A Design Method of a Full Closed Loop Sampled Servo Control for Hard Disk Drive

SICE Journal of Control, Measurement, and System Integration, Vol. 1, No. 3, pp. 242 250, May 2008 A Design Method of a Full Closed Loop Sampled Servo Control for Hard Disk Drive Takashi YAMAGUCHI and Takenori ATSUMI Abstract : This paper presents a design methodology for fast and precise positioning using a full closed loop sampled servo control system. A servo control of hard disk drive (HDD) achieves 3-4 ms fast access and nanoscale positioning accuracy. To achieve the nanoscale precise positioning, a full closed loop feedback control is a key structure. From control theory viewpoint, the full closed loop is an ideal method, but it is difficult to take this method in industries due to sensor allocation. In HDD, this full closed loop feedback control has been applied for last 20 years. The full closed loop sometimes brings drawbacks to the servo control design. In HDD case, that is a limited sampling rate selection. In this paper, based on these two features which are the full closed loop and a sampled servo, uniquely developed servo design methods for HDD are presented, which include two-degrees-of-freedom (TDOF) controller with multi-rate sampling, reference trajectory design not to excite higher order mechanical resonances, settling servo to compensate for tracking error near the target, phase stabilized design of feedback control to have better sensitivity, and multi-rate filter design to suppress disturbances above the Nyquist frequency. Key Words : hard disk drive, servo control, positioning, multi-rate sampling, phase stabilized, full closed loop control. 1. Introduction This paper presents a design methodology for fast and precise positioning based on a head positioning servo control design of hard disk drive (HDD). A head positioning servo of HDD has become a well known typical example of mechatronics motion control with fast and precise positioning capability. Recent HDD servo system can achieve less than 10 nm positioning accuracy (3 sigma) and 3-4 ms average seek time to reach a target track. It would be useful for other industries to understand the design methods of HDD to achieve such nanoscale servo control. HDD industry has been taking collaborative approaches to develop new technology by forming consortium and various kinds of committees in academic societies. In servo control area, many new servo algorithms for mass production have been presented in conferences. Some of unique industry-university collaborative activities in Japan could have lead this area by proposing HDD benchmark problem [1], publishing nanoscale servo control textbook [2], and presenting several tutorials [3],[4]. Through these activities, an HDD servo control design method has been discussed as one of common design methods over mechatronics field. In this paper, authors will propose the design method of fast and precise positioning servo control based on above mentioned activities held in HDD industry. Feedback control is one of the most fundamental structures to achieve good positioning. In HDD, after various attempts, a full closed loop feedback servo has been accomplished and now every HDD takes this method. Most of other motion con- Hitachi Global Storage Technologies, Fujisawa 252-8588, Japan Central Research Laboratory, Hitachi, Ltd., Fujisawa 252-8588, Japan E-mail: takashi-yamaguchi-apricot@mopera.net, takenori.atsumi.ta@hitachi.com (Received February 1, 2008) trol systems tend to take a semi-closed loop servo mainly due to difficulty of sensor location. In this case, engineers have to design disturbance reduction mechanism outside of the feedback loop to achieve required positioning accuracy. So HDD case must be a very good example to discuss a design method of precise positioning servo control system. The full closed loop servo system implies that all of the dynamics such as mechanical resonances and disturbances are in the feedback loop. This makes the servo controller design difficult, and several unique control algorithms have been proposed to suppress disturbances and maintain robust stability. The full closed loop sometimes brings drawbacks to the servo control design. In HDD case, that is a limited sampling rate selection. Several unique design methods have been proposed to overcome this issue, and a controller design considering frequency range above the Nyquist frequency and multi-rate sampling technique are shown in this paper. In this paper, basic description of HDD and its servo structure are shown in Section 2. From Section 3, design objectives, features of HDD servo system, and servo control design indices are described, and then a couple of key subjects of servo control design method are shown. 