A fuzzy scheduling controller for the computer disk file track-following servo

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A Fuzzy Scheduling Controller For The Computer Disk

File Track-Following Servo

Jia-Yush Yen: fi-Jeng Wang! Yung-Yaw Ched

Abtract- In this paper, a fuzzy tuning algo-

rithm is developed for the computer disk drive track following servo system.

A

Zentek 3100 disk

drive is modified, and a controller scheduling capability is added to the servo loop to compensate for the plant variations as the actuator is locked on to dierent tracks. The mathematical models for the act u a t o r on a number of tracks chosen are experimentally identified. The

Hm

design technique is then employed to obtain a robust optimal controller for each operating point.

A

com- bined controller b then calculated using a h s s y algorithm. The fuzzy algorithm is used to repre- sent the complex relationship between the track number and the corresponding controller. It is shown that with the controller scheduling action, the closed-loop performance is improved for the actuator at every track positions.

I.

INTRODUCTION

One of the most popular research topics addressed by the control engineera nowadays is the use of "fussy logic control" in high performance systems. The fussy logic controller is based upon linguistic rules which translate hu- man thinking into machine codes. It is thus very suitable for applications where the system characteristics or the control actions are hard to be expressed by mathematical expressions. The fussy controller is known to have very nice performances such as fast settling time and performance robustness against plant variations (Li and Lau, 1989, Peng and Liu, 1988). Many successful applications have also been reported (Sugeno, 1985), and new systems are seeking to use this technology. While the fussy controller is gaining its popularity, it ie noted that the fussy logic operation involves very complicated calculation. Therefore, before fast fussy logic CPU8 are available, it is not suitable for direct implementation in high speed, high bandwidth systems.

In this paper, a fuzzy tuning algorithm is developed

*Auociak Profe-, Department of Mechanical Engm-g, t Gradudc Student, Depsrtment of Mechanical E+uing, Z A d a k Profeuor, Department of Electrical Engineering, N*

tional Taiwan Univumity, Taipei, Taiwan, R.O.C.

for the computer diek drive track following servo system. The computer diek drive, often called the hard disk drive (HDD), is the most popular on-line data storage device used in today's computer system. Over the years, HDD has survived the challenges from the magnetic tape drives, the electronic on-board memory (RAM), the optical disk drives, and has become the fastest and most reliable on- line massive data storage device used by many computer manufacturers (Bajorek, 1990). Recently, both IBM and Futamoto Hitachi had announced new experimental drives which records more than 1 Giga bits/ina (Wood 1990, Zorpette 1991). Thie achievement has made the HDD the most promising memory device for future miniaturised palm top or pocket computers.

As the recording density further increases (more than

20,000 trackti/in in the new experimental disk drives), the head positioning servo will now have to position the head to within 0.lprn accuracy (one tenth of the today's accuracy). Many mechanical problem will start to emerge. The stiction of the actuator bearing caused by the manu- facturing tolerances will start to deet the achievable servo resolution. The drag force and the bias force introduced by the flexible cable linking the moving part of the drive to the disk drive controller board will also cause dramatic variation in the system behavior. Traditional linear servo will no longer be satisfactory, and some tuning ability is necessary.

In thie paper, the track following servo controller of a Zentek 3100 disk drive manufactured by the Zentek Co., Taiwan is modified. The design of the computer diek file servo controller is the result of many year's experiences. Over the years, the design technology has to gradually evolve from simple P-I-D controller to the

H m

optimization technique used in today's disk drive (Commander and Taylor, 1980, Workman, 1987, Hanselmann, 1988, Franklin, et.al., 1990, Yen, et& 1991). It is very dif- ficult to just discard all these progresses and design a t- tally new compensator. Therefore, instead of replacing the traditional linear controller, a controller scheduling c a p bility is implemented so that the plant variations due to different tracks can be compensated. The mathematical model for the actuator on various tracks is experimentally identified. The

Hm

design technique is then employed to 0-7803-0614-7/93$03.00 81993IEEE 1016

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obtain a robust optimal controller for the disk head actuator at each track. The actual controller for the disk drive actuator at various tracks is then calculated form all these controllers using a fussy interpolation. The fussy inter- pretation in used here mainly for its convenience at r e p resenting the relationship among various controllers. The identified track models do not show any convenient cor- relation with the track position. A simple function to in- terpolate among the controllers can not be obtained. The fussy interpolation is therefore the moet adequate tool in this situation.

