Position Error Signal Estimation at High Sampling Rates Using Data and Servo Sector Measurements

Transcription

1 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 11, NO. 3, MAY Position Error Signal Estimation at High Sampling Rates Using Data and Servo Sector Measurements Petros A. Ioannou, Fellow, IEEE, Elias B. Kosmatopoulos, and Alvin M. Despain Abstract The sampling rate in most hard disk drives (HDDs) is limited by the number of servo burst sectors that have prewritten position error signal (PES) data and by the spinning speed of the HDD. This paper presents an algorithm that can generate estimates of the PES during read at high sampling rates by processing the dedicated servo burst measurements and the mean square error (MSE) path metric data used to choose the correct bit sequence using the Viterbi decoding process of the read signal. The MSE metric is a nonlinear function of the absolute value of the true position of the head relative to the center of the written data. The position estimation algorithm is nonlinear and is based on several logic statements together with the use of two state observers. The estimation algorithm is tested on an actual disk drive and demonstrated to provide values of the PES at a frequency four times higher than that generated by the servo burst measurements. Index Terms Digital control, disk drives, observers, servosystems, signal estimation. I. INTRODUCTION HARD DISK drives (HDDs) serve as an important data storage medium for data processing systems. The demand for high-capacity HDDs is estimated to correspond to an annual increase of areal density of about 60% [2], [3]. In a HDD, rotating disks, sputtered with a thin magnetic layer or recording medium, are written with data in concentric circles, called tracks [1]. Data is written by a head, which is a small horseshoe-shaped electromagnet with a very thin gap. The head is positioned only micro inches above the recording medium on an air-bearing surface where the energized electromagnet produces a strong magnetic field in the air gap, which magnetically polarizes the recording medium. Once polarized the recording medium remains so until rewritten. The recording head of the HDD is moved with an actuator across the disk surface to reach each track. A head-positioning servomechanism (called hereafter the HDD servo system) is a control system, which positions the head (mounted on the actuator) over a desired track and repositions the head from one track to another. The time needed to reposition the head as well as the position accuracy of the head over the center of the track are the most important performance characteristics of any HDD control system. Even though the servo system is only one component of the HDD, it is a critical Manuscript received September 14, 2001; revised May 24, Manuscript received in final form December 4, Recommended by Associate Editor D. Gorinevsky. P. A. Ioannou and E. B. Kosmatopoulos are with the Department of Electrical Engineering Systems, University of Southern Calornia, Los Angeles, CA USA ( ioannou@usc.edu; ikosmato@usc.edu). A. M. Despain is with Acorn Technologies, Pacic Palisades, CA USA ( despain@acorntech.com). Digital Object Identier /TCST one in increasing the track density and, therefore, the storage capacity. Track density in HDD is related to the performance characteristics of the HDD servo system. Higher track density can be achieved by improving the control system s performance characteristics and especially the position accuracy over the center of the track. In order to achieve higher track density or, equivalently, smaller track width, the steady-state position error relative to the center of the track achieved by the servo system has to be reduced. In a typical HDD servo control system, the position of the head relative to the center of the desired track is sensed and used by the servo system to generate the appropriate commands to the actuator, which in turn moves the head in an effort to reduce the position error. The sensing of the position error signal (PES) depends on the kind of the servo system used. In general, there are two kinds: the dedicated servo and the embedded sector servo [1], [4]. In the dedicated servo, one disk surface is dedicated to store the position data referred to as servo data or servo signal. In the embedded sector servo, the PES exists on each disk in selected sectors referred to as servo burst sectors. The area of the servo burst sectors is kept small in an effort to maximize the area for storing data. In the case of the embedded sector servo, since the PES exists in every disk a more accurate positioning of each head is possible. The drawback of the embedded sector servo, however, is that the PES is available only when the head is reading the servo bursts. Consequently, the sampling rate at which the servo control system will get a reading of the PES is limited by the spinning speed of the disk and the number of servo burst sectors on the disk. This in turn limits the bandwidth of the controller and, therefore, the ability of the servo controller to maintain smaller position errors despite the presence of noise, modeling errors and other inaccuracies. In general, the rule of thumb is that the sampling rate has to be greater than about ten times the bandwidth of the closed-loop system in order to reduce the effect of folding and quantization error [20], [21]. The HDD servo control problem generated a considerable number of research activities in an effort to improve track seeking and track following by improving the control design and/or using dferent actuators and instrumentation [5] [10], [13] [16]. A fundamental problem in the HDD servo control design is to obtain a controller that meets the performance requirements despite the presence of disturbances and unmodeled dynamics [17], [18]. The servo burst sectors on the HDD provide position error measurements relative to the center of the track that are used by the servo controller to control the position of the head to be as close to the track center as possible. During the time that the head reads the data sectors the controller receives no direct information as to the position of the head. It is known however, /03$ IEEE