2. Hard Disk Drive (HDD) 2.1 HDD Mechanics Figure 1 shows a photo of HDD. Several disks are stacked on the spindle motor shaft and rotate at 15,000 rpm in hi-end 3.5-inch drives and 5,400 to 7,200 rpm in 2.5-inch drives. On the surface of a disk, several hundred thousand data tracks are magnetically recorded, and the latest track pitch is about 100 nm. A slider is supported by a suspension and a carriage, and it is suspended less than 10 nm above the disk surface. An actuator, called a voice coil motor (VCM), actuates carriage and moves slider on a desired track. The mechanical part of the plant, that is, the controlled object, consists of VCM, car- JCMSI 0003/08/0103 0242 c 2008 SICE

SICE JCMSI, Vol. 1, No. 3, May 2008 243 riage, suspension, and sliders. Figure 2 shows an example of Bode plot of the plant, showing many mechanical resonances in higher frequency region. On the back of the head-disk assembly mechanism (HDA), there is a circuit board on which a microprocessor or a digital signal processor (DSP) is mounted. The plant model is given by 1 τ/2 s ω VCM P(s) = K POS K A M(s) (1) 1 + τ/2 s s + ω VCM where K POS is a sensor gain, K A is an amplifier gain, τ is a time delay, ω VCM is a cut-off frequency of voice coil motor amplifier, and M(s)isgivenby M(s) = K m s 2 + N r=1 Kr 1 ω 2 r s 2 + 2ς r ω r s + ω 2 r where K m is a gain of inertia, Kr 1 is residue, ω r and ζ r are a natural frequency and a damping ratio of mechanical resonance, and N is a number of mechanical resonances. (2) as shown in Fig. 3. Since a displacement between a targeted data track and a head to read/write is a controlled value, this system is a full-closed loop control and called a sector servo system (position information has been originally embedded between data sectors.) One drawback of this system is a limited sampling rate selection for detecting the position information, which has to be long (low sampling rate) to gain better data format efficiency. After assembling the HDA, the position signals are recorded magnetically on each disk by using servo-writing equipment (servo track writer). The position signals are recorded at a certain time interval on each track. Consequently, the position error between the head and the track can be detected directly by reading the signal. It should be also noticed that the position information is a discrete time signal from the beginning of detection, so any filters to truncate higher frequency noise in the signal (anti-aliasing filter) cannot be set in the loop. Figure 4 shows an example of servo control structure of the head positioning system. The objective of HDD servo is to have a head move to a target track, settle it with minimum residual vibration, and position it on the track with required accuracy. These motions are called track-seeking, track-settling, and track-following mode respectively. This means each mode has its own servo design index and the controller has been designed based on it. Fig. 1 Photo of HDD. Fig. 3 Basic schematic diagram of HDD position signal. Fig. 2 Bode plot of the plant. 2.2 HDD Servo Structure The history of HDD servo design has been a transition from open loop to closed loop. Stepping motor was used for early stage HDD for desktop PC, which is an open loop control. Next a linear sensor was attached to detect actuator displacement which is a semi-closed loop control. Then one disk surface is dedicated to write position patterns and a magnetic head on the disk surface detects the position information [5]. Data is stored on the rest of disk surfaces. This is an advanced semi-closed loop for data head. Finally position information is written on a data track with a certain interval then read/write head itself can detect this position information during reading or writing data Fig. 4 HDD servo control structure. 3. Design Method for Fast and Precise Positioning Servo Control 3.1 Design Objectives The objective of this design is certainly fast and precise positioning. But it can be said that the objective is the improvement of quality of motion control. Motion control includes (1) have the controlled object move to a target and (2) have the controlled object do a specified mission such as positioning, tracking, scanning, etc. with a required accuracy.