It is shown that, provided with an accurate plant model, the H, design procedure for optimal control is very straight forward. The simulation results for each track can be directly implemented. The Schur balanced truncation technique is applied to ensure a low order controller. Without the controller scheduling capability, the quality of the control depends very much on the nominal track which the design is baee on. Without careful selection of the nominal track, the servo system can become unstable at some situations. With the controller scheduling action, the servo loop remain stable for all the track poeitions. Furthermore, the error can be kept at a lower level then the case when only a single controller

is

used.

11. SYSTEM IDENTIFICATION

The disk drive used in this experiment is a Zentek 3100 hard disk drive manufactured by the Zentek Co., Shin- Chu, Taiwan. The disk drive holds up to 120 megabytes formatted data with an access time of 15mu. Digital data

is recorded as different magnetisations in concentric rings on the surfaces of several spinning diaka.

An

actuator is used to drive the read/write head to access the data. For the Zentek 3100 disk drives, a rotary type actuator is

used. The data tracks are spaced 20pm apart on the disk

surface, and the servo controller will have to maintain the head to within less then lpm from the data track center. The actuator ia driven by a voice coil motor. The positioning information in thie dbk drive is written on a dedicated servo surface and all the heads are assumed to follow the servo head rigidly. For the servo design purpose, the signal entering the voice coil motor current amplifier is defined

aa the plant input, and the position error signal (PES)

measured by the data channel demodulator for the servo surface is defined ae the plant output. A linear system model is usually used to describe the system behavior.

The model identification ie performed by curve fitting the frequency response of the actuator dynamics. An HP3563A dynamic structural analyser is used for measur- ing the frequency response and for performing the curve fit. The signal into the voice coil motor is defined as the plant input, and the PES signal from the demodulator b defined as the plant output. The actuator is running under

closed loop control while a sweep sine signal is added to the plant input to excite the plant dynamics. The c l a d - loop identification b neceoaary for the actuator system

ia

very close to unstable without proper compensation. It is ale0 well known (Ljung 1987) that the persistence excita- tion condition can still be met under cloeed loop control provided the disturbance signal is rich enough. A linear system is assumed 80 that least square curve fit in the frequency domain can be conducted.

The frequency response of the actuator at track 0 and the response of its curve fit model using a 6th order model is shown in Fig.1. It is noted that the first resonance peak of the actuator occurs at around 2 K H z . Higher order system model has been used, and not much detail is obtained. Therefore, a 6th order model

ie

decided to be an adequate choice for the plant. The plant model at tracks

0, 300, 500, 700, and 992 are identified. The comparison among the frequency responses of the identified models for various tracks are shown in Fig.2. It can be seen that

a simple function to describe the relationship between the track number and the low frequency gain can not be easily obtained. The fussy description thus becomes the moet effective tool for this occasion. It is also observed that the major changes in the responses occurs in the low frequency region. The remnance frequency, however, remain almost unchanged. Quite contrary to our expectation. Al-

though a full controller interpolation is used in this work, in practice only a change in the low frequency response is necessary.

111. Hm DESIGN OF THE COMPUTER DISK DRIVE The H, optimisation technique

is

used for the controller design. The complementary sensitivity transfer function of the syetem is denoted by T(u), and the sensitivity transfer function is denoted by S(u). The weighting function for the sensitivity transfer function is Wl(u), and the weighting function for the complementary sensitivity transfer function is

Wa(u).

The control objective is to maintain the head cen- tered within lpm range from the track center. The desired closed-loop bandwidth

is

defined to be 400Hz. A -4OdBldecade attenuation beyond the bandwidth is de- sired for robustness. In order to over come the steady state error, a very low gain lead type weighting function for the complementary sensitivity transfer function is used. The responses of the weighting functions are shown in Fig.3. Notice that the frequency is normalised to 400Hc in these equations. The H , calculation for the 6th order model is conducted to obtain a 12th order compensator. Schur balanced truncation technique is then used to obtain a 6th order controller. The design procedure is carried out for all the plant models identified in the previous section.

TRACK FOLLOWING CONTROLLER

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Fig. 4 shows the frequency reaponsea of the resulting com- pensators for each operation point. All the controllers are basically composed of a very large lag compensator in the low frequency region to provide enough loop gain, and in the high frequency area are basically a lead-lag compensator followed with a sharp high frequency roll-off.

IV. THE

FUZZY

SCHEDULING CONTROLLER DESIGN The scheduling algorithm is designed baaed upon the concept that "the best controller for the system should be used whenever it is available". Since the optimal controller is not available for all the tracks, the desired controller will be obtained by interpolating the nearest neighboring controllers. The actual M S values for the track following error will be compared in the experiment.

