WO1999040585A1

WO1999040585A1 - Apparatus and method for sensing disk-drive head-arm speed during head loading

Info

Publication number: WO1999040585A1
Application number: PCT/US1999/002596
Authority: WO
Original assignee: Seagate Technology, Inc.
Priority date: 1998-02-06
Filing date: 1999-02-05
Publication date: 1999-08-12
Also published as: EP0974143A1; JP2001519961A

Abstract

Apparatus for estimating the speed of a disk drive's head arm during loading of the drive's read/write head onto a disk platter. The speed is estimated by a model of the head-arm actuator plant. The model is implemented by a digital state machine that tracks the head-arm's velocity, friction and voice-coil motor (VCM) current using a readily available sense voltage which is based on the VCM current. The apparatus of the invention is particularly advantageous because it allows a head-arm control system to have sufficient control over the head arm's movements so as to prevent the drive's read/write head from crashing into and damaging the drive's data recording surface.

Description

APPARATUS AND METHOD FOR SENSING DISK-DRIVE HEAD-ARM SPEED DURING HEAD LOADING

FIELD OF THE INVENTION

The invention relates generally to apparatus and

methods for sensing the speed of a read/write head in a

disk drive, and more particularly, to a state estimator

for modeling the head speed with feedback based on a

current through a voice coil motor that actuates a head

arm. The state estimator thus yields an estimate for

describing the head's state based on voltage signals

commonly available from a head-arm actuator current

driver.

BACKGROUND OF THE INVENTION

It has become common to supply disk drives that

have a power saving mode in which the disk drive shuts

down during periods of inactivity. When the disk stops

spinning, the disk's read/write head will stop "floating"

over the disk surface. Thus, it is generally desirable to

park the head on to a ramp during non-operating time to

prevent head crashes onto disk surface during

transportation, to prevent static "stiction" during startup, and to prevent scratches on the disk as the head

contacts when disk starts and stops spinning.

To unpark a head from a ramp, it is necessary to

load the head over the disk after the drive's spindle

motor starts spinning. To prevent the head from crashing

into the disk, the speed of the head movement must be

controlled within a certain range depending on each

particular drive design. Accordingly, it is desirable to

measure the head's speed without significantly affecting

the drive's cost.

Existing head speed control systems take

advantage of the fact that a back emf is generated that is

proportional to the head speed. Thus, the speed may be

determined by measuring the back emf. However, the back

emf is often not a directly measurable parameter because

it is superimposed with a voltage across the head's voice

coil due to voltage drops associated with the coil's

internal resistance and inductance. The value of the coil

voltage is much larger than the back emf by a factor of

about one-hundred. One technique for addressing the coil current

measurement problem involves pulsing the driving current .

A calculated control current is turned on for a fixed

time period to cause the head move. The head's voice coil

current is then turned off for another fixed period of

time so that there is no voltage drop across the coil due

to current. Theoretically, the back emf due to the head

movement is thus measured and used as the speed

indication. However, since there is fair amount of

friction associated with the head, it has been found that

the head slows (or may even stop) immediately after the

current is turned off. Thus, the voltage measured during

the interval in which the current is turned off often

fails to accurately represent the head speed.

Furthermore, the head movement resulting from pulsing the

current generates vibrations in the system.

Accordingly, there exists a need for a circuit

to accurately monitor the head arm velocity without unduly

increasing the cost of the disk drive. - 4

SUMMARY OF THE INVENTION

The present invention is embodied in a system,

and related method, for estimating state variables of a

disk-drive head-arm. The system includes a processor and

a current sense circuit . The current sense circuit

monitors current through a head-arm actuator during operation and generates a sensor signal based on the

current through the actuator. The processor receives the

sensor signal and generates at least one estimated head-

arm state variable based on the sensor signal .

In more detailed features of the invention, the

estimated head-arm state variable represents the velocity

of the head arm. Also, the processor includes a state

estimator that models a plurality of estimated head-arm

state variables. Further, the actuator may include a

voice coil motor coupled to the head arm for actuating the

head arm. Accordingly, the state variables that the state

estimator models may include the velocity of the head arm,

the friction associated with the head arm, and the current

through the voice coil motor. Additionally, the processor - 5 -

may be a digital signal processor that implements a

digital state estimator that models a plurality of head-

arm state variables.

