Disturbance Rejection Through Disturbance ... - Semantic Scholar

IEEE TRANSACTIONS ON MAGNETICS, VOL. 45, NO. 6, JUNE 2009

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Disturbance Rejection Through Disturbance Observer With Adaptive Frequency Estimation Qing Wei Jia R&D Center, Hitachi Asia Ltd., 049318 Singapore In this paper, a new adaptive disturbance rejection scheme is introduced. In the proposed scheme, adaptive frequency estimation technique is incorporated into the traditional disturbance observer method. The frequency of the dominant disturbance is estimated online by a fast stable adaptive algorithm, and the estimated frequency is used to adaptively tune the bandwidth of the disturbance observer. Application to a HDD system shows that the proposed method exhibits good capability of disturbance rejection. Comparing with the traditional disturbance observer method, the new method incurs much less drop in phase margin. Index Terms—Adaptive frequency estimation, disturbance observer, disturbance rejection, hard disk drive.

I. INTRODUCTION RACK following servo systems in hard disk drives (HDDs) are required to hold read-write heads to very small off-track errors to support the increasing track density of today’s products. Tracking errors can be induced due to many effects including disk and bearing run-out, servo-track-writer induced irregularities, electronic noise, spindle and actuator resonances, and external shock and rotary vibration (RV) excitations. Usually these disturbances are classified into two categories: repeatable runout (RRO) and nonrepeatable runout (NRRO). RRO is locked to the spindle rotation in both frequency and phase. RRO can be rejected by servo control algorithms, for example, [1]–[3]. NRRO, like shock and RV disturbances, contains frequency components with time-varying phases and magnitudes at unknown frequencies. Small form factor hard disk drives are being used in portable environments where there is an increased exposure to continuous shocks and random vibration due to daily activities like jogging, cycling, etc. Portable device like MP3 player requires a smooth flow of music without interruption during jogging. External shocks to the portable device may cause the read/write head in the disk drive to move off-track due to mechanical imbalance of the actuator and hence unable to load information from drive to memory buffer. If the drive cannot recover fast enough from shocks, the system may hang and thus cause the portable device to stop operation [4]. Feed-forward disturbance rejection technique based on hardware sensors has long been adopted to deal with NRRO disturbances. This kind of technique is a disturbance compensation method using signals from additional sensors such as accelerometer or velocity transducer, for example, [5], [6]. However, any extra hardware implies extra cost; and cost factor has become a very critical issue involved in HDD industry, especially for low-end HDDs. On the other hand, sensorless control schemes based on disturbance observer (DO) have been a hot topic these years and many successful applications can be listed

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Manuscript received October 09, 2008. Current version published May 20, 2009. Corresponding author: Q. W. Jia (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMAG.2009.2018605

[7], [8]. As its name suggests, the disturbance observer creates an estimate of the disturbance and uses this estimated signal to make compensation for the disturbance. A low pass filter is used to filter out high frequency components in the observed disturbance. For better disturbance rejection, it is required that the cutoff frequency or bandwidth (BW) of the low pass filter is higher; however, higher filter bandwidth will cause significant drop of phase margin, and thus may incur stability problems. To keep balance between the disturbance rejection performance and maintaining reasonable stability margins, the adaptive frequency estimation method is incorporated into the traditional DO scheme in this paper. In practical situation, the frequencies of the dominant NRRO disturbance components have to be identified online. The reasons lie in that, firstly the frequencies are usually unknown, and secondly they vary with operational environments and other factors. The problem of unknown frequency estimation has been studied extensively by means of different techniques, such as adaptive notch filtering, extended Kalman filer frequency estimation, phase-locked loop (PLL) technique, adaptive identifier/ estimator, etc. [9]–[16]. In this paper, the adaptive frequency estimation method similar to that in [17] is adopted due to its simplicity. It will be shown that the proposed method can achieve fast stable convergence in identifying the disturbance frequency and good disturbance rejection. At the same time, the stability margins are not affected significantly by introducing the adaptive identification technique into DO scheme. This paper is organized as follows: in Section II, the traditional DO technique is first introduced. And then the new disturbance rejection scheme with adaptive frequency estimation is proposed in Section III. Experiment results are shown in Section IV. Conclusions are given in Section V. II. DISTURBANCE REJECTION THROUGH TRADITIONAL DO The block diagram of the traditional DO scheme for HDD is shown in Fig. 1. is the digital controller; and represent the sampler and zero order holder, respectively. The plant to be controlled is subject to an external RV/shock disturbance and measurement noise as well. The sampled plant model is denoted as , the inverse of which is denoted by . A low pass filter (LPF) is used to filter out high frequency components in the observed disturbance . A compensation signal , which contains

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Fig. 1. Traditional compensentor based on disturbance observer.