244 SICE JCMSI, Vol. 1, No. 3, May 2008 3.2 Features of HDD Servo System A control structure is a single-input single-output (SISO) full closed loop feedback control where controlled variable can be directly detected. This means that the achievement of precise positioning fully depends on the design of this full closed loop control. Since position signals are written on track at a certain interval, the signal is detected as a sampled data. A feature of the full closed loop control is that all of the plant and disturbances are in the loop as shown in Fig. 5, and the feedback control has to be designed based on these dynamics. In the case of semi-closed loop control which is a conventional servo design structure, it can avoid including a portion of plant dynamics and disturbance. So it becomes easier to have the loop stable and to avoid amplifying disturbances in high frequency ranges. But the full closed loop control design has to face these issues. Considering that this system is a sampled servo, the controller has to have specific design method for the plant and disturbances above the Nyquist frequency. In terms of the sampled servo system, although a sampling rate of detecting position signal is fixed by a number of written servo signals on track and disk rotational speed, a sampling rate selection of control input can be a design freedom. So another feature of HDD servo is the multi-rate sampling servo as shown in Fig. 6. Fig. 5 Block diagram of HDD feedback servo control. A5 are characterized by complimentary sensitivity function (T) of the feedback control. A3 and A4 are characterized by sensitivity function (S ). So design indices of servo control can be described by the design of (a) feedforward controller of TDOF control and (b) feedback controller design considering S and T. It should be noted that S + T = 1 and Bode theorem are two main essential problems to design the feedback controller. There are four design indices of motion control design [7]. B1. Trajectory planning (reference design) B2. Tracking capability to the reference trajectory B3. Settling control design to suppress tracking error caused by various practical reasons like unknown disturbances, unpredictable plant changes, model uncertainty coming from nonlinearity, and so on. B4. Disturbance suppression capability As described in Section 2, HDD servo system has three servo modes; (1) track-seeking mode, (2) track-settling mode, and (3) track-following mode. In the track-seeking mode, above mentioned A1, B1, and B2 are the design indices. In the tracksettling mode, B3 is the index. In the track-following mode, A2-A5 and B4 are the indices. Considering the HDD features, design methods to avoid influence of mechanical resonance and disturbances are important for all modes, and design methods to utilize multi-rate sampling technique are also important to handle stability and disturbance suppression in a region above the Nyquist frequency. Table 1 shows design subjects based on the HDD features. Detail design methods will be described from next section. Table 1 Design subjects based on the HDD features. Fig. 6 Block diagram of multi-rate sampling servo. 3.3 Design Indices of HDD Servo System There are five well known design indices for servo control [6]. A1. Tracking capability to the reference trajectory A2. Robust stability A3. Sensitivity to the plant fluctuation A4. Disturbance suppression capability A5. Noise rejection A1 can be handled by designing two-degrees-of-freedom (TDOF) control, and this feedforward controller of TDOF can be independently designed from feedback controller. A2 and 4. Track-Seeking Mode Servo Design The servo design of the track-seeking mode is divided into two parts, one is reference trajectory planning and another is servo control design. Since HDD has been required to achieve faster movement time (seek time), the servo design has aggressively utilized saturation of a power amplifier. When the distance of the movement is bigger than a certain value, a power

SICE JCMSI, Vol. 1, No. 3, May 2008 245 amplifier is saturated due to large control input because of large position error. The servo controller starts working after the error becomes small enough to enter a linear region. In this case, the servo design is required to achieve smooth transition from open loop to closed loop. In short distance case without such saturation, reference trajectory and servo controller is designed to satisfy required tracking error from the beginning. In this case, well known TDOF control with full closed loop has been widely applied. where u is a control input, U c is a Fourier transform of u, q i is a weighting coefficient, and ω i is frequency to be suppressed [8]. Other than minimizing a quadratic of control input u, gainof specific frequency spectrum is also minimized. Figure 8 shows an example of control input and its spectrum. In this example, frequencies from 3.5 to 7.5 khz are selected as ω i. Gain of the spectrum in the area are certainly smaller than before, and moreover its seek time is the same. The SRS (shock response spectrum) analysis based design is defined to search an optimal set of parameters of a given seek trajectory to minimize gain of specified frequency in time response [9]. Figure 9 shows an example of reference trajectory and its six parameters to be optimized. Maximum amplitude of acceleration time response for a second order system is calculated for this trajectory input. For various natural frequency of the second order system, the trajectory