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IEEE TRANSACTIONS ON MAGNETICS, VOL. 44, NO. 11, NOVEMBER 2008
A New Adaptive Method for Identification of Multiple Unknown Disturbance Frequencies in HDDs QingWei Jia1 and ZhongFeng Wang2 R&D Center, Hitachi Asia Ltd., 049318 Singapore Broadcom Corporation, Irvine, CA 92617 USA In hard disk drive (HDD) system, disturbances like rotary vibrations and shocks usually contain frequency components with timevarying phases and magnitudes. The effect of these disturbances has to be attenuated for better servo performance, and the dominant frequencies of these disturbances need to be estimated. In this paper, a new adaptive identification method for frequency estimation is introduced, and adaptive estimation of multiple unknown frequencies has been studied. The proposed adaptive method has been applied to an actual HDD drive, and the experimental results confirm its effectiveness. Index Terms—Adaptive identification, hard disk drive (HDD), frequency estimation.
I. INTRODUCTION
I
NCREASING real data densities in hard disk drives (HDDs) continues to motivate the development of high performance servo schemes to suppress external disturbances as well as mechanical resonances. As data track width becomes narrower and narrower, the HDDs become more and more easily affected by external disturbances like the operating shock and vibration disturbances, especially when HDDs are used in portable electronic products [1]. Disturbances in HDDs include repeatable runout (RRO) and non-repeatable runout (NRRO). RRO disturbance is locked to the rotation of spindle motor in both frequency and phase. RRO can be rejected either by improving the servo-writing precision during the manufacturing processes to reduce written-in disturbances, which are the main source of RRO in HDDs [2], or by servo control algorithms, like the adaptive feed-forward compensation (AFC) method [3]–[5], the internal model based repetitive control method [6], etc. Unlike RRO, NRRO contains unknown frequency components with time-varying phases and magnitudes. NRRO disturbances can be rejected by improving the mechanical design, however, this will increase the cost of hard disk drives, and it is well known that the cost factor has become a very critical issue involved in HDD industry, especially for low-end HDDs. The other way to handle NRRO is to design a control algorithm that reduces the gain in the error rejection function at the frequency range where NRRO dominates, for examples, see [7] and [8]. The dominant frequencies of NRRO disturbances need to be estimated in advance in order to design control algorithms. One well-used method to estimate unknown disturbance frequencies is adaptive notch filter [9], [10]. For cases of multiple unknown disturbances, when the unknown frequencies are distinct and roughly known, band-pass filters can be applied to each frequency and thus for each frequency, an adaptive notch can be designed independently. However, if the unknown frequencies are totally unknown or close to each other, it is hard to design the adaptive notch filters independently. A global frequency estimation method using adaptive identifier has been proposed in [11]. While the global stability of the control system is guaranteed, the computation in this method is
Digital Object Identifier 10.1109/TMAG.2008.2002624
complicated, and the method has to be simplified before it can be applied practically. Global frequency estimation was also realized in [12] by designing an adaptive observer for the case of a single frequency and generalized the method to multiple frequencies. It is worth noting that the order of the frequency estimator is for the case of frequencies, and it is not easy to implement in practical applications. In this paper, a new adaptive identification method is introduced, and adaptive estimation of multiple unknown frequencies has been studied. Experimental results show that the proposed method can guarantee fast stable convergence, and the computation is much reduced compared with the method in [11] and [12]. This paper is organized as follows. Frequency identification methods based on adaptive notch filter technique as well as adaptive identifier technique are summarized in Section II. In Section III, the proposed identification method is introduced. Experimental study is discussed in Section IV and a conclusion is given in Section V. II. ADAPTIVE IDENTIFICATION OF UNKNOWN FREQUENCIES In this section, the basic ideas of the frequency identification methods based on adaptive notch filter technique as well as adaptive identifier/observer techniques will be roughly introduced. A. Adaptive Notch Filter Technique Various adaptive notch filter techniques for frequency estimation have been proposed. An adaptive identification scheme using IIR digital notch filter is shown in Fig. 1, where is a sinusoid signal and represents Gaussian white noise. are applied to reject disturbances at the Band-pass filters frequency range other than the dominant unknown frequency. The adaptive notch filter is in the form
(1.1) The nominal value of is , where is the is the factor of unknown frequency to be estimated. the notch width, namely, the larger the value of , the narrower the notch. The optimal value of can be adaptively updated by
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JIA AND WANG: A NEW ADAPTIVE METHOD FOR IDENTIFICATION OF MULTIPLE UNKNOWN DISTURBANCE FREQUENCIES IN HDDS
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and amplitudes
multiple unknown frequencies
(1.4) We have
Fig. 1. Frequency estimation using adaptive notch filter.
