In a preferred embodiment, q=one-half the width of a track, whereby q=0.5 lp. Thereby, in the preferred embodiment, if head TEL reads an address ADL.sub.j from a track of serial number j, head TEL is disposed opposite the track of serial number j, at approximately half a track. The quantity 1q therefore represents the distance traveled by head TEL during a time interval k.sub.0.T seconds.

Calculating network CALVIT determines the speed of head TEL according to the formula v.sub.m =1q/k.sub.0 T. The calculated or measured speed value v.sub.m signal derived by network CALVIT is reversed in polarity and supplied in binary form to the other input of adder ADDIT.

As described in more detail infra, the measured speed v.sub.m derived from network CALVIT at time instant (nT+k.sub.0 T) is not equal to the actual speed v of head TEL at the instant (nT+k.sub.0 T). Instead, the output signal of network CALVIT at instant (nT+k.sub.0 T) is indicative of the speed of head TEL at a previous time, designated as (nT+k.sub.0 T) -.theta., where .theta.=(k.sub.0 +1)T/2; thereby, .theta. is referred to as an average estimation delay.

Because of the delay in the calculated speed signal derived from network CALVIT, the acceleration instruction calculation network ACCEL includes a compensation network COMPRET, which compensates for the average estimation delay .theta. of measured speed v.sub.m with respect to the actual speed v of head TEL. Network COMPRET responds to signal .gamma. as derived from measuring device MES to derive compensation signal .gamma..sub.F that is supplied to one input of adder ADD, having a second input responsive to the combined outputs of function generator GF and network CALVIT. For simplification, adder ADD and adder ADDIT are shown as a single block in FIG. 3.

Network COMPRET is preferably an analog, low-pass filter network responsive to the analog output signal of measuring device MES. Network COMPRET derives an analog output signal .gamma..sub.F such that compensation is provided for the delay inherent in the operation of binary network CALVIT. That such compensation occurs can be seen by designating the quantity (V.sub.m +.gamma..sub.F)=v, the estimated speed of head TEL. Thus, the magnitude of the output signals of networks COMPRET and CALVIT is the estimated speed. The speed difference .DELTA.v is defined as v-v=v-v.sub.m -.gamma..sub.F. The characteristics of low-pass filter network COMPRET are established so that the speed difference .DELTA.v is a minimum, i.e., approximately zero. Thus, the estimated speed v is practically equal to the actual speed v of head TEL. It can be shown that this result is obtained for a value of .gamma..sub.F =.gamma..multidot.G, where G is the transfer function of low-pass filter COMPRET.

The analog output signal of compensating network COMPRET is reversed in polarity and supplied, in analog form, to analog adder ADD. Analog adder ADD is also responsive to an analog signal representing the amplitude and polarity of the binary signal derived from binary adder ADDIT. To this end, the binary output of adder ADDIT, having a polarity and magnitude representative of f(.epsilon..sub.1)-v.sub.m is supplied to a digital to analog converter CDA. Adder ADD thus derives an analog signal having a magnitude and polarity in accordance with f(.epsilon..sub.1)-v.sub.m -.gamma..sub.F. The output of analog adder ADD is thereby a relatively constant signal representing the acceleration instruction .gamma..sub.c. In effect, the output of adder ADD can be represented as:

The output signal of adder ADD, having a magnitude represented by .gamma..sub.c /C.sub.2 =-.epsilon..sub.3 /C.sub.2 is supplied to one input of analog comparator COMP, having a second input, in the form of an analog signal having a magnitude and polarity represented by .epsilon..sub.3 /C.sub.2, as derived from analog multiplier MUL.

Multiplier MUL responds to an analog output signal of measuring device MES, having a magnitude and polarity represented by .gamma.=-.epsilon..sub.3 (t), where t is an instantaneous time value. Acceleration measuring device MES derives an analog signal .gamma. by relying upon the principle that the acceleration of movable system SYSMOB is proportional to the current supplied to the voice coil of electro-dynamic motor ML. Thus, the acceleration of system SYSMOB can be determined by measuring the current supplied to the voice coil of motor ML and multiplying a signal proportional to the measured current by a proportionality constant to obtain the signal .gamma.. Thus, measuring device MES monitors the current supplied to the coil of motor ML and derives a suitable analog signal indicative of the monitored current. For diagrammatic purposes, the measuring device is shown as being connected to the output of motor ML, but it is to be understood that in actuality it is responsive to the current supplied to the coil of the motor. The analog signal derived from measuring device MES is supplied in parallel to compensation network COMPRET and to multiplier MUL, where it is scaled or multiplied by the factor 1/C.sub.2, and then supplied to comparator COMP.