parameters are searched so that the amplitude of specific frequency can be small enough. Figure 10 shows results of SRS analysis. The control input and sound pressure before (dotted line) and after optimization (solid line) are shown. The reduction of sound pressure can be seen with the same seek time. N-delay based TDOF feedforward design aims at reduction of specific frequency above the Nyquist frequency by optimizing sampling interval of multi-rate sampling feedforward signal [10]. Feedforward signalcanhave N times higher sampling rate than feedback signal s one (T s ), for example T 1 = T 2 = T 3 = T 4 = 0.25T s. But in this design, T 1 = 68.8 ms,t 2 = 77.4 ms, T 3 = 83.3 ms,andt 4 = 56.2 ms are selected. Figure 11 shows time response and Fig. 12 shows frequency spectrum of noise at track-seeking mode. The amplitude of specific frequency which are 4 and 10 khz to be minimized, are reduced but with the same seek time. Then, seek noise is reduced. 4.1 Reference Trajectory Design Since the plant has many mechanical resonances, the trajectory has been designed not to excite the resonances. (1) Jerk (derivative of acceleration) minimum trajectory This trajectory is given by minimizing J defined by Ts ( ) 2 du J = dt (3) 0 dt where T s is a seek time and u is a control input assuming that the plant is an inertia model. This kind of smooth trajectory could roughly reduce gain of frequency spectrum of the trajectory in higher frequency ranges, but seek time tends to be longer. Figure 7 shows its trajectory. (2) Frequency shaped trajectory This method is designed to remove or suppress specific frequency components of the trajectory with minimum penalty for seek time so that the trajectory does not excite specific mechanical resonance modes. Several design algorithms have been applied to HDD servo. Due to limited pages, detail algorithms cannot be disclosed here but key idea and effectiveness will be shown below. FFSC (frequency-shaped final state control) defines performance index J given by, Fig. 7 Jerk minimum trajectory. N 1 J = u 2 [k] + k=0 l q i U c (ω i ) 2 (4) i=1 Fig. 8 Control input and its frequency spectrum of FFSC. Fig. 9 Reference trajectory of SRS analysis based design. Fig. 10 Control input and sound pressure of SRS analysis based design.

246 SICE JCMSI, Vol. 1, No. 3, May 2008 Fig. 11 Time response of N-delay based feedforward design. 4.2 Servo Controller Design Proximate time optimal servo (PTOS) [5] and mode switching control (MSC) [11] are two well known structures to be applied to track-seeking mode with saturation. PTOS is a single mode controller from track-seeking to trackfollowing mode considering power amplifier saturation. Its block diagram is shown in Fig. 13. There is a minor loop velocity feedback whose velocity trajectory is generated by a nonlinear function whose input is a position error (residual distance to a target position.) So when the position error is large, maximum velocity is set. Then the power amplifier is saturated. When the error becomes small, velocity control loop is tracking the velocity reference trajectory, which is a linear control mode, and reach to a target position. Another advantage is that one velocity trajectory for reference signal can be used for all distances. MSC is a multi mode controller with a specifically designed controller for each mode and the mode is switched from one to the other as shown in Fig. 4. For track-seeking mode, basic structure is similar to PTOS. In short distance track-seeking, TDOF control structure has been widely applied. In TDOF control case, feedforward controller design is a key point and various methods have been developed since the proposal of ZPETC design [12]. Gain tuning of the controller has also been attempted to compensate for gain mismatch between controller and actual plant [13]. Based on above mentioned two HDD features, several controller designs have been uniquely proposed for HDD. One is perfect tracking control (PTC) design using multi-rate sampling technique described below [14], and the other is final state control (FSC) design which has a feedforward controller design with mechanical resonances defined by practically simple model [8]. The discrete-time plant discretized by the N-th multi-rate sampling control becomes x[i + 1] = A d x[i] + B d u[i] y[i] = C d x[i] (5) where x[i] = x(it), T is a sampling period, and A, B, C, and vector u are given by [ ] Ad B d C d 0 [ e A c T b 1 ] b N c c 0 0 (6) b j (1 μ( j 1) )T (1 μ j )T e A cτ b c dτ (7) Fig. 12 Frequency spectrum of noise during track-seeking. u [u 1,, u N ] T (8) 0 = μ 0 <μ 1 < <μ N = 1 (9) Figure 14 shows a block diagram of PTC, and its control law is given by u = F PTC ˆx + Q PTC e y + K PTC r (10) Fig. 13 Block diagram of PTOS. Under the assumption that the estimation errors of the observer become zero for a nominal plant, by substituting (10) into (5), this system is represented by x[i + 1] = (A d + B d F PTC )x[i] + B d K PTC r[i] (11) Matrix B d becomes square and non-singular if N equals the order of the plant. Then F PTC and K PTC can be selected so that the following equations are satisfied. A d + B d F PTC = 0 B d K PTC = I (12) From (12), F PTC and K PTC are given by Then, F PTC = B 1 d A d K PTC = B 1 d (13) x[i + 1] = r[i] = x r [i + 1] (14) where x r [i + 1] is the desired states. PTC has been experimentally applied to an actual HDD and it was shown to reduce seek time. Figure 15 shows experimental results. Comparing with ZPETC, PTC can improve the transient waveform better.

