Phase Lead Peak Filter Method to High TPI Servo Track Writer with Microactuators

Transcription

1 Prceedings f the 6 American Cntrl Cnference Minneaplis, Minnesta, USA, June 4-6, 6 WeB8.5 Phase Lead Peak Filter Methd t High TPI Serv Track Writer with Micractuatrs Jinchuan Zheng, Chunling Du, Guxia Gu, Yuyi Wang, Jingliang Zhang, Qing Li, and Branislav Hredzak Abstract A serv track writing (STW) platfrm with dual piezelectric (PZT) micractuatr is prpsed fr higher track density hard disk drives (HDDs). We mainly deal with the serv cntrl issues t achieve high track density. Vibratin and nise analysis based n the measured psitin errr signal (PES) indicates that the PES is significantly disturbed by narrw-band vibratins. Hence, we prpse a general secnd-rder phase lead peak filter (PLPF) that is applicable t reject narrw-band disturbances at all frequency ranges. The filter zer is designed t minimally degrade the clsed-lp system stability and btain a smth sensitivity curve arund the disturbance frequency. A feedback cntrller is emplyed t stabilize the serv lp and then a PLPF is embedded t further suppress the specific vibratins. The readback psitin errrs are evaluated and 6.4 nm 3σ value f the true PES NRRO is achieved, crrespnding t 395k track-per-inch (TPI) track density. I. INTRODUCTION As hard disk drive (HDD) track density has been grwing s rapidly, s have the requirements n the serv track writing (STW) [7], which is the prcess t pattern the recrding media with serv infrmatin fr the HDD serv system. As the track density, measured by track per inch (TPI), is increasing, amng all track mis-registratin (TMR) surces [], the cntributins f disk vibratin, spindle nnrepeatable runut (NRRO), and suspensin and slider vibratins are becming mre significant. High bandwidth [5] is necessary in bth HDDs and STW fr suppressing all vibratins t achieve higher TPI numbers. Althugh single stage vice cil mtr (VCM) based serv lp bandwidth is increased whenever pssible, a mre effective way is t use dual-actuatr systems []. A secndary actuatr such as a micractuatr attached n the VCM becmes an attractive candidate t achieve this target. The secndary actuatin allws the mtr, disk and suspensin induced vibratin t be actively cmpensated especially in the STW prcess [4]. Fr high-density recrding, we have prpsed a new STW platfrm by using multiple micractuatrs with multiple read/write (R/W) heads. Rughly speaking, the multiple micractuatr STW system is cmpsed f ne primary actuatr r MicrE [], a few micractuatrs, and an E-like arm blck. The primary actuatr is psitined by its ptical sensr signal. Each micractuatr is psitined by the readback psitin errr signal (PES) frm the disk surface. The Jinchuan Zheng, Chunling Du, Guxia Gu, Jingliang Zhang, Qing Li and Branislav Hredzak are with A*STAR, Data Strage Institute(DSI), 5 Engineering Drive (Off Kent Ridge Crescent, NUS), Singapre JCZheng@pmail.ntu.edu.sg; Guxia Gu@ieee.rg Jinchuan Zheng and Yuyi Wang are with the Schl f Electrical and Electrnic Engineering, Nanyang Technlgical University, Singapre Fig.. Overview f the serv track writing (STW) platfrm with dual PZT micractuatrs. readback PES reflects the disturbances f disk, suspensin, head, slider and spindle mtr, and the measurement nise as well as the written-in errr. Based n the measured PES, disturbances and nise f the STW platfrm are analyzed and a few narrw-band disturbances at mid-high frequency range are bviusly bserved. In the HDD serv, the cnventinal peak filter [8] was effectively emplyed t reject the lw-frequency ( 6 Hz) narrw-band disturbance caused