2 326 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 11, NO. 3, MAY 2003 Fig. 1. HDD system (out of scale). that during reading, the magnetic field sensed by the head gets converted or decoded into a sequence of zeros and ones in the PRML channel. During that decoding process an estimate of an absolute value function of the PES can be generated from the reading of the stored data at frequencies as high as 300 khz [22] [24]. This absolute value function can be inverted using an inverse mapping to generate two possible values of the PES while the head is reading the data sectors. The problem is that it is not known which one of the two values is the correct value of the PES. In this paper, we use this absolute value function of the PES together with the PES readings generated from the servo burst sectors to develop a scheme that provides accurate estimates of the PES at high sampling frequencies. The algorithm is based on several logical statements, a predictor and two state observers. We have demonstrated 1 experimentally that the estimated PES at a higher sampling rate is possible. The estimator, referred to as the ACORN estimator could open the way for designing high-bandwidth high-performance servo controllers that would lead to a much smaller settling time, better disturbance rejection properties and smaller PES at steady state. These properties in turn imply that data can be tracked more efficiently, saving read time. The ACORN estimator is designed for use during the read phase. Current investigations are under way to extend the estimator to be used during the write phase. II. HDD SERVO SYSTEM Fig. 1 shows a disk drive system where a number of sectors on the disk are allocated to provide PES data relative to the center of the target track. As the head goes over these dedicated sectors, referred to as servo bursts it reads how far off the read head is from the 1 Patent filed under P. A. Ioannou, et. al., Servo Control Apparatus and Method Using Absolute Value Input Signals U.S. Patent Filing no. 09/439,055, November 12, 1999, (Patent not yet issued.) center of the track in the positive or negative direction at that particular point of time. After the servo burst, however, it has no PES information until it reaches the next servo burst point. The PES measurements are used by the servo controller to position the head as close to the center of the track as possible by minimizing the magnitude of the PES. The rate at which the servo controller reads the PES measurements is proportional to the number of the servo burst sectors present on the disk and the spinning speed of the disk. The spinning speed of the disk cannot be increased arbitrarily due to mechanical constraints. Increasing the number of servo bursts will take away space that is used to write data and is undesirable. Therefore, for a given disk drive the frequency of the PES measurements is upper bounded. The servo burst measurements correspond to a natural sampling system where the output of the system, in this case PES, is sampled at a certain fixed sampling frequency. In a feedback system, the choice of the sampling frequency plays a signicant role in designing the control system to meet the performance requirements. For example, a high sampling frequency often leads to a more accurate control action, since a controller using samples at higher frequencies is closer to the corresponding continuous time controller and contains more signal information. It requires, however, faster and more frequent computations, which for a given processor may put limitations on the complexity of the controller. Given that the processor is not a limitation another advantage of a high sampling frequency is that a higher bandwidth controller can be implemented that can lead to better performance. The rule of thumb is that the sampling rate has to be greater than around ten times the desired closed-loop bandwidth of the system. In the case of the disk drive, the limited sampling frequency, does not allow the bandwidth of the controller to increase considerably. In most servo controllers the closed-loop bandwidth is around khz. In this case, sampling rates of 10 khz and above appear to be satisfactory [1]. Another reason that the bandwidth is kept low in most HDD systems is the presence of high-frequency modes (neglected in the control design) that could be excited by a high bandwidth controller. Given a high sampling frequency of the PES, a high-bandwidth controller could be designed by taking into account some of the dominant high-frequency resonant modes in order to push the performance envelop further. A linear time invariant (LTI) model of the HDD servo system can be obtained by making certain reasonable approximations and simplications similar to those described in [1]. While the model may vary from one disk manufacturer to another, its form is very similar and is given by (2.1) Here, and are the PES and actuator input, respectively, represents the resonance characteristics and higher frequency flexible modes.