The output of comparator COMP is an analog signal having a magnitude and polarity representative of an error between the measured and instructed values of acceleration of system SYSMOB. To this end, the magnitude and polarity of the analog output signal of comparator COMP is represented as (.gamma..sub.c -.gamma.)/C.sub.2 =(.epsilon..sub.3 -.epsilon..sub.3)/C.sub.2 =.DELTA.(.epsilon..sub.3 /C.sub.2). The analog output error signal of comparator COMP is coupled, as a control input, to voltage supply generator ALIM. In response to .DELTA.(.epsilon..sub.3 /C.sub.2) being positive and negative, supply generator ALIM respectively supplied voltages +U and -U to the coil of linear electro-dynamic motor ML. It is to be understood that in a preferred embodiment, adder ADD and comparator COMP are a single element, but that they are shown as separate elements for the purposes of clarity. Thus, adder ADD and comparator COMP can, together, be considered as a single means for combining signals representative of f(.epsilon..sub.1), v.sub.m, .gamma..sub.F, and .epsilon..sub.3 /C.sub.2 to derive the analog error signal .DELTA.(.epsilon..sub.3 /C.sub.2).

Reference is now made to FIG. 5 of the drawing wherein the speed of movable system SYSMOB is plotted as a function of time while traversing between tracks A and B. Between track A and an intermediate track C, the coil of motor ML is permanently supplied with a positive voltage +U.sub.0 in response to the output of generator ALIM, since the error signal .DELTA.(.epsilon..sub.3 /C.sub.2) derived by comparator ADCOMP is positive throughout the interval. The positive voltage supplied by generator ALIM to motor ML between time t.sub.A and t.sub.C is also shown by the waveform of FIG. 6 as having a constant value +U.sub.0. As illustrated in FIG. 5, between tracks A and B during the intervals between times t.sub.A and t.sub.B, head speed v, as represented by the curve r.sub.1, is approximately of exponential form, with the head speed remaining less than speed v.sub.m. For sufficiently large values of .epsilon..sub.1, it is estimated that at each abscissa point, such as abscissa point .epsilon..sub.1i (FIG. 4), f(.epsilon..sub.1) has a relatively small value, represented by:

where .alpha.=df(.epsilon..sub.1)/d.epsilon..sub.1, and .alpha. is a very small value. The movement of movable system SYSMOB is controlled by a differential equation of the form

The solution of Equation (3) is of the type

where B.sub.1 is a constant. Thereby, between tracks A and C, the movement of system SYSMOB is speed regulated.

As head TEL approaches track B, where there are smaller deviations of address .epsilon..sub.1 and the value of the error signal .DELTA.(.epsilon..sub.3 /C.sub.2) is changing polarity, the approximation given by Equation (2) is no longer valid. Thereby, the movement of system SYSMOB is defined by the nonlinear second order differential Equation (1), supra. Because of the changing polarity of error signal .DELTA.(.epsilon..sub.3 /C.sub.2), the output of ALIM varies between +U.sub.0 and -U.sub.0. Therefore, after track C has been passed, i.e., after time t.sub.C, the speed versustime curve of system SYSMOB is represented by curve r.sub.2. The trajectory of curve r.sub.2 corresponds to the non-linear second order differential Equation (1) and is approximated as a cylindrical helix having an axis extending along approximately a straight line between times t.sub.C and t.sub.B, i.e., in the interval between the intermediate and final track positions.

In FIG. 5 is also shown a curve of the speed v of system SYSMOB as a function of time for a situation where the starting address A' is removed by a greater extent from the starting address than for the situation indicated by curve r.sub.1. Such a situation is indicated by curves r'.sub.1 and r'.sub.2. Curve r'.sub.1 indicates the speed versus time trajectory of system SYSMOB between pount A' and intermediate point C' for the modified situation, while curve r'.sub.2 represents the trajectory between tracks C' and B. During the deceleration interval, between time t.sub.C ' and time t.sub.B for this situation, the voltage supplied by generator ALIM to motor ML constitutes a set of constant amplitude pulses of alternate polarity in response to the polarity reversals of error signal .DELTA.(.epsilon..sub.3 /C.sub.2). The duration of successive pulses derived from circuit ALIM has a tendency to decrease over the interval between times t.sub.C ' and t.sub.B so that the average voltage during this interval has a negative value, with a positive slope. The last two pulses in the interval, i.e., immediately before track B is reached, have the same duration, but opposite amplitude, whereby the voltage supplied by circuit ALIM to motor ML is zero at time t.sub.B, as illustrated in FIG. 6. It is to be understood that the waveform of FIG. 6 is reversed for a reversal in the relative amplitudes of the initial and final track addresses.