In other more detailed features of the

invention, the digital state estimator may include first

and second summers, a unit delay and a feedback control

element . The first summer adds control data to estimated

control data provided by the feedback control element

based on estimated head-arm state data to generate

predicted data. The unit delay delays the predicted data

to generate delayed predicted data. The second summer

adds the delayed predicted data to a sensor error signal

generated based on the difference between the sensor

signal and an estimated sensor signal to generate the

estimated head-arm state data. The estimated head-arm

state data includes information for constructing the

estimated sensor signal.

Other features and advantages of the present

invention should become apparent from the following

description of the preferred embodiments, taken in

conjunction with the accompanying drawings, which - illustrate, by way of example, the principles of the

invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic block diagram of a head-

arm control system, according to the invention, for

estimating the state of the arm, according to the

invention, including determining the velocity of a disk-

drive's head arm.

FIG. 2 is a block diagram of an estimator model,

according to the invention, for modeling the disk-drive's

head-arm velocity.

FIG. 3 is a block diagram of the estimator

model, according to the invention, showing the signals the

estimator model receives in relation to a current driver

of the control system of FIG. 1.

FIG. 4 is a block diagram of a digital signal

processing system, according to the invention, for

modeling the disk-drive's head-arm movements.

FIG. 5 is a block diagram for modeling the

head-arm hardware and actuator-control system. FIG. 6A is a plan view of the disk drive and the

disk-drive head arm in the parked position before

unloading from the ramp.

FIG. 6B is an elevation view of the disk drive

and the disk-drive head arm of FIG. 6A, showing the head

arm in the parked position before unloading from the ramp.

FIG. 7 is a plan view of the disk and disk head

arm as the head is sliding off from the parking ramp.

FIG. 8 is a plan view of the disk and disk head

arm as the head is off from the parking ramp and over the

data surface of the disk.

FIG. 9 is a graph showing a simulated friction

profile having ramp and step disturbances and showing the

model's estimated friction.

FIG. 10 is a graph showing the actual head

velocity and the estimated head velocity for the simulated

friction profile of FIG. 9.

FIG. 11A is a flow diagram of a head load setup

subroutine for implementation of the estimator according

to the invention. FIG. 11B is a flow diagram of a timer interrupt

routine which implements the estimator of FIG. 2 and is

referenced by the head load setup subroutine of FIG. 11A.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The invention is embodied in a state estimator

and related method, for sensing and determining the

movement speed or velocity of a disk drive's head arm

using a model of the actual head-arm and actuator, that

tracks a readily available drive parameter. More

particularly, the estimator tracks the state of the head-

arm and actuator using a voltage signal which is provided

by typical current drivers of most existing actuator

control circuits. The estimator, in accordance with the

invention, is particularly advantageous because its head-

arm velocity estimate allows a head-arm control system to

have sufficient control over the head arm's movements so

as to prevent the drive's read/write head from crashing

into and damaging the drive's data recording surface.

The state estimator of the invention is

preferably implemented by a digital state machine using a

microprocessor. However, it should be noted that the - 9 -

estimator may be implemented by an analog control circuit

without departing from the principles of the invention.

The head-arm actuator estimation system 20 of

the invention, described with reference to FIG's. 1-3,

operates in conjunction with a head-arm control system 18

that controls the head position during normal disk drive

operation and the head-arm velocity during head loading.

The head arm control system typically includes a head

position control circuit having a feedback loop. The

position control circuit receives a desired head position

signal or command and uses a comparator 24 to compare the

desired head position signal with an actual head position

signal to generate a position error signal. A tracking

error compensator circuit 26 generates a compensated

signal based on the position error signal. A select

switch 28 couples the compensated signal to a current

driver 30 that drives the current flowing through the

actuator's voice coil motor (VCM) 32. The current driver

has a selectable gain switch or control 34 and generates a

sensor voltage signal representing the current through the

VCM. The sensor voltage is taken from the terminal leads

of the VCM coil and sense resistor network. - 10 -

The current through the VCM 32 generates a

torque on the head arm 36 shown in Fig. 6A. The torque

causes the head arm to rotate about its pivot point 38 at

a velocity related to the torque. The torque is

controlled so that the drive head 40 moves to a position

over the desired portion of a disk platter 42. The head

position over the platter is determined by position

indicators encoded or embedded in the surface of the disk

platter. A detection and demodulation circuit 44

generates a detected head position signal based on the

detected head position which is compared with the desired

head position signal. Unfortunately, unless the drive

head is over the surface of the disk platter, it cannot

read the position indicators and thus the head position

cannot be determined. During head parking and unloading,

the head leaves the surface of the disk platter and, thus,

the head velocity may not be determined based on the head

arm position control circuit .