3 IOANNOU et al.: PES ESTIMATION AT HIGH SAMPLING RATES 327 Fig. 2. Bode plots of the actual system (2.1) and the reduced-order system (2.2) dynamics. A Bode diagram of shown in Fig. 2 is generated for a 30 GB disk drive (WD300ABRTL), which has a rotational speed of 5990 rpm and 128 servo bursts symmetrically located around the disk. The resonant frequencies of the system are identied, using experimental data, to be at 5.6 khz, 7.77 khz, 8.3 khz, 9.0 khz, 9.98 khz, and 11.9 khz. If we keep the closed-loop bandwidth less than 1.5 khz, we can neglect the modes corresponding to these frequencies. These considerations lead to the simplication and can be approximated by the reduced-order transfer function (2.2) Fig. 2 demonstrates that, for frequencies up to about 1.5 khz, the reduced-order and full-order responses are almost identical. If the closed-loop bandwidth is desired to be higher than about 1.5 khz, the higher order flexible modes need to be considered and in this case the reduced order model is not adequate for control design purposes. In this case, a higher order model that includes the modes in the frequency range close to the higher bandwidth has to be used for control design. If the sampling frequency at which the PES is generated is limited by the number of servo bursts and spinning speed, then a high bandwidth controller cannot be implemented which implies that further performance improvement of current disk drive servo systems cannot be achieved. The method developed in this paper, allows the generation of the PES at higher sampling rates by extracting PES information not only from the servo bursts but also from the data sectors during read. The method opens the way for improving the servo controller performance considerably by increasing the controller bandwidth and taking into account some of the high-frequency resonant modes. III. ACORN ESTIMATOR When the head is reading the data sectors the PRML channel is using a mean square error (MSE) metric and the Viterbi algorithm to choose the correct bit sequence as part of the decoding of the error signal process. Fig. 3 shows the results of measuring the MSE for various track offsets. The general trend of the curve has desirable properties, changing in a useful way as the read element moves away from the track center, even while the bit error rate is still 10 across the bottom of the bathtub. It increases as the read element moves away from the track center, and this change becomes quite pronounced well before the bit error rate gets worse than 10. The signal, as is evident from Fig. 3, increases with distance from track center, but does not tell which side of the track center the read element is on. In other words, the signal has magnitude, but not sign (it is an absolute-like value signal). As the head reads the data, the MSE values are computed from the PRML channel as described in [22]. An average of the MSE values over a certain time interval are used with the MSE error metric curve to obtain two possible values of PES at that point in time. In this paper, we demonstrated our approach by using 800 MSE points averaged over a period corresponding to 1/16 of the period with which we read the servo burst PES. Given that the disk considered has a rotational speed of 5990 r/min and 128 servo bursts, the servo burst PES is generated at khz. Therefore the MSE data are generated at 16 khz and our proposed estimator will use this data to generate the estimated PES at 4 khz. Below we describe the proposed estimator in general and then demonstrate its properties using the disk drive described above. We like to emphasize that the values considered above are for demonstration purposes and that the estimator is applicable to other disk drives with dferent characteristics.