SICE JCMSI, Vol. 1, No. 3, May 2008 247 Fig. 14 Block diagram of PTC. Fig. 16 Experimental results of IVC. Table 2 A set of control algorithms proposed for track-following servo. Fig. 15 Experimental results of PTC. 5. Track-Settling Mode Servo Design If tracking error during seek mode can be reduced sufficiently small, then the servo mode can be directly transferred to the track-following mode. However as mentioned in 3.3, unexpected tracking error is often seen in actual products. Many studies have improved the tracking error during track-seeking mode which is a major approach, but a different one has also been proposed. If plant state variables such as position and velocity can be measured or estimated, these values can be utilized to modify initial values of the controller state variables at mode switching in MSC. Then a new controller after mode switching achieves an appropriate free response with non-zero initial values [15] [17]. This idea has been useful for lower sampling rate servo system. The z-transform from head position y to the initial values of plant X p (0) and controller X c (0) is given by y(z) = N p(z) D(z) X p(0) + N c(z) D(z) X c(0) (15) where D(z) is polynomial whose roots are poles of the feedback loop. The initial values X c (0) is calculated by introducing a real coefficient matrix K INV. X c (0) = K INV X p (0) (16) Substituting (16) into (15) gives y(z) = N p(z) + N c (z)k INV X p (0) (17) D(z) Equation (17) shows that the characteristics of the z-transform of sequencey(k), with respect to the non-zero initial conditions, can be shifted to the desired values by selecting appropriate values of K INV. This suggests that the transient characteristics after mode-switching can be improved by shifting zeros in order to cancel undesired poles of (17). This initial value compensation (IVC) technique can thus produce smooth and fast transient responses. Figure 16 shows experimental results. The major advantage of IVC is improvement of transient performance without changing any feedback characteristics such as stability and sensitivity. Another advantage of the IVC is that this can be applied to any track-seeking mode from track-to-track seek to full tracks seek. 6. Track-Following Mode Servo Design A purpose of this mode is the achievement of required positioning accuracy, in other word, the achievement of required disturbance suppression capability with a sufficient robust stability. The controller design method can be divided into two, one is for known disturbances and another is for unknown disturbances. The known disturbances include a one with known and fixed frequency spectrum. The unknown disturbances are also able to be divided into two, one is a detectable disturbance and another is an undetectable one. Considering the feature of HDD servo system, the controller can also be categorized into two, one is a controller for frequency ranges less than the Nyquist frequency, and one is for above the Nyquist one. Table 2 shows a set of control algorithms proposed for HDD servo system. As a known disturbances, HDD has specific periodic disturbances called repeatable run-out (RRO) whose frequency is disk rotation speed and its harmonics. Figure 17 shows an example of a peak filter to reduce RRO. This partially high gain approach can be extended to a region above the Nyquist frequency using multi-rate peak filter. Mechanical resonance peaks can also be utilized to suppress disturbances around resonance, if the resonance is phase stabilized. In HDD, some of innovative approaches such as multi-sensing, active damping, and dual stage actuator have been attempted to increase servo bandwidth [11],[18] [20] and some of them have been applied to commercial products. But so far, due to mainly cost reason, these innovative ideas have not been major solutions yet. Therefore evolutional approaches to increase the servo bandwidth are quite important. Here phase stabilized design and peak filter design above the Nyquist fre-