Reference is now made to FIG. 7 of the drawing wherein the details of circuit CIRCAD are illustrated as including threshold circuit GS responsive to the analog output signal of head TEL. Threshold circuit GS derives a serial binary signal that is supplied to converter register TRANSCOD, also responsive to sampling pulses derived from sample generator ECHANT, which pulses are derived every T seconds, which defines the sampling times.

Threshold circuit GS responds to output signal ST of head TEL to transform the analog pulses in signal ST into a set of logic pulses. To this end, threshold circuit GS includes a pair of thresholds S.sub.1 and S.sub.2 which are a function of the absolute value of the average amplitude of the signals derived by head TEL for binary one bits in the interval under consideration.

It will be recalled, by reference to FIG. 2, that a binary one is represented at the output of head TEL by two opposite polarity pulses, while a binary zero is represented at the head output as a zero amplitude. The thresholds S.sub.1 and S.sub.2 are respectively set to 0.25 AMP and 0.75 AMP, where AMP is equal to the average absolute magnitude of the amplitude of each pulse derived for a binary one bit from head TEL.

Circuit GS determines the value of bits derived by head TEL while the head is in the reference zone by comparing the output signal of the head with the set threshold values. Because addresses are written in the reference zones in Gray code, a head TEL that perfectly straddles a pair of reference zones derives, for corresponding cells of adjacent track addresses, one of three values, namely a zero level, a maximum level, approximately AMP, and an intermediate level, approximately 0.5 AMP. For any particular pair of adjacent track addresses being read by head TEL, only one cell can be associated with signals of approximately 0.5 AMP; all of the remaining voltages derived from the head, for a particular pair of adjacent reference zones, must be approximately zero or approximately AMP. The approximately zero and approximately AMP values read from head TEL respectively occur for cells having zero and one values; thus, in FIG. 1e, voltages of zero or AMP are derived from all of the cells, except for the last cell. For correspondingly numbered cells of adjacent reference zones that differ from each other, the output of head TEL is approximately 0.5 AMP. This is the situation of the binary one and binary zero values for the last cells of zones ZRP.sub.124 and ZRP.sub.125, FIG. 1e.

If corresponding bits B.sub.kj and B.sub.k(j+1) of adjacent reference zones are both zero, the output signal ST of head TEL is zero, and therefore less than the threshold S.sub.1. Circuit GS thus derives a binary zero output signal. The binary output signal is derived from circuit GS even if head TEL is not positioned so it exactly straddles axis Ax.sub.j, between adjacent reference zones ZRP.sub.ij and ZRP.sub.i(j+1), so long as the edges of the head are positioned anywhere between boundaries Ax.sub.(j-1) and Ax.sub.(j+1).

If corresponding cells in the addresses of reference zones ZRP.sub.ij and ZRP.sub.(j+1) both have a binary bit value on one, the output voltage of head TEL has a positive amplitude, followed by a negative amplitude. The positive and negative amplitudes have absolute values equal to AMP, which is greater than S.sub.2. Circuit GS responds to the positive and negative amplitude pulses and the magnitude of ST to derive a binary one value as long as the edges of head TEL are positioned between axes Ax.sub.(j-1) and Ax.sub.(j+1).

If it is assumed that corresponding cells of the address of zones ZRP.sub.ij and ZRP.sub.(j+1) are respectively equal to one and zero, as occurs for one bit of a pair of adjacent reference zones, an ambiguity bit is detected by detector GS. The absolute value of the signal derived for an ambiguity bit can vary continuously from zero to one hundred percent of AMP, depending upon the position of head TEL relative to axis Ax.sub.j, as long as the edges of head TEL are confined between axes Ax.sub.(j-1) and Ax.sub.(j+1). In the extreme left position illustrated in FIG. 8, the center of head TEL is at position POS.sub.1, midway between axes Ax.sub.(j-1) and Ax.sub.j. In the intermediate position illustrated in FIG. 8, head TEL is located so that the center thereof is at position POS.sub.2, on axis Ax.sub.j. Head TEL may also be at the extreme right position illustrated in FIG. 8, whereby the center of the head is coincident with position POS.sub.3, which is halfway between axes Ax.sub.j and Ax.sub.(j+1). The distance between positions POS.sub.1 and POS.sub.3 is equal to the width of a zone ZRP.sub.ij, which in turn is equal to the width lp of a track. The distance lp is also referred to as the pitch between tracks.