4 328 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 11, NO. 3, MAY 2003 Fig. 3. MSE error metric curve (solid line shows fit of the experimental points denoted by *: 10 counts = 3:9% of track width). from the MSE data are generated at say. Given this information we would like to estimate the PES at. Fig. 4 describes the generation of the values of PES at dferent sampling rates that are to be used by the estimator to be presented subsequently. In Fig. 4, denotes the time-index at khz sampling rate and is the time index that corresponds to the sampling rate at khz. The index denotes the time-index at khz sampling rate. The relation of the time indexes is shown in Fig. 5, while the abbreviations and symbols used throughout the paper are presented in the Appendix. Let,, and denote the sampling periods at sampling frequencies,, and khz, respectively. The nonlinear function used in Fig. 4 is the MSE smooth curve shown in Fig. 3 obtained by fitting the experimental data. Let us consider the reduced-order dynamics (2.2) written in the state-space form Fig. 4. Generation of y, f (y) at dferent rates. where (3.1) Furthermore the factors 16 and 4 for the frequencies discussed above are chosen for demonstration purposes and could be changed without having to mody the estimator. If we denote the MSE value by the possible PES values are denoted by, as shown in Fig. 3. These two possible values of PES can be generated at very high frequencies of our choice (as high as 300 khz) and could be used by the servo controller we know which one of the two values is the correct one. Let us consider a disk drive where the PES from servo bursts is generated at khz and the two possible values of the PES The discrete-time version of (3.1) at the sampling frequency of khz is given by (3.2) where the triplet (,, ) denotes the discrete-time counterpart (at khz sampling rate) (,, ). Using and

5 IOANNOU et al.: PES ESTIMATION AT HIGH SAMPLING RATES 329 Fig. 5. Time indexes. Fig. 6. Flowchart of the ACORN estimation algorithm. Fig. 3 we obtain the two possible values of, i.e., and which we use to generate the signals otherwise otherwise. (3.3) (3.4) It follows from (3.3), (3.4) that in the absence of computational errors and noise and where is the position at which the smooth approximation of has its minimum. In the case of Fig. 3,. In other cases and that has to be accounted for. Since the sign of is not known for, we use the following two observers to generate estimates of as follows. Observer 1 estimates assuming that in Fig. 3, is the correct position and Observer 2 estimates assuming that in Fig. 3, is the correct position.

6 330 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 11, NO. 3, MAY 2003 Fig. 7. Block diagram of experimental setup. Fig. 8. Burst PES and its FFT when excitation signal R(t) = 0(10 counts = 3:9% of track width). Observer 1 If then at instant ( ) we check whether the previous of track width. If yes, then Observer 2 where denotes the gain of the observer and, denotes the state vector of the observer. The gain of the Observers is chosen so that the matrix is a stable matrix with eigenvalues in appropriate locations. The estimation of is generated by utilizing the above two observers in addition to other considerations. Let be the estimate of at and. The algorithm for generating is described below. The estimation algorithm is shown in the flowchart of Fig. 6 and is explained in detail below. At the time instance where the measurement of the PES, is available from the servo sector and, therefore otherwise. The scalar is a design constant and is chosen so that the magnitude of track width is slightly higher than the anticipated or measured noise level in the PES. The rationale behind it, is that is above the noise level, no sign change is anticipated from the previous sample and, therefore, the estimate of the sign at instant is the same as in the previous instant. If of track width then we form the predicted value of based on linear interpolation between and as Then we have two cases to consider. Case 1). In this case, the sign of the predicted value of is the same as that of. Therefore, we assume that most likely no sign change took place and take