The plant model at the five track positions ia denoted by

PO,

PWO,

&00,

P m ,

and Poga, and the corresponding Hm

controllers are denoted by CO,

Cm,

Csm, CTW, and &a.

As

mentioned in the beginning of this section, the basic concept for tuning is to used the moat proper controller when available. When the best controller is not available, then the controller ia obtained by the nearest neighboring controllers. Thie concept can be achieved with various methods. The moat direct method is to use the entire transfer function for the interpolation. This method will produce a resulting controller with an order as high as twice the original controller. In our approach, the controllers are represented with their poles and seros. It is noted that the poles and seros can be grouped into four different k i d s . Thie is reasonable under the assumption that the plant does not under go abrupt changes moving from the inside of the diek to the outside. Thus, the poles and zeros of the corresponding optimal controller will also move gradually BB the actuator move tracks.

The controller scheduling algorithm can now be designed. The 6th order controller ia defined as

c(,)

=

K.

(' - '()1'

-

a)('

- - - '6)(' -

a)

(2 - Pl)(z - n ) ( z -Pa)( z - R ) ( Z - W ) ( Z - P6) (1) The numbers

K,

21,

.

.,

26, p1,

. .

.,

ps are determined by the following fussy rules:

Rule 1: (Rl-1): If Tr is about 0, then p1 is 0.5327

+

j0.5638. (Rl-2): If Tr is about 300, then p1 is 0.4213+j0.5760. (Rl-5): If Tr is about 992, then p1 is 0.4807

+

j0.5825. (R2-1): If Tr is about 0, then pa is 0.5327 - j0.5638. Rule 2: Rule 13: (Rl3-1): If Tr is about 0, then

K

is 0.3004. (R13-5): If Tr is about 992, then

K

ia 0.4096.

The symbol Tr represents the present track number where the actuator in at. The numbera for the poles and zero13 are the ones obtained by the E,,,, optimization procedure.

K

is a constant gain term in the transfer function. The fussy variables are then defussified by the weighted average method. Five rules are involved for each variable, even though usually not more than two rules will

be fired. This well not sffect the operation since the controller scheduling proce%e can be carried out in the back ground process. Since one always know the target track before track accessing process begins, the tuning procedure can always start first and proceed during the accessing process and convert to the target controller when the calculation ia complete. Even if the conversion ia not complete before reaching the target track, the original controller will still keep in action, preventing the track- ing error from diverging as long as the unstable situations denoted in table.1 are avoided.

V. CONTROLLER IMPLEMENTATION In this section, the experimental results from the fussy scheduling controller implementations will be presented. Applying the five operating design track data to the fussy rules presented in section 5, a linear controller for all the tracks, from track 0 to track 992, on the disk can be ob- tained. Let C, denotes the controller for track number

n obtained by the fussy controller echeduliig process, the performance of the fussy scheduling controller will be pre- sented. First the controller C& is used to control the actu- ator at track n. Then the controller C, ia used to control the actuator at neighboring tracks for comparison.

A

TMS320C30 digital signal processor board is used for the controller implementation. The board is equipped with 4096 x 32 bits of

ROM,

2048 x 32 bits of

RAM.

Us-

ing 33.3MHz clock with 16 bit

A/D

and

D/A

channel, the board ia capable of sampliig at 100KEz; however, in this experiment only 10.43KHz sampling rate and a very s m a l l amount of

RAM

space is used so that practical application of the method will be possible. The demodu- lated position error signal (PES) is fed into the controller aa the error signal, and the calculated manipulated control input is send to the voice coil drive to close the loop. The controller and the tuning process are all performed in real time. While the control action is being calculated in the foreground loop, the tuning process is performed in the microprocessor aa well in the background process.

Only the typical situations will be presented. Fig~.5a,b shows the

PES

signal when CSOO is used on track number 500 and on track number 600, and Figs.7a,b shows the power spectrum density of the signals. Even though the

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PES signal it self does not show much difference, it can be observed in the PSD plot that using CSOO on track number 500 has lower error signal intensity in the 10 to 200

Hc

region. This indicates that the controller tuning has in fact improved the system performance. This tendency is further enhanced when the CSOO controller is used for track number 400 (Fig.7~).

VI. CONCLUSIONS

In this paper, the fuzzy logic was used for a high performance system. A fuzzy controller scheduling capability was implemented on a computer disk file actuator track following controller. The fuzzy scheduling controller was implemented in the back ground process so that the original high bandwidth loop obtained by the traditional lin-

ear controller can be maintained. It was shown that, as the requirement for system accuracy and performance was raised, several mechanical problem appears in the design. These problem made the adequate actuator plant model varies from the inside tracks to the outside tracks on the disk. It was also shown that the variation of the model can not be described by a simple function. Therefore, the fuzzy interpretation becomes the most effective tool to describe the variation.