The amplitude of the signal derived from head TEL is dependent upon the location of the center of the head relative to positions POS.sub.1 and POS.sub.3. Let x represent the position of the center of head TEL, such that x=0 when the center of head TEL is at position POS.sub.1 and x=1 when the center of head TEL is at position POS.sub.3. The amplitude of the ambiguity bit is thus a function of x and is represented as A(x). Considering the situation of the two least significant bits in the addresses of FIG. 1e, wherein cell C.sub.kj has a value of zero and cell C.sub.k(j+1) has a value of one, it is seen that if x is less than lp/4, A(x) is less than the threshold S.sub.1, equal to 0.25 AMP. On the other hand, if x is greater than 3 lp/4, A(x) is greater than the maximum threshold, equal to 0.75 AMP. If x is between lp/4 and 3 lp/4, A(x) is between the maximum and minimum thresholds S.sub.1 and S.sub.2, i.e., between 0.25 AMP and 0.75 AMP.

For the ambiguity situation, if one pulse for a particular address cell has an amplitude greater than upper threshold S.sub.2, the other pulse has an amplitude less than S.sub.1. Detector GS responds to a pair of such pulses for a single cell, as well as to pulses between the thresholds S.sub.1 and S.sub.2, to derive binary values for the ambiguity bit such that if the amplitude of the two pulses is between the two thresholds, a binary weighted value a.sub.-1 (j) value of one is derived. If, however, the value of one pulse is less than the lower threshold and the value of the other pulse within a cell is above the upper threshold, the binary weighted value a.sub.-1 (j) is assumed to be zero.

The pulses supplied by detector GS are supplied to converter TRANSCOD, which responds to the Gray coding of the pulses to derive address ADG.sub.j or ADG.sub.j+1. Converter TRANSCOD responds to the output of threshold circuit GS at a frequency of 1/T, equal to the frequency of the sampling pulses derived by a timing source (not shown) and supplied to sampling generator ECHANT. Converter TRANSCOD responds to the Gray coded pulses derived from detector GS to derive a weighted or standard binary coded signal. Converter register TRANSCOD therefore derives every T seconds, on a parallel output bus, the address ADL.sub.j in weighted binary code and supplies this signal to acceleration coefficient calculating network ACCEL. The output signal of converter register TRANSCOD responds to successive binary outputs of detector GS to derive address ADL.sub.ji, such that

where

a.sub.1 (j), a.sub.2 (j) . . . a.sub.n (j).epsilon.{0, 1}

weight 2.sup.-1 -lp/2.

From the foregoing, any position whatsoever of head TEL opposite the face of the disc with which it is associated can be represented by an address quantified as a half-step, i.e., half track width. Thus if it is assumed that serial number j equals 124 and x is less than lp/4, i.e., A(x) is less than S.sub.1, head TEL occupies track 124. If, on the other hand, x is greater than 3 lp/4, whereby A(x) is greater than S.sub.2, head TEL is located above track 125. If the value of x is between the thresholds S.sub.1 and S.sub.2, it is assumed that head TEL is above track 124.

If it is assumed that the final position of head TEL is such that the head is positioned directly on magnetic axis Ax.sub.f of address AD.sub.f,

where a.sub.0 (f), a.sub.1 (f) . . . a.sub.n (f) belong to {0, 1}.

The separation .epsilon..sub.1 =AD.sub.f -ADL.sub.j, expressed as a half-step, can be calculated in binary form as:

where .epsilon..sub.1i (j) {0, 1}.

The accuracy with which the position of head TEL can be determined and of the separation .epsilon..sub.1 equals lp/2=q.

Network CALVIT for calculating the speed of head TEL, v.sub.m, includes, as illustrated in FIG. 7, a circulating memory MEMOCIRC, a binary subtractor-divider SUBDIV, and an inhibiting device BLOC. Circulating memory MEMOCIRC is supplied every T seconds with address ADL(nT+k.sub.0 T) and supplies the address ADL(nT) to subtractor-divider SUBDIV. Subtractor-divider SUBDIV is also responsive to the address ADL(nT+k.sub.0 T). Circulating memory MEMOCIRC retains all of the values of addresses read between times (nT) and (nT+k.sub.0 T). Thus, all of the addresses ADL(nT), ADL(nT+2T) . . . ADL(nT+k.sub.0 T) are serially stored in memory MEMOCIRC as they are read. Subtractor-divider SUBDIV calculates the speed value v.sub.m by determining the difference ADL(nT+k.sub.0 T)-ADL(nT) and by dividing the difference by the quantity k.sub.0 T. Subtractor-divider SUBDIV performs these operations once each sampling interval, i.e., every T seconds. An output signal is derived from subtractor-divider SUBDIV at the same frequency that signals are supplied to the subtractor-divider by memory MEMOCIRC, by inhibiting the output of the subtractor-divider with output pulses from inhibiting network BLOC that is activated once every T seconds in synchronism with activation of memory MEMOCIRC.