7 IOANNOU et al.: PES ESTIMATION AT HIGH SAMPLING RATES 331 Fig. 9. Burst PES and its FFT when excitation R(t) =500sin(!t + '). (10 counts =3:9% of track width). Fig. 10. FFT of PES generated by ACORN estimator versus FFT of burst PES (10 counts =3:9% of track width). Case 2). In this case, the sign of the predicted value of is dferent from that of and, therefore, there is a possibility a sign change took place due to the noise or to an actual change of the sign. In this case we use the observer outputs to decide about the value of as follows: otherwise. (3.5) The estimate is generated using the sign estimate as follows: otherwise. (3.6) The states of the two observers are reset to the ones of the observer that happened to use the right sign as estimated in (3.6) otherwise (3.7) The resetting of the initial conditions of the observers is essential, otherwise the use of (3.5) in subsequent instances may lead to misleading results. The use of the predicted value of in cases 1 and 2 was found to lead to better results than using (3.5) alone to make a decision about in both cases. The observers act as filters, therefore, the effect of noise and/or erroneous data points is reduced. The ACORN estimation algorithm described above is implemented on an actual disk drive and the results are presented in the following section.

8 332 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 11, NO. 3, MAY 2003 Fig. 11. Estimated PES points by ACORN estimator (star) versus burst PES points (circle) (10 counts = 3:9% of track width). Fig. 12. Reconstructed PES using mathematical model versus PES generated by the ACORN estimator. (10 counts =3:9% of track width). IV. IMPLEMENTATION AND TESTING The ACORN estimation algorithm described in Section III is implemented on an actual Western Digital WD300ABRTL 30 GB disk drive. The disk drive could generate PES measurements using the servo bursts at khz. The MSE curve of Fig. 3 is generated a priori for this particular disk. The MSE curve is used to generate the two possible values of PES at the frequency khz. Fig. 7 shows the block diagram of the set up. In Fig. 7, the ACORN estimator and digital controller are implemented in a DSP. The magnitude of the control input is limited and is saturated at 800 input counts. The PRML algorithm is implemented on a Texas Instruments (TI) channel chip. A digital low-pass Butterworth filter with a cutoff frequency at 8 khz is used to filter the raw MSE data in order to reduce the effect of noise. An external signal is used as shown in Fig. 7 in order to excite the head in a particular track at steady state. The signal is selected as a pure sinusoid whose frequency, phase, and amplitude are chosen so that the PES generated by the servo bursts cannot detect the signal. This is achieved by choosing the frequency of the external signal to be half of khz and shting the phase so that at the servo bursts the value of PES is theoretically zero and between the servo bursts the PES is away from zero. Fig. 8 shows the PES generated by the servo bursts

9 IOANNOU et al.: PES ESTIMATION AT HIGH SAMPLING RATES 333 when together with the corresponding fast Fourier transform (FFT). Fig. 9 shows the PES generated by the servo bursts when, khz, with the corresponding FFT. It is clear from Figs. 8 and 9 that the PES measurements contain almost zero information about the high-frequency signal. Fig. 10 shows the values of the ACORN estimator together with the corresponding FFT. It is clear that the estimator captures the effect of the excitation signal which appears clearly in the FFT. Fig. 11 shows the servo burst PES together with the ACORN PES sampling points. We should note that the servo burst PES points coincide with those of the ACORN PES at the servo burst sampling points as described by the ACORN estimator. Fig. 11 demonstrates again that the ACORN estimator carries signal information that is not present in the servo burst PES signal. A mathematical model of the servomechanism validated with real data is used to reconstruct the continuous-time value of the PES and compare it with that generated from the ACORN estimator. Fig. 12 shows this comparison and demonstrates that the ACORN estimator is able to generate a good approximation of the PES values. The units of PES in Figs are in counts. The width of the track is parameterized to be 256 counts that corresponds to about 1.5 m. TABLE II SYMBOLS V. CONCLUSION In this paper, we presented the design and experimental testing of an estimator, referred to as the ACORN estimator, which can generate values of the PES in a disk drive at much higher sampling rates during the read phase. The estimator uses information from the servo burst PES and the MSE data from the PRML channel together with a nonlinear curve that maps MSE data to PES values to compute the PES at a higher sampling rate. We have demonstrated experimentally that with the ACORN estimator the sampling rate at which PES is generated can be increased by four times. The ACORN estimator is designed for the read phase, its extension to the write phase is currently under investigation. APPENDIX TABLE I ABBREVIATIONS ACKNOWLEDGMENT The authors would like to acknowledge the help of B. Fidan and H. Xu, University of Southern Calornia; W. Kalcheck and C. Callaway, ACORN Technologies; and E. Siu, BES Technology Group; for many discussions and assistance in putting together the experimental setup and performing the experiments. REFERENCES [1] G. F. Franklin, J. D. Powell, and M. Workman, Digital Control of Dynamic Systems. Reading, MA: Addison-Wesley, [2] B. Frank, Rigid disk drive price trends, IDEMA Insight, vol. X, no. 4, pp , [3] Grochowski and R. Hoyt, Future trends in hard disk drives, IEEE Trans. Magn., vol. 3, pp , May [4] S. E. Back and S. H. Lee, Design of a multi-rate estimator and its application to a disk drive servo system, in Proc. American Control Conf., June 1999, pp