248 SICE JCMSI, Vol. 1, No. 3, May 2008 Fig. 17 quency will be presented. Bode plot of peak filter. 6.1 Phase Stabilized Design Since mechanical resonance modes of the actuator have been treated as unmodeled uncertainty in many cases, notch filters have been widely used for decreasing the gain at these frequencies. Although such control systems can avoid the instability caused by mechanical resonances, they reduce the phase margin and increase the H norm of the sensitivity function. In response to the above-mentioned problems, an integrated designing method for a controller and a mechanical structure based on vector locus design has been proposed [21]. This example shows that the mechanical system in which all major resonances are in-phase, can be designed. The frequency response of the mechanical system is shown in Fig. 18 (a) and vector loci of these mechanical systems are show in Fig. 18 (b). Solid line indicates the result in which temperature is 25 degree and dashed line is at 55 degree. These figures show that these resonance modes could keep in-phase condition for the temperature change. When all resonances are in-phase, the control system can stabilize the all resonance modes by phase condition. Then the feedback controller is just an integrator and a phase lead filter. The measured vector loci of open-loop characteristics are shown in Fig. 19 (a). This figure indicates that all of resonance modes are stabilized by phase condition. Figure 19 (b) shows frequency response of the sensitivity function. The gain of the sensitivity function is below 0 db at all high-order resonance frequencies. Fig. 18 (a) (b) (a) Frequency response of in-phase mechanical system. (b) Vector loci of in-phase mechanical system. (a) 6.2 Multi-rate Sampling Servo Design considering Regions above the Nyquist Frequency Multi-rate notch filters have often been applied to HDD servo system to avoid instability due to mechanical vibrations above the Nyquist frequency. Although such control systems can avoid the instability caused by mechanical resonances, they cannot suppress their vibrations. A design method is proposed for a sampled-data control system that suppresses vibrations whose frequencies are higher than the Nyquist frequency [22]. The block diagram of the head-positioning system is indicated in Fig. 20, where P c is a controlled object in continuous time, C is a digital controller, H is a hold, and S is a sampler, d c is a disturbance signal, y c is a head position in continuous time, and y d is a measurement signal of head position in discrete time. It is obvious that a servo system has to control the maximum displacement of the control variable. This means that the in- (b) Fig. 19 (a) Vector loci of open-loop characteristics. (b) Sensitivity function. finity norms of signals are used for defining the norm of the sensitivity function for the track-following servo. Therefore, the gain of the sensitivity function in sampled-data system at ω 0 is defined as follows.