The head velocity is estimated using a current

driver and VCM model that preferably models four states of

the head-arm actuator. These states are the VCM's applied

voltage, the head arm's velocity, the friction, and the - 11 -

delay between the sample time and the actual control

output time (the delay due to computation time) .

Accordingly, all of the internal states of the system,

including the head arm's angular velocity, may be derived

from the output of the model .

During head parking and unloading, the select

switch 28 is positioned to couple the current driver's

input to a velocity control signal generated by a velocity

control circuit 48 and the current driver's gain is

lowered by the gain control 34. The current driver's loop

gain Ka may be set by components external to the driver.

More specifically, the driver is normally configured as a

transconductance amplifier having a relatively large loop

gain. In this configuration, the current usually

converges to the commanded value in a very short period of

time with negligible error. During head loading, however,

the loop gain is set to a relatively small value so that,

for a given actuator configuration, the states are

observable and may be derived using the sensor signal .

The velocity control circuit 48 also provides

the velocity control signal to the actuator model 46. The - 12 -

actuator model also receives an error signal to be

discussed in more detail below. The model generates a

head-arm velocity estimate signal which is compared by a

comparator 50 with a desired velocity signal. The

comparison results in a velocity error signal which is

input into the velocity control circuit. The model also

generates an estimated sensor voltage signal . A

comparator 52 compares the model's estimated sensor

voltage signal with the actual sensor voltage to generate

a sensor error signal which is fed back into the model .

The sensor error signal operates to keep the model in

close agreement with the actual state of the head arm and

actuator.

The driver and actuator model 46 is shown in

more detail in FIG. 2. As discussed above, the model

receives two input signals and generates two output

signals. The first input signal is the velocity control

signal. The control signal, in conjunction with the

current states, predicts the states at next sample time.

The next predicted states equals the control signal

multiplied by a constant vector GAMMAe plus the current

states multiplied by a matrix PHIe. At next sample time, -13-

the predicted states are further corrected by the error

signal multiplied by the correction vector Le as the true

states for that sample. The current estimated states

includes head arm's velocity. The estimated sensor voltage

is obtained by multiplying the current states with an

output matrix He .

Accordingly, the estimation system 20 is

implemented using the model 46 and the comparator 52. The

model is a digital state estimator implemented in software

comprising first and second summers 90 and 92, a unit

delay 94 and a feedback control element 96. The first

summer adds control data to estimated control data

provided through the feedback control element to generate

predicted data xp (k+l ) . The unit delay delays the

predicted data to generate delayed predicted data xp (k) .

The second summer adds the delayed predicted data to the

sensor error data y (k) - ye (k) generated by the comparator

52 to generate the estimated head-arm state data xe (k) .

The error data is generated based on a comparison between

estimated sensor data from the output matrix He and the

actual sensor data generated based on the current through

the head-arm actuator. - 14 -

The operation of the head arm 36 is discussed

with reference to FIGS. 6A-8. FIG. 6A shows the head arm

in relation to the disk platter 42 and a head parking

ramp 54. The head arm pivots about a pivot point 38.

Opposite the head 40 is the voice coil motor 32 which

applies a torque to actuate the head-arm. As shown in

FIG. 6B, several platters may be stacked to increase the

drive's data capacity and the head-arm would accordingly

be a stack of mechanically coupled head arms and the

parking ramp would be a stack of parking ramps . The head

arm has a slider 56 that extends a slight distance above

and to the side of the head 40 to engage and slide up and

down the ramp during head loading and unloading,

respectively. The slider is shown in FIG. 6A in a parked

position on the ramp. In this position, the drive's

read/write head is not over the disk platter. As the

slider slides down the ramp, the head begins to be over

the disk platter as shown in FIG. 7. Once the head arm is

unloaded from the ramp, the select switch 28 (FIG. 1)

couples the current driver's input to the tracking

compensator circuit and the head arm is free to travel - 15 -

across the platter's surface under the control of the head

position signal.