A Zentek 3100 disk drive was used for the research. Five operation points were chosen for the design. The results showed that the performance can be improved with the controller adjusting itself. In the fussy tuning algorithm, the controller was expressed in pole-zero form, and groups were formed for the poles and zeros of the controllers. Five rules were used for each fuzzy variable, and a total of 65 rules were used for the 6th order controller with five design points. Simulation results showed that the resulting controller has an improved overall performance. Experi- mental results also showed that real time implementation of the algorithm is realistic.

VIZ. ACKNOWLEDGEMENT

This work is supported by the Opto-Electronics & Systems Lab., the Industrial Technology Research Institute, Shin-

Chu, Taiwan. R.O.C. Special thanks to the Research and Development Group at Zentek Co., Shin-Chu, Taiwan for supplying the disk drives and the technical assistance.

REFEFLENCES

[l] Bajorek,C.H., 1991, "Trends in recording and control technologies and evolution of subsystem architectures for data storage," Advances in Information storage systems, edited by Bharat Bhushan, The American Society of Mechanical Engineering, pp.1-14.

[2] Bell,T.E., 1991, "Incredible shrinking computers", IEEE spectrum, May 1991, pp.37-41.

[3] Commander,R.D., and Taylor,J.R, 1980, "Servo de- sign for an eight-inch disk file", IBM Disk Storage Tech- nology, Feb., pp.90-98.

[4] Workman,M.L., 1987, "Digital servo control system for a data recording disk file", US. Patent Number: 1,679,103, July.

[5] Franklin,G.F. Powell,J.D., Work",M.L., 1990, Dig- ital Control of Dynamic Systems, 2nd ed, Addison- Wesley publishing Co.

[SI Harker,J.M., Brede,D.W., Pat tison,R.R., Santana,G.R, Taft,L.G., 1981, "A quarter centruy of disk file innovation", IBM J. Res. Dev., Vo1.25, N0.5, Sep., pp.677-689.

[7] Hanselmann,H., Engelke,A., 1988, "LQG-control of a highly resonant disk drive head positioning actuator", IEEE trans. on indurtrital ekctmnics, Vo1.35, No.1, Feb., pp.100-104.

[8] Intel 18-bit embedded controllers, 1991, Hand- book intel Co.

[9] Ljung,L. and Soderstrom,T., 1987, Theory and practice of recursive identification, The MIT Press.

[lo]

Mayer,J.H., 1988, "3 1/2-in. Winchestera seek slots in high-performance disktep sytems"

,

Computer design, April 15, pp.144150.

[ll] Wood,R, 1990, "Magnetic megabits", IEEE Spec- trum, May, pp.32-38.

[12] Yen,J.Y., Hallamasek,K., Horowitz,R., 1991, "Track- following controller design for a compound disk drive actuator", ASME !!kana. of Darn. Sys., Mecr., and Con- trol, V01.112, Sep., pp.391-402.

[13] Zorpette,G., 1991, "Fujitsu predicts optical-density magnetic disk", IEEE the institute, Nov/Dec., pp.6. 10 19

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W I L; W3 -hip SpoiTnticas F R E O RESP CUR 5 0 . 5 0 . dB d B -50 : -50 : F x d Frrpancy-("rulku.iiO NU&) 10J 101 102

Fig*1

Actuator

frequency response

and least square curve

fit

Fig.3 Weighting functions

for

the

H,

design

Hz-(noi-ulinJoclwich*#)H.) ~ - ( - U n l h l 4 O O H ~ )

Fig.2

Actuator frequency responses

on

different tracks

Fig.4 Frequency responses for the compensators on different

tracks

1020

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Fig.5a

PES

signal

C S O O / & J

(Vertical scale

200

muldiu)

r I I

L

r

I

1

I

Fig.5b

PES

signal

c600/p600

(Vertical scale

200 muldiu)

I I 1 - 4 POWER SPEC1 2 5 . 0 1 2 . 5 /oiv d 8 r m m v 2 - 7 5 . 0 F x d Y 10 LOP HZ 1Ok

Fig.6a

PSD

of

the

PES

signal

C ~ O O / P ~ O O

POWER S P E C I 2 5 . 0 12.s / o i v dB r m s - 1 1 1 1 1 1 v 2 - 7 s . 0 F x d Y

Fig.6b

PSD

of

the PES signal

c600/p600

POWER SPECl 2 S . 0 1 2 . 5 /oiv d B r m s v 2 - 7 s . 0 Prd Y