SICE JCMSI, Vol. 1, No. 3, May 2008 249 where S sd ( jω 0 ) = y c(t) = sup y c (t) d c (t,ω 0 ) = Γ(ω 0 ) + l=, 0 t Λ(l,ω 0 ) (18) d c (t,ω) = e jωt, Γ(ω) C[e jωt s ]H( jω)p c ( jω) = 1, T s + H( jω + jω s k)p c ( jω + jω s k)c[e jωt s ] k= Λ(l,ω) = C[e jωt s ]H( jω + jω s l)p c ( jω + jω s l), T s + H( jω + jω s k)p c ( jω + jω s k)c[e jωt s ] k= (19) T s is the sampling time, ω 0 is the disturbance frequency and ω s is the sampling frequency. In order to suppress vibration whose frequency is ω 0, the control system should have a certain level of HP c at ω 0 so that Γ becomes small. And it should have small amount of HP c at the aliasing frequencies so that l=, 0 becomes small. Λ(l,ω 0 ) (20) Fig. 20 Block diagram of the servo system. Fig. 21 Frequency response of the mechanical system P m. A servo system is designed to illustrate an example. The sampling time T s is 153.46 μs (ω s = 2π 6516 [rad/s] and the Nyquist frequency is 3258 Hz). The frequency response of the mechanical system P m is indicated in Fig. 21 (solid line: fitting model, dashed line: measurement data). From this frequency response, it assumes that HP c is vanishingly small when ω> 2ω s. Thus, to save the calculation load, the frequency response of P c is defined as { Pm ( jω) : ω < 2ω P c ( jω) = s, (21) 0: ω 2ω s In this case, we focus on the vibration caused by the primary mechanical resonance at 4100 Hz. The discrete-time system is periodic with ω s. Thus, to stabilize the phase of the resonance mode of the discrete-time system P d, P d = 1 H( jω + jω s k)p c ( jω + jω s k) (22) T s k= at 2400 Hz enables S sd < 1 at 4100 Hz. In order to stabilize the phase of the resonance mode in P d, C is set based on the following equation. (z + 1)(z 0.9529)(z 0.908) C[z] = 0.5597 (23) (z + 0.5882)(z 1)(z 0.01812) The sensitivity function in the sampled-data system and the discrete-time system are calculated. Figure 22 shows these results and S sd is below 0 db at 4100 Hz. This means that the control system can suppress the vibrations above the Nyquist frequency. The effectiveness is also verified in experiment [23]. 7. Conclusions Many technical papers and presentations regarding HDD servo control have been published, but there seem only a few approaches to discuss comprehensive HDD servo control design method. In this paper, feature of HDD servo control is identified. It is a full closed loop sampled servo system. In order to solve issues coming from the features, several unique design methods for HDD servo control have been proposed, and some of them are summarized here. There are so many outstanding servo algorithms which are not mentioned in this paper. So authors would appreciate it if more comprehensive design methodology based on HDD servo control will be proposed in the future. Many servo systems in industries including HDD have been designed referring advanced control theory. This approach for enhancing product s performance, cost, and safety to human and environment is definitely important. However at the same time, it is necessary to learn neighbors control application technologies which must be optimized and best practice under specific conditions. The point is how well the industries could learn the essence of the design each other. In this paper, servo design methodology of fast access and precise positioning for HDD is presented focusing on its features of a full closed loop sampled servo. Authors wish that this method could give some hints to other industries. Fig. 22 Sensitivity function. Acknowledgments Authors would like to express our gratitude to Prof. Hirata at Utsunomiya Univ., Prof. Fujimoto at Yokohama National Univ., Prof. Okuyama at Tokai Univ., Mr. Hara at Fujitsu, Mr.