A processor 58 for implementing the estimation

system 20 is shown in FIG. 4. The model processor

includes a digital signal processor (DSP) 60 coupled by a

data bus 62 to flash memory 64, random-access memory

(RAM) 66, and a gate array 68. The gate array receives

commands from a host controller 70, or from an RS-232

port 72 coupled to an external computer. The gate array

controls signals to an analog-to-digital (A/D)

converter 74 and also receives A/D conversion data from

the A/D converter. The DSP is also connected by a serial

bus 76 to a dual digital-to-analog converter 78 that

generates the estimated sensor voltage signal and the

velocity control signal. An analog amplifier 80 compares

the estimated sensor voltage signal to the actual sensor

voltage signal and generates an error signal representing

the difference between the two signals. The sensor error

signal is further amplified by an analog voltage

amplifier 82 having a predetermined gain selected to

advantageously use the A/D converter's conversion range.

The amplified sensor error signal is provided to the A/D - 16 -

converter that converts it to a digital sensor error

signal which is provided to the gate array.

In a preferred embodiment, the DSP 60 is Part

No. TMS320C52, the dual DAC 78 is Part No. TLC5618C, the

current driver 30 is Part No. TLS2235, and the analog

amplifiers 80 and 82 are Part No. TLC2272, all available

from Texas Instruments. The gate array 68 is Part

No. XC4010PQ, available from Xilinx. The flash memory 64

is Part No. 29C1024, available from Atmel . The RAM 66 is

Part No. CY7C1021, available from Cypress Semiconductor.

The A/D converter 74 is Part No. 35H6522, available from

Silicon Systems Inc.

To derive the mathematical equations used by the

DSP 60 for implementing the estimation system 20, a model

20' of the actual mechanical plant of the head-arm and

actuator, shown in FIG. 5, is used. The state equations

derived from this model are as follows:

-f4(κ,*. -/(0) (1)

v_0Ut (t) = L - _t +K_e - ω(t)+R i(t) = K_a - v_in (t)-K_aK_sR_s - i(t) (2) -17-

- di . R ', +Λ -„y ~K_r -R ^■, ._m-y K„ _ω(t)+y K„ _{v t)} ,3,

where :

Vin is the actual command voltage;

L is the VCM coil inductance;

Rt is the VCM coil resistance plus the sense resistor;

Rs is the sense resistor inside the current driver for

monitoring the VCM current. Ka, is the internal driver

gain; Ke, is the electrical constant; Ks is the current

sensing amplifier gain; Kt is the mechanical torque

constant; and J is the head arm's inertia.

The exact values for the friction force f (t) are

not generally known and vary from drive to drive.

However, for a given design, the profile of the friction

along the ramp is usually known. In most cases, the

friction changes little with time since the ramp material

and the mass of the moving parts do not change .

Combining equations (l)-(3), into a state

equation format provides the following state equation: -18-

-χ(t) = A-x(t) + B-v_in(t) (4)

where x(t) is a vector comprising of three states

t., x(t) = ω(t) (5) Kf(t\

where: i(t) is the VCM coil current; ω(t) is the head-arm's angular velocity; and f(t) is the friction force.

The above equation describes the three states of

the physical system in the continuous domain. To

implement the model in the DSP, the continuous domain

model is converted to its discrete equivalent. The same

symbols are used for the states and state vectors in the

discrete model without causing confusion. The following

equation represents the discrete equivalent for the

continuous system:

x(k + ϊ) = Φ-x(k) + T-v_in(k) (6)

where - 19

ω(k)

X(k) ( 7 ) f(k) d(k)

and where

i (k) is the VCM coil current;

ω (k) is the head arm's angular velocity;

f (k) is the friction force; and

d (k) is the computational delay.

The k parameter denotes the sample sequence

number, corresponding to time t in the continuous system.

The parameter i (k) means the coil current at k-t sample,

for example. Equation (6) indicates that the states at

sample k+1 may be predicted once the states and control

input at k-th sample is known. The delay state d (k)

accounts for the delay between the sample time and the

actual control output time due to computation by the DSP.