.. .
(1.5)
.. .
where
.. . and
.. .
..
.
.. .
. It follows that
Fig. 2. Multiple frequency estimation using cascaded adaptive notch filters.
minimizing the mean squared error , and an adaptive law based on gradient algorithm can be designed as (1.2) where (for stability reason) is the estimate of ; is the convergence parameter which controls the step size of the updates. The unknown frequency can be calculated as (1.3) is not easy to realize It should note that the operation of in practice. As stated earlier, when there are multiple unknown frequencies to be identified, an adaptive scheme using cascaded adaptive notch filters can be designed. Fig. 2 shows the case of 2 unknown frequencies to be identiand are disturbances with unknown fied. In Fig. 2, represents other noises. frequencies to be identified, and Band-pass filters and can be applied to each unknown frequency, and for each unknown frequency, an adaptive and notch filter can be designed independently. are notch filters in the same form as in (1.1). The estimation scheme will become quite complicated with the number of unknown frequencies. Furthermore, if the unknown frequencies are not distinct, it is hard to separate the unknown frequencies using band-pass filters, and the estimation of one unknown frequency will be affected by other adjacent unknown frequencies.
B. Global Frequency Estimation via Adaptive Identification Technique and Adaptive Observer
(1.6) The previous expression is in “linear-in-parameter” form, and the unknown parameters can be estimated using can be calcuthe adaptive identifier method, and lated accordingly. The order of the adaptive identifier is . A global frequency estimation method using adaptive observer is discussed in [12]. The signal in (1.4) can be generated by
(1.7) . Following Note that system (1.7) is observable for any the systematic design procedure given in [13], (1.7) can be transformed into an adaptive observer form through some linear transformation, and an adaptive observer with the order can be designed. Like in [11], the computation is of very complicated to calculate from the estimates of the adaptive observer. III. PROPOSED ADAPTIVE IDENTIFICATION METHOD In this section, a new adaptive identification method for estimation of multiple unknown frequencies is proposed. First, a disturbance with two unknown sinusoidal signals is considered
A global frequency estimation method using adaptive identifier has been proposed in [11]. For a sinusoidal disturbance with Authorized licensed use limited to: Qingwei Jia. Downloaded on December 18, 2008 at 03:14 from IEEE Xplore. Restrictions apply.
(1.8)
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IEEE TRANSACTIONS ON MAGNETICS, VOL. 44, NO. 11, NOVEMBER 2008
we can easily have
(1.9) . In discrete time, from (1.9) we have
where
(1.10) with . is the sampling time. The previous expression is in “linear-in-parameter” form, and the unknown parameters and can be estimated using the traditional adaptive method. Let the adaptive identifier output and identifier error be
Fig. 3. Spectrum of measured disturbance.
Substituting (1.5) into (1.14), we get (1.6). In discrete time, can be substitute by the equation shown at the bottom of the page. Then we have the description of (1.6) in discrete time
(1.11) , are the estimates of
.
is defined as (1.15) (1.12)
Based on the standard gradient algorithm, the adaptive laws can be chosen as
(1.13) and are the adaptation gains. Compared with the adaptive identification method in [11] and [12], it is obvious that the proposed adaptive algorithm is much simplified. The proposed method can be extended to estimate unknown frequencies. For the cases of unknown frequencies which is given in (1.4)
.. . (1.14)
Following similar procedure as (1.11)–(1.13), an adaptive identifier can be designed and can be estimated online. The order of the adaptive identifier will be 2 . Obviously the proposed method is much simplified compared with the frequency estimation methods provided in [11] and [12], in and , which the order of estimation algorithms are respectively. IV. EXPERIMENTAL STUDY The proposed method has been evaluated using a 2.5-in form factor HDD product. The measured signal is shown in Fig. 3. It is obvious that there exist two dominant disturbance components that are close to each other. Fig. 4 shows the diagram of the proposed adaptive scheme. and represent the is a band-pass filter. actual plant and the modeled plant. is the estimated disturbance. The estimated unknown frequencies are shown in Fig. 5. It shows that the convergence is very fast and stable, although fluctuations around the peak frequencies due to the disturbances other than the dominant frequencies can be observed. The avand are erage frequencies calculated from
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JIA AND WANG: A NEW ADAPTIVE METHOD FOR IDENTIFICATION OF MULTIPLE UNKNOWN DISTURBANCE FREQUENCIES IN HDDS
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Fig. 4. Block diagram of the proposed adaptive frequency identification scheme.