by disk shift, disk warp and spindle vibratin. Hwever, the peak filter is hardly applied t reject the mid-high frequency disturbances because f its intrinsic phase lss that negatively impacts the phase margin and distrts the sensitivity gain arund the disturbance frequency. Thus, previus filter designs are nly effective t reject the narrw-band disturbances in a limited frequency range. This paper presents a new peak filter methd, namely, phase lead peak filter (PLPF) methd, t reject the narrw-band disturbance in an unlimited frequency range and simultaneusly minimize the phase lss. Mre advantageus than cnventinal peak filters, the PLPF zer is assigned t minimally degrade system stability and ptimally reject the disturbances. The applicatin f the PLPF methd t the abve mentined STW serv system shws that by rejecting specific frequency vibratins the true PES NRRO is reduced t 3σ =6.4 nm, i.e, 395 ktpi is achieved. II. SYSTEM DESCRIPTION AND VIBRATION ANALYSIS The prpsed STW platfrm is shwn in Fig., which invlves ne MicrE as the s-called primary actuatr and /6/$. 6 IEEE 39

2 TABLE I PARAMETERS OF THE MSTW PLATFORM Spindle 3.5 inch fluid bearing Spindle speed 54 revlutins/minute Disks.5 inch diameter.33 mm thickness Glass Number f sectrs 5 Fig. 3. Blck diagram f serv mechanism f the MSTW platfrm. Fig.. Serv mechanism f the MSTW setup (MicrE lp uses ptical sensing signal as feedback signal t a PID cntrller. We fcus n the cntrl design fr PZT micractuatr with readback PES as feedback signal. tw PZT micractuatrs attached t the E-blck arms. There are tw disk platters that can be accessed by the heads simultaneusly. The parameters f the STW platfrm are listed in Table I. The serv mechanism f the tw-micractuatr STW (MSTW) is shwn in Fig., MicrE uses its ptical sensing signal as feedback signal and its cntrller is adjusted accrding t prprtinal-integral-derivative (PID) standard frm. Here we fcus n the cntrl design fr the micractuatr with the readback PES as the feedback signal. The cntrl algrithm is implemented with the digital PES generated frm DSP TMS3C67. The blck diagram f the STW serv lp is drawn in Fig. 3, P me and C me dente MicrE plant and cntrller, and P and C are PZT micractuatr plant and cntrller, respectively. d represents all trque disturbances including windage due t air-turbulence impinging upn the actuatr, the R/W head suspensin, r the slider. d represents disk and mtr vibratins as well as external vibratin. n represents electrnic nise, media nise and A/D quantizatin nise. The frequency respnses f the micractuatr P (s) are measured using a dynamic signal analyzer (DSA). The micractuatr transfer functin is btained by curve fitting t the measured frequency respnses and its zers, ples and gain are given by zers = 4 [6.56 ± 6.473j,.68 ± 7.4j,.36 ± 5.75j,. ± 3.397j,.8 ±.3497j], () ples = 4 [.336 ± 9.469j,.596 ± 7.978j,.3 ± j,.4335 ± 4.337j,.539 ± 3.749j,.37 ±.345j], () gain =.858. (3) Fig. 4 shws the identified mdel, which includes six resnance mdes at 3.7, 4.9, 6.9, 9,.7 and 5 khz. A ttal f cnsecutive revlutins f PES data are cllected and the pwer spectrum f NRRO is btained by using FFT and shwn in Fig. 5. The disturbance distributin is reflected in the NRRO pwer spectrum, disturbances in lw-frequency range are mstly due t external vibratins, 65 Hz mde is due t disk vibratin, and the 3.8 khz and abve if any are caused by the excited suspensin resnances. The fllwing cntrl design will deal with the disturbances arund 65 Hz specifically. The nise level f the whle PES generatin channel is als measured and shwn in Fig. 6. It turns