Since deviations always exist between the

physical world and the ideal mathematical model, the

equation implemented in the DSP model, i.e., the - 20 -

estimator, is distinguished by a subscript "e" added to

all the states and the state vector as follows:

x_e (k + l) = Φ_e -x_e (k) + T_e - v_in (k) (8)

where :

*.(*) = [ 9 )

As discussed above, deviations between the

actual system (Eqn. 4) and estimator (Eqn. 6) eventually

cause the estimated states to diverge from the real states

unless feedback is provided to the estimator. Note that

the estimator may model and output many states of the

head-arm actuator plant. For estimating and controlling

the head-arm' s velocity, it is desirable to select an

output that corresponds to an actual measurable quantity.

Advantageously, the sensor voltage signal measured across

the VCM coil and the sense resistor network is selected

since it is practical to measure.

Mathematically, if a system is fully observable,

all states may be derived from the estimator's output. - 21 -

Further, if the estimator deviates from the real system

(the actuator plant) , its output will also deviate from

the plant . The error between the estimator output and the

plant output is then used to keep the estimator from

diverging from the plant. The output equations for the

sensor voltage are as follows:

y(k) = H -x(k) (10)

y_e (k) = H_e -x_e (k) (11)

where y (k) is the actual plant output and ye (k) is the

estimator output. The modified estimator equation is:

x_e (k + l) = Φ_e -x_e (k) + r_e - v_in (k) + L_e -(y(k) -y_e )) (12)

The parameter Le is a vector, which is selected such that

the overall system, the estimator plus the plant, is

stable.

Once the above estimator is constructed,

estimated states are used in place of the real plant

states. If one uses a classical control technique, such as

PID control, the estimator needs to provide only the

estimated velocity. If a state space control technique is

used, one can output all the states from estimator. - 22 -

The estimator of equation (12) thus has two

inputs, the velocity control signal, Vin (k) , and the

sensor error signal, erro (k) =y (k) -ye (k) . The estimator

has at least two outputs, the estimated sensor voltage,

ye (k) , and the estimated head-arm velocity, ω (k) . Other

states may be brought out if desired.

A simulation of the velocity estimation system

operating under adverse conditions is generated using a

representative "worst case" ramped friction profile plus

an external step disturbance along the ramp, shown in

FIG. 9. The simulated head arm and actuator friction or

force profile is indicated by the dotted line. The

estimated friction or force profile generated by the model

circuit is indicated by the solid line. The close

tracking of the simulated force by the model's estimated

force is readily apparent from the graph. At t=0.01

seconds (s), a step is applied to the system. At t=0.015

s, the disturbance starts ramp down to simulate the ramp

slope. The ramp down in this simulation takes only 0.015

s. Actual head unloading takes about 0.2 s. Accordingly,

the simulated unloading time shown of Fig. 9 is about 13

times shorter than the actual head unloading time. - 23 -

Corresponding simulated and estimated head

unload velocity is shown in FIG. 10. The head velocity

increases to a relatively steady state once the static

friction is overcome. The velocity settles to 0.4 inches

per second (ips) without any steady error. The system

reacts to the step disturbance input and the velocity

recovers in less than 50 msec. During the ramp down time,

the model lags the plant by a steady error which is within

an acceptable range .

Accordingly, the simulation demonstrates that

system is able to track the head-arm velocity even under

adverse conditions. Further, errors in the velocity

estimate do not accumulate and external vibrations or

noise do not cause the system to become unstable.

Although the plant velocity may be greater than the

modeled velocity, the modeled velocity is sufficiently

accurate to provide adequate control of the head unload

velocity so as to prevent damage or scratching of the disk

platter surface.

The model is implemented in the DSP 60 by

software coded in accordance with the flowcharts shown in - 24 -

FIGS. 11A and 11B. To perform a headload, the control

system calls a subroutine named start_load (FIG. 11A) .

The start-load subroutine first initializes all states to

zero except the friction state which is initialized to a

nominal value of 0.024 Newton-meters (N-m) . This nominal

value is scaled up for integer calculation within the DSP.

The subroutine then sets the VCM current driver 30 and

related hardware to a head load made and enables the

current driver. The start_load subroutine then starts a

timer which gives a precise sample clock having a 100

microsecond interval . This causes the DSP to regularly

attend to a timer interrupt routine (FIG. 11B) at 100

microsecond intervals. The timer interrupt routine

implements the model equation.