Fig. 6. PES before and after attenuation.
REFERENCES
Fig. 5. Estimation of unknown frequencies.
370 Hz and 529 Hz, which are exactly the two peak frequencies shown in Fig. 3. This verifies the effectiveness of the proposed method. Based on the frequency estimates, adaptive peak filters have been designed to attenuate the dominant frequencies in Fig. 3. The position error signals (PES) before and after attenuation are shown in Fig. 6. V. CONCLUSION In this paper a new adaptive identification method is introduced to estimate multiple unknown frequencies. The algorithm in the proposed method is much simplified compared with the methods provided in [11] and [12] in the sense that the order of the estimator is significantly reduced. Experimental results show that the proposed method can guarantee system stability and fast convergence in practical scenarios.
[1] Q. W. Jia, “Write fault protection against shock disturbance in HDDs without a shock sensor,” IEEE Trans. Magn., vol. 43, no. 9, pp. 3689–3693, Sep. 2007. [2] J. C. Morris, B. R. Pollock, and T. F. Ellis, “Compensation for repeatable runout error,” U.S. Patent 6 069 764, May 30, 2000. [3] M. Bodson, A. Sacks, and P. Khosla, “Harmonic generation in adaptive feedforward cancellation schemes,” IEEE Trans. Autom. Control, vol. 39, no. 9, pp. 1939–1944, Sep. 1994. [4] A. Sacks, M. Bodson, and W. Messner, “Advanced methods for repeatable runout compensation,” IEEE Trans. Magn., vol. 31, no. 2, pp. 1031–1036, Feb. 1995. [5] Q. W. Jia, Z. F. Wang, and F. C. Wang, “Repeatable runout disturbance compensation with a new data collection method for hard disk drive,” IEEE Trans. Magn., vol. 41, no. 2, pp. 791–796, Feb. 2005. [6] K. L. Moore, “Iterative learning control: An expository overview,” Appl. Comput. Controls, Signal Process. Circuits, vol. 1, no. 1, pp. 151–213, 1998. [7] M. Kobayashi, S. Nakagawa, and S. Nakamura, “A phase-stabilized servo controller for dual-stage actuators in hard disk drives,” IEEE Trans. Magn., vol. 39, no. 2, pp. 844–850, Feb. 2003. [8] D. W. Wu, G. X. Guo, and T. C. Chow, “Midfrequency disturbance suppression via micro-actuator in dual-stage HDDs,” IEEE Trans. Magn., vol. 38, no. 5, pp. 2189–2191, May 2002. [9] C. Kang and C. Kim, “An adaptive notch filter for suppressing mechanical resonance in high track density disk drives,” Microsyst. Technol., pp. 638–652, 2005. [10] Y. Xiao, Y. Takashita, and K. Shida, “Tracking properties of a gradientbased second-order adaptive IIR notch filter with constrained poles and zeros,” IEEE Trans. Signal Process., vol. 50, no. 4, pp. 878–888, Apr. 2002. [11] X. Xia, “Global frequency estimation using adaptive identifier,” IEEE Trans. Autom. Control, vol. 47, no. 7, pp. 1188–1193, Jul. 2002. [12] R. Marino and P. Tomei, “Global estimation of unknown frequencies,” IEEE Trans. Autom. Control, vol. 47, no. 8, pp. 1324–1328, Aug. 2002. [13] R. Marino and P. Tomei, Nonlinear Control Design—Geometric, Adaptive and Robust. Upper Saddle River, NJ: Prentice Hall, 1995.
Manuscript received March 03, 2008. Current version published December 17, 2008. Corresponding author: Q. W. Jia (e-mail:
[email protected]).
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