ut that the nise level fits well the baseline f the NRRO distributin in Fig. 5. The 3σ (σ means standard deviatin) f the NRRO is btained as nm with the nise 3σ=5. nm. III. SERVO LOOP DESIGN WITH PLPF METHOD AND ITS APPLICATION ON MSTW PLATFORM This sectin presents a generalized ptimal PLPF methd and its applicatin n the MSTW platfrm t reject the narrw-band vibratins arund 65 Hz fr imprving the track density. A. Disturbance Filter Structure with Parallel Realizatin The disturbance filter r phase lead peak filter (PLPF) structure with parallel realizatin added n t a baseline serv (C n (z)) system is shwn in Fig. 7. The baseline serv system is assumed t have basic stability and perfrmance. The filter is cnnected t the baseline cntrller C n (z) in 3

3 4 3 Measured Mdeled x 3 Phase(deg) Magnitude(dB) Fig. 4. Frequency respnses f the PZT micractuatr. Nise magnitude(μm) Fig. 6. Nise level mainly cnsisting f media nise and electrnic channel nise (3σ=5.nm). x 3.8 NRRO magnitude(μm) Hz 3.8 khz Fig. 5. NRRO pwer spectrum calculated frm measured PES withut serv cntrl, reflecting the vibratin distributin f the MSTW platfrm (3σ=nm). a parallel frm such that the filter can be easily enabled r disabled in the tracking mde r seeking mde. Mrever, the parallel realizatin has better numerical reslutin than cascade realizatin in the case f fixed-pint implementatin. The mst imprtant advantage fr this kind f structure is that the cntrl design can be decupled int tw stages. This can be illustrated by the sensitivity functin: S(s) = +PC n ( + F ) = +PC n +PC n +PC n + PC n F = S S F, (4) S (s) =, +PC n (5) S F (s) = +T F, (6) T (s) = PC n. +PC n (7) Nte that S and T are the sensitivity functin and cmplementary sensitivity functin f the baseline serv system, respectively. Equatin (4) shws that the verall Fig. 7. Cntrl structure with peak filter implemented as an add-n filter. sensitivity functin f the clsed-lp system is the multiplicatin f tw subsystem S and S F, which implies that the cntrllers can be designed by a tw-stage apprach. In the first stage, we can design the baseline cntrller C(s) fr basic clsed-lp stability and disturbance rejectin perfrmance indicated by S. In the secnd stage, we can design the filter F (s) based n the pseud-plant T as shwn in (6) such that S F is shaped t a desired curve fr rejecting disturbances in sme frequency ranges. Since we aim at rejecting the narrw-band disturbances, the disturbance filter f the fllwing frm can be adpted F (s) =K s[ω cs(ϕ) sin(ϕ)s] s +ζω s + ω, (8) ω : is the disturbance frequency, at which high disturbance rejectin is required; ζ: is the damping rati with ζ (, ); ϕ: is the phase angle determined by [ ] ϕ =arg T (jω ) [ π, π]. (9) K: is the psitive filter gain. Mrever, the clsed-lp system will be guaranteed t be stable if <K<γ, () γ is the minimal psitive real slutin f K in the fllwing tw equatins { Re[Q(ω, K)] = () Im[Q(ω, K)] = Q(ω, K) =+T (jω)f (jω). () 3

4 Here, Re( ) and Im( ) dente the real and imaginary part f a cmplex number, respectively. Nte that if () has n slutin except K = ω =, then γ =+. The disturbance filter in (8) is quite a general high-gain cntrller structure t reject narrw-band disturbances in a wide frequency range because the filter zer lcatin can be autmatically shifted accrding t the disturbance frequency assciated with the baseline serv system. The next tw subsectins will discuss the serv prperties f stability and sensitivity gain shaping due t the zer lcatin and the filter gain. B. Stability Prperties Using the Disturbance Filter The disturbance filter has tw cmplex