only the low frequency signals of , is obtained to counteract the effect of the disturbance . To compensate for the phase loss due to computational and other delays, steps delay is introduced. The rationale of the disturbance observer can be shown as follows: if we ignore the nominal feedback from the plant output to the controller input, and denote the transfer function from to to , and to as and , respectively. It was shown in [8] that, if the filter is set to unity and the delay is supposed to be small then , which is well attenuated. However, the implies the disturbance measurement (sensor) noise is unattenuated as . Conversely, if the filter is set to be zero, the sensor noise is eliminated as , but the attenuation of the disturbance is limited because . The above analysis shows that design of the -filter is critical in the DO scheme. It is well known that sensor noise is typically high frequency, while the frequency range of RV/shock rejection is, from the HDD specification, between 20 Hz to 500 Hz [4]. By designing the -filter to be a low-pass filter with unity DC gain, the sensor noise can be attenuated in high frequency range and at the same time the effect of the RV/shock is cancelled in low frequency range. The bandwidth of the -filter has a significant influence upon the system performance. This is clearly shown in Figs. 2 and 3. In Fig. 2, when the bandwidth of the -filter is higher, the amplitudes of sensitivity functions at lower frequency become smaller, which implies that the capability to reject low frequency disturbance gets larger. However, the phase margins (PM) get smaller as shown in Fig. 3. We can observe that the PM drops from 25.8 degree to 17.4 degree when the bandwidth of the -filter is increased to 500 Hz.

Fig. 2. Sensitivity functions.

Fig. 3. Open-loop functions.

is the unknown constant amplitude, is the angular frequency and the unknown frequency to be identified. Following the trigonometric identity (2) we have

(3) III. THE PROPOSED DISTURBANCE REJECTION SCHEME Before introducing the new disturbance rejection scheme, we first discuss the adaptive frequency estimation technique.

Equation (3) is a classical relation [17]. The unknown frequency can be obtained by utilizing the above relationship

A. Adaptive Frequency Estimation of Unknown Frequency Let

(4)

represent a discrete sinusoid signal (1)

where tively.

and represent the estimations of and , respecis the sampling time of the signal in (1).

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JIA: DISTURBANCE REJECTION THROUGH DISTURBANCE OBSERVER WITH ADAPTIVE FREQUENCY ESTIMATION

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Fig. 4. Proposed adaptive DO scheme.

Fig. 6. Estimated frequency.

The adaptive law by the LMS algorithm for

is

(8) The unknown frequency of can then be obtained through (4) and (6). In the following section, the above adaptive frequency estimation scheme will be incorporated into the traditional DO technique to form a novel disturbance rejection scheme. Fig. 5. NRRO spectrum.

B. Disturbance Rejection Through Adaptive DO

Although the unknown frequency can be calculated very fast according to (4), however, there will be trouble in the calculation when is around zero. The situation may be further aggravated by the presence of noises, which may result in a large spread in the values of . When the signal in (1) is corrupted by a white Gaussian noise , let . Following (3), we have

(5) where

is defined as

. Denote (6)

The well-known least-mean-square (LMS) method or the recursive-least-square (RLS) method can be directly applied to adaptively estimate , and thus . In the following, the LMS method is adopted due to its simplicity. According to (5), the estimation error is naturally given as (7)

Based on the adaptive frequency estimation method discussed above, the proposed disturbance rejection scheme using an adaptive disturbance observer is shown in Fig. 4. The disturbance signal is actually of quite broad frequency band. To have a fast and accurate frequency estimation of the dominant disturbance and avoid the inference from other noises and disturbance, a band pass filter , which covers the possible frequency range of the dominant disturbance component, is applied to isolate the interested frequency band. The estimated frequency can be obtained following the procedures discussed in previous section. in Fig. 1 It is worth noting that, the low-pass filter is replaced by an adaptive bandpass filter in Fig. 4. The center frequency of is adaptively tuned by the estimated frequency . The filter bandwidth can be adjusted according to real situation to make balance between the disturbance rejection performance and maintaining reasonable stability margins. IV. APPLICATION TO HDD The proposed adaptive disturbance rejection method has been evaluated using a 2.5 inch form factor HDD drive. The NRRO spectrum is shown in Fig. 5. Many spikes, which represent significant NRRO components, can be observed. The dominant one is around 870 Hz.


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scheme, which is much less comparing with the traditional DO method. V. CONCLUSION In this paper a new adaptive DO method is introduced by incorporating the adaptive frequency identification technique into the traditional DO method. The main advantage of the proposed scheme is that it provides a good disturbance rejection performance while can maintain reasonable stability margins of the HDD servo system. The effectiveness of the proposed method is evaluated by application to a HDD system. REFERENCES Fig. 7. Sensitivity function with proposed disturbance rejection scheme.

Fig. 8. Open-loop response with proposed disturbance rejection scheme.

is chosen to be of 500 Hz bandwidth [500 Hz 1000 a bandpass filter with 100 HZ bandwidth. Hz], and is adaptively tuned according The center frequency of to the estimated frequency. To guarantee a fast convergence and less fluctuation in steady state, the adaptation gain in (8) is gradually reduced from the initial value 0.1 to 0.01. Fig. 6 shows the estimated frequency, which is very close to the actual dominant frequency shown in Fig. 5. The sensitivity function with the adaptive DO is shown in Fig. 7. It can be observed that the disturbance around the dominant disturbance frequency can be well attenuated. This is confirmed by the NRRO spectrum shown In Fig. 5. Fig. 8 shows that there is about 2 degree phase drop with the new adaptive

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