The average estimation delay .theta. is determined by relying upon the facts that the time interval separating sampling times (nT) and (nT+k.sub.0 T) is a sufficiently small interval (a few milliseconds) such that the variation in the actual speed v of head TEL can be considered as a linear function. The corresponding variation in the speed of head TEL as a function of time is illustrated in FIG. 9, wherein the symbols t.sub.0, t.sub.1, t.sub.2, t.sub.3, t.sub.4, t.sub.5, etcetera, respectively designate the sampling times (nT), (nT+T), (nT+2T), (nT+3T), (nT+4T), (nT+5T), (nT+6T), etcetera; it is assumed that k.sub.0 equals 4. At time t.sub.4, subtractor-divider SUBDIV calculates the value v.sub.m1 =(ADL(nT+4T)-ADL(nT))/4T. The calculated value of v.sub.m1 is blocked for T seconds by inhibiting device BLOC, i.e., between times t.sub.4 and t.sub.5. At time t.sub.5, the value (ADL (nT+5T)-ADL(nT+T))/4T=v.sub.m2 is calculated. The calculated value of v.sub.m2 is blocked for T seconds between times t.sub.5 and t.sub.6. Similarly, at time t.sub.6, the speed v.sub.m3 is calculated as (ADL(nT+6T)-ADL(nT+2T))/4T. The calculated value of v.sub.m3 is blocked for T seconds between times t.sub.5 and t.sub.6. It is apparent that measured speed v.sub.m for times before t.sub.4 and after t.sub.6 is determined identically to that described for times between t.sub.4 and t.sub.6. The measured speed derived from network CALVIT is thus a series of steps, as represented by curve r.sub.5, FIG. 9, with the average speed v.sub.m being represented by a relatively straight line r.sub.6. Because of the linear evolution of actual speed v as a function of time, the measured speed v.sub.m at times t.sub.1, t.sub.2, t.sub.3, t.sub.4, t.sub.5, etcetera, equals the actual speed v measured at the time (nT+k.sub.0 T/2). This fact can be verified by comparing curves r.sub.4 and r.sub.5, FIG. 9. Thereby, the speed measured at time t.sub.4 is equal to the actual speed at time t.sub.2, such that t.sub.2 =(t.sub.4 +t.sub.0)/2=t.sub.0 +(t.sub.4 -t.sub.0)/2-t.sub.0 +k.sub.0 T/2=t.sub.0 +2T. This correlation between measured and actual speed results from the fact that when speed evolves linearly as a function of time, the average speed between two times equals the measured speed at the middle of the time interval separating a pair of sampling times. Because the value of average speed v.sub.m is blocked for T seconds. It is clearly seen, particularly from FIG. 9, that the average estimated delay .theta.=k.sub.0 T/2+T/2=(k.sub.0 +1)T/2.

The optimum value of k.sub.0 is determined from the known relationship that v.sub.m =1q/k.sub.0 T and that the accuracy with which the quantity 1q is determined is equal to the value of q. Thereby, a quantification error .epsilon..sub.q exists in determining the measured speed v.sub.m, which quantification error is equal to q/k.sub.0 T. To the quantification error .epsilon..sub.q is added an error .epsilon..sub..theta. due to the average estimation delay .theta.=(k.sub.0 +1)T/2. The result is that the absolute value of .epsilon..sub..theta. is equal to the absolute value of .gamma..multidot..theta., whereby, in effect, .gamma.=dv/dt, i.e., dv=dt. If a function Q, known as a "cost function", is defined such that Q=.epsilon..sub.q +.epsilon..sub..theta., there exists a value k.sub.0 =1/T.sqroot.2q//.gamma./, to minimize the cost function. It is found that k.sub.0 =4 in the described embodiment.

While there have been described and illustrated several specific embodiments of the invention, it will be clear that variations in the details of the embodiments specifically illustrated and described may be made without departing from the true spirit and scope of the invention as defined in the appended claims.