ples at p, = ω e ±jθ, θ = arcctan( ζ ). The ples can ζ prvide the high lp gain at the disturbance frequency. The filter cntains tw real zers at z =, z = ω ctan(ϕ). z is specified at the rigin in rder t maintain the DC gain substantially belw the disturbance frequency as that f the baseline serv system such that the crrespnding sensitivity gains are nt affected. The ther zer z is specified in rder t achieve phase stabilizatin, mre specifically, the zer will make the departure angles f the filter ples apprach t π in the rt lcus f T (s)f (s). This is the crrect chice since the ples mve in the mst stable directin, which als prvides a phase margin f ± π [6]. This prperty can be verified by Fig. 8. Applying the rule fr departure angles frm the rt lcus design methd [3], the departure angle frm the ple p is given by φ dep = θ + α + β π + πi, (3) {, fr ϕ [ π, ] i = (4), fr ϕ [,π], [ ] α =arg T (p ) (5) dentes the sum f the angles frm the zers f T (s) t p minus the sum f the angles frm the ples f T (s) t p.in practice, the filter damping rati ζ is chsen as a small value (<.) t prvide the high gain at the disturbance frequency. Thus, the filter ples will be very clse t the imaginary axis, and we can make the fllwing apprximatins θ π, (6) α arg[t (jω )] = ϕ, (7) { ϕ, fr ϕ [ π, ], β (8) π ϕ, fr ϕ [,π]. Substituting (6) (8) int (3), it gives that φ dep π. (9) Therefre, the rt lcus at the filter ples will mve twards the left-half plane (LHP) when the lp gain K increases frm. The pint the lcus crsses the imaginary axis can be cmputed by (); and the crrespnding K value equals t γ, belw which the ples f the clsed-lp system are all in the LHP, which guarantees the system stable. β z = ω ctan( ϕ) φ dep + + Im(s) j = ωe θ p θ z = + j p =ωe θ α Re(s) Fig. 8. Rt lcus fr the system T (s)f (s). The departure angles frm the disturbance filter ples p, apprach t π by assigning the lcatin f the filter zer z. C. Sensitivity Shape Prperties Using the Disturbance Filter The zer placement f the disturbance filter can furthermre lead t anther imprtant advantage f minimizing the sensitivity gain at the disturbance frequency withut bviusly distrting the gains at ther frequency bands. This can be cnfirmed by the sensitivity functin f (6), frm which it gives that S F (jω ) = +T (jω )F (jω ) + T (jω ) F (jω ). () By cmputing the phase angle f F (s) at the disturbance frequency s = jω, it is easy t derive that arg[t (jω )] + arg[f (jω )] =. () Therefre, the equal mark in () hlds, which implies that S F (jω ) appraches the minimum value that can be derived as fllws S F (jω ) min = + K ζ T (jω ). () In fact, the equatin () indicates that the filter zer prvides the exact phase lead amunting t the phase lag f T (s) at ω such that the pint f T (jω )F (ω ) is assured t lcate n the psitive real axis, S F (jω ) reaches the minimum. This prperty can be clearly illustrated frm the Nyquist plt in Fig. 9. Anther feature bserved frm the figure is that the phase lead prvided by the filter zer tends t mve the verall curve f T F away frm the circle. Thus, the sensitivity gains arund ω are reduced, and in the meantime the sensitivity gains at ther frequencies are nt bviusly increased because the curve segments at these frequencies are clsed t the neighburhd f circle. Fig. further shws the cmparisn f the sensitivity gains 3