The state equation (12) is implemented in two

parts. The first two terms of the equation are the

prediction of sample k+1 at sample k. The second two

terms represent an error value which is used to correct

any errors based on the predication. The predication can

be made as soon as the control signal Vin(k) is calculated

at sample time k to save time in processing the next - 25 -

sample. At each sample time, x_e is corrected based on the

predication from the last sample by the Le*est_err amount

and is immediately used in the control system.

In one embodiment of the invention, a state-

space based control technique is used. In this technique,

the control law is given by the following state equation:

V_in(k) = W-x(k) + REF = W-x_e(k) + REF (13)

The value of W is calculated beforehand and is chosen so

that the control system is stable. Reference ω_ref is

predetermined number related to the desired velocity, for

example, 0.4 ips . Note that the friction state does not

change with the control input, so no prediction is

preformed for it. The delay state is directly equal to

vin(k) . An integrator state is introduced in the control

law so as to zero out velocity error. Further, in a

specific implementation, examination of the actual PHI

matrix, and Gamma matrix often results in the

identification of many zero terms. The calculations

involving these terms may be eliminated thus saving some

unnecessary processing load on the DSP. - 26 -

As readily apparent to one skilled in the art,

once the head speed is available, the head speed may be

readily controlled using, for example, a PI control

system, a PID control system, or preferably, a state-space

based feedback control system since all the states are

available using the model.

While the foregoing has been with reference to

specific embodiments of the invention, it will be

appreciated by those skilled in the art that these are

illustrations only and that changes in these embodiments

may be made without departing from the principles of the

invention, the scope of which is defined by the appended

claims.

Claims

-27-What is claimed is:

1. Apparatus for estimating the state of a

disk-drive head-arm, comprising:

a current sense circuit for monitoring current

through a head-arm actuator during operation and

generating a sensor signal based on the current through

the actuator;

a processor for receiving the sensor signal and

for generating at least one estimated head-arm state

variable based on the sensor signal ; and means for

outputting data signals representing the estimated head-

arm parameter.

2. Apparatus for estimating the state of a

disk-drive head-arm as defined in claim 1, wherein the

estimated head-arm state variable represents the velocity

of the head arm.

3. Apparatus for estimating the state of a

disk-drive head-arm as defined in claim 1, wherein the -28-

processor includes a state estimator that models a

plurality of estimated head-arm state variables.

4. Apparatus for estimating the state of a

disk-drive head-arm as defined in claim 3, wherein the

actuator includes a voice-coil motor coupled to the head

arm for actuating the head arm.

5. Apparatus for estimating the state of a

disk-drive head-arm as defined in claim 4, wherein the

state variables that the state estimator models are the

velocity of the head arm, the friction associated with the

head arm, and the current through the voice-coil motor.

6. Apparatus for estimating the state of a

disk-drive head-arm as defined in claim 1, wherein the

processor is a digital signal processor that implements a

digital state estimator that models a plurality of head-

arm state variables.

7. Apparatus for modeling a disk-drive head-arm

parameter as defined in claim 6, wherein the digital state

estimator comprises first and second summers, a unit delay

and a feedback control element, wherein the first summer - 29 -

adds control state data to estimated control data provided

by the feedback control element based on estimated head-

arm state data to generate predicted data, the unit delay

delays the predicted data to generate delayed predicted

data, and the second summer adds the delayed predicted

data to a sensor error signal generated based on the

difference between the sensor signal and an estimated

sensor signal to generate the estimated head-arm state

data which includes information for constructing the

estimated sensor signal .

8. A digital state estimator comprising first

and second summers, a unit delay and a feedback control

element, wherein the first summer adds control data to

estimated control data provided by the feedback control

element based on estimated head-arm state data to generate

predicted data, the unit delay delays the predicted data

to generate delayed predicted data, and the second summer

adds the delayed predicted data to sensor error data

generated based on the difference between estimated sensor

data and sensor data generated based on current through a

head-arm actuator to generate the estimated head-arm state - 30 -

data which includes information for constructing the

estimated sensor data.

9. Method for estimating the state of disk-

drive head-arm, comprising adding control data to

estimated control data based on feedback from estimated

head-arm state data to generate predicted data, delaying

the predicted data to generate delayed predicted data,

adding the delayed predicted data to sensor error data

generated based on the difference between estimated sensor

data and sensor data generated based on current through a

head-arm actuator to generate the estimated head-arm state

data which includes information for constructing the

estimated sensor data.