250 SICE JCMSI, Vol. 1, No. 3, May 2008 Takakura and Dr. Sado at Toshiba, Dr. Bando at JAXA, and Mr. Numasato and Mr. Uchida at Hitachi Global Storage Technologies, for their proactive industry-academy collaborations and contributions to HDD servo technology development. References [1] http://mizugaki.iis.u-tokyo.ac.jp/nss/ [2] T. Yamaguchi, M. Hirata, and H. Fujimoto: Nanoscale Servo Control, Tokyo Denki University Press, 2007 (in Japanese). [3] T. Yamaguchi: HDD servo control development - Present and future, SICE-ICCAS International Joint Conference, FA17-1, pp.2756-2759, 2006. [4] T. Yamaguchi: Design points of mechatronics servo control - HDD servo control, Workshop 2, 2007 IEEE Multi-conference on Systems and Control (MSC), 2007. [5] G. Franklin, J. Powell, and M. Workman: Digital Control of Dynamic Systems second edition, Addison Wesley, 1990. [6] J. Doyle, B. Francis, and A. Tannenbaum: Feedback Control Theory, Macmillan Publishing Company, 1992. [7] M. 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Yamaguchi: Modelling and Control of a Disk File Head- Positioning System, Journal of Systems and Control Engineering, Vol.215, No.I5, pp.549-568, 2001. [12] M. Tomizuka: Zero phase error tracking algorithm for digital control, ASME Journal of Dynamic System, Measurement and Control, Vol.109, pp.65-68, 1987. [13] M. Kobayashi, T. Yamaguchi, and H. Hirai: Adaptive seeking control for magnetic disk drives, JSME International Journal, Series C, Vol.43, No.2, pp.300-305, 2000. [14] H. Fujimoto, Y. Hori, T. Yamaguchi, and S. Nakagawa: Proposal of seeking control of hard disk drives based on perfect tracking control using multirate feedforward control, 6th International Workshop on Advanced Motion Control, pp.74-79, 2000. [15] T. Yamaguchi, S. Shishida, S. Tohyama, Y. Soyama, H. Hosokawa, H. Ohsawa, H. Numasato, T. Arai, K. Tsuneta, and H. Hirai: A Mode-Switching Controller with Initial Value Compensation for Hard Disk Drive Servo Control, Control Engineering Practice, Vol.5, No.11, pp.1525-1532, 1997. [16] T. Yamaguchi, H. Numasato, and H. Hirai: A Mode-Switching Control for Motion Control and Its Application to Disk Drives: Design of Optimal Mode-Switching Conditions, IEEE/ASME Trans. Mechatronics, Vol.3, No.3, pp.202-209, 1998. [17] Y. Li, Y. Sun, C. Smith, L. Guo, and W. Guo: Optimization of initial value compensation for settle control in hard disk drive, IEEE Trans. Magnetics, Vol.41, No.2, pp.797-801, 2005. [18] M. Kobayashi, T. Yamaguchi, T. Yoshida, and H. Hirai: Carriage acceleration feedback multi-sensing controller for sector servo systems, ASME, Advances in Information Storage Systems, Vol.10, pp.33-47, World Scientific Publishing, 1999. [19] F. Huang, W. Imaino, T. Semba, and F. Lee: Rotary actuator dynamics with active damping, Proc. 11th Annual Symposium on Information Storage and Processing System, Session 8, 2000. [20] M. White, T. Hirano, H. Yang, K. Scott, S. Pattanaik, and F. Huang: High-bandwidth hard disk drive tracking using a moving-slider MEMS microactuator, 8th IEEE Int. Workshop on Advanced Motion Control, pp.299-304, 2004. [21] T. Atsumi, T. Arisaka, T. Shimizu, and T. Yamaguchi: Vibration Servo Control Design for Mechanical Resonant Modes of a Hard-Disk-Drive Actuator, JSME International Journal Series C, Vol.46, No.3, pp.819-827, 2003. [22] T. Atsumi, A. Okuyama, and S. Nakagawa: Vibration Control above the Nyquist Frequency in Hard Disk Drives. Proceedings of the 9th IEEE International Workshop on Advanced Motion Control, pp.103-108, 2006. [23] T. Yamaguchi and T. Atsumi: HDD Servo Control Technologies, What we have done and where we should go, IFAC World Congress, MoA21.1, 2008 (to be published). Takashi YAMAGUCHI (Member) Received the B.S., M.S., and Dr. Eng. degrees from Tokyo Institute of Technology, Tokyo, Japan, in 1979, 1981 and 1998, respectively. He joined Mechanical Engineering Research Laboratory, Hitachi, Ltd. in 1981. From 1986 to 1987, he studied at the University of California, Berkeley as an industrial visiting researcher. Since 2003, he had been with Advanced HDD Technology Division, Hitachi Global Storage Technologies, Ltd. He received engineering awards from the Society of Instrument and Control Engineers and the Japan Society of Mechanical Engineers in 1997 and 2000 respectively. His interest includes mechatronics technology development and management. Takenori ATSUMI (Member) Received the B.S., M.S., and Ph.D. degrees from Chiba University, Chiba, Japan, in 1997, 1999, and 2006, respectively. Since 1999, he has been with the Research and Development Group, Hitachi, Ltd., Kanagawa, Japan. His current research interests include servo control technologies and integrated design of a controller and a structure in hard disk drives.