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Despain et al., Read Channel Generating Absolute Servo Signal, U.S. Patent Filing 09/ , November 12, [24] P. Ioannou et al., Servo Control Apparatus and Method Using Absolute Value Input Signals, U.S. Patent Filing 09/ , Nov. 12, Petros A. Ioannou (S 80 M 83 SM 83 F 94) received the B.Sc. degree with First Class Honors from University College, London, U.K., in 1978 and the M.S. and Ph.D. degrees from the University of Illinois, Urbana, in 1980 and 1982, respectively. In 1982, he joined the Department of Electrical Engineering-Systems, University of Southern Calornia, Los Angeles, where is currently a Professor and the Director of the Center of Advanced Transportation Technologies. His research interests are in the areas of adaptive control, neural networks, nonlinear systems, vehicle dynamics and control, intelligent transportation systems, and marine transportation. He was a Visiting Professor at the University of Newcastle, Australia in fall 1988, the Technical University of Crete in summer of 1992 and served as the Dean of the School of Pure and Applied Science at the University of Cyprus in He is the author/coauthor of five books and more than150 research papers in the area of controls, neural networks, nonlinear dynamical systems, and transportation. Dr. Ioannou recieved the Outstanding IEEE TRANSACTIONS Paper Award in 1984 and a Presidential Young Investigator Award in Elias B. Kosmatopoulos was born in Greece on April 1, He received the Diploma, M.Sc., and Ph.D. degrees from the Technical University of Crete (TUC), Greece, in 1990, 1992, and 1995, respectively. He is currently a Lecturer (tenure-track faculty position) with the Department of Production Engineering and Management and Deputy Director of the Dynamic Systems and Simulation Laboratory at TUC. Prior to joining TUC, he was Research Assistant Professor with the Department of Electrical Engineering-Systems, University of Southern Calornia (USC), Los Angeles, and a Postdoctoral Fellow with the Department of Electrical and Computer Engineering, University of Victoria, BC,Canada. His research interests are in the areas of neural networks, adaptive control, and intelligent transportation systems. He is the author of more than 20 journal papers and book chapters and more than 40 conference publications. Alvin M. Despain received the B.S., M.S., and Ph.D. degrees in electrical engineering from the University of Utah, Salt Lake City. He is the Chief Technology Officer of Acorn Technologies, which he cofounded while on leave from the University of Southern Calornia (USC), Los Angeles. At USC, he was Powell Professor of Computer Engineering. In 2001, he became Professor Emeritus at USC. He has also been a Professor at the University of Calornia, Berkeley, Stanford University, Stanford, CA, Utah State University, Logan, and the University of Utah. He has founded three enterprises to develop basic university research into commercial products.