5 Imaginary axis circle F T ω ω ω T F 3 3 Real axis Fig. 9. Nyquist plt. The filter zer prvides the exact phase lead such that T F at ω is lcated n the psitive real axis. Mrever, the verall curve f T F is mved away frm the circle, implying reduced sensitivity gains arund ω and n bvius distrtin f the gains at ther frequencies. The circle represents the unit circle whse center is at pint. Gain [db] Frequency [Hz] with ptimal zer z zer placed at 3z zer placed at 3z Fig.. Frequency respnses f the sensitivity gain f S F (s) with different filter zer placements. The curve achieved with ptimal zer is smth withut exhibiting sharp peak. btained with different filter zer placements. It is bvius that the filter with ptimal zer design achieves a smth sensitivity curve arund the disturbance frequency, at which the ther tw filters with different zers exhibit sharp peaks. D. Applicatin n the MSTW platfrm The serv track writer writes serv pattern int 5 sectrs using 54 rpm spindle rtatinal speed. Thus 45 (i.e., 5 54/6) khz sampling rate is used in the serv cntrl design and the cntrller is restricted t be less than th rder due t the DSP speed limitatin in ur case. The cntrl algrithm is realized by C prgramming with DSP TMS3C67. The cntrller C(z) t be designed fr the micractuatr n the MSTW platfrm invlves three parts: ntch filters, a prprtinal-integral (PI) cntrller and a peak filter. Ntch filters at 3.7 khz, 9 khz and 5 khz are used t suppress the resnances excitatin f the micractuatr. The resnance mdes at 4.9, 3 and 6.9 khz, as seen in Fig. 4, culd be simply ignred in the cntrl design as there have relatively smaller magnitudes that are nt easily excited t affect the whle lp stability. The PI-lag cntrller with the frm: z C pi =.7( z.5).z.9889 z.9986, (3) is applied. Nte that a lag cmpensatr is used in (3) t further increase the lw-frequency magnitude f the cntrller. Based n the baseline feedback serv, the PLPF in Fig. 7 is then used t deal with the disturbances arund 65 Hz as shwn in Fig. 5. In Fig. 7, C f (z) =+F (z), with a f s F (s) = s +ξ f ω f s + ωf, (4) a f = Δω f Δ (ω f Δ),ξ a f f = M/, (5) and F (z) is btained by discretizing F (s) with matched ple-zer methd. In (4) and (5), ω f dentes a frequency center f the disturbances t be suppressed, Δ means the frequency range frm the center (i.e., ω f ± Δ), and M dentes the suppressin level M db, i.e., the sensitivity functin magnitude is M db at ω f. Here, Δ = 5, ω f = 636, M = 4. Nte that (4) is a special case f (8) and is discussed in detail in [9]. Dente C n (z) =C pi ntchfilters. The resultant cntrller C(z) =C n (z) C f (z) is a th rder cntrller. Fr cmparisn, a cnventinal peak filter (PF) with the fllwing frm is als designed t reject the disturbances arund 65 Hz. C f (s) = s +ξ ω f s + ωf s +ξ ω f s + ωf, (6) ξ =.8, ξ =. and ω f = π 65. The pen-lp serv system with the designed peak filters (4) and (6) are cmpared in Fig., the phase margin (PM) with PLPF methd is much higher, which is the main advantage f PLPF methd. Als, the bandwidth is higher and the gain margin (GM) is lwer, as it is still high enugh. The sensitivity functin is shwn in Fig.. The imprvement caused by the PLPF (4) is bviusly seen, especially arund 65 Hz. This is reflected in the pwer spectrum f measured PES NRRO as shwn in Fig. 3. Dente Ψ(f i ), S(f i ), and T (f i ) as the pwer spectrum, sensitivity functin, and cmplementary sensitivity functin at the frequency pint f i (i =,, 3,..., N). Derived frm Fig. 3, with the assumptin that d, d and n are independent f each ther, the measured and the true PES NRRO pwer spectra are given by 33

6 Phase (deg) Magnitude (db) NRRO magnitude(μm) x 3 65Hz PLPF PF 36 PF PLPF 3 4 Frequency (Hz) Fig.. Cmparisn f pen lp frequency respnses (PF: GM=4 db, PM=49 deg, Bandwidth=77 Hz; PLPF: GM=9 db, PM=68 deg, Bandwidth=. khz). Magnitude(dB) PF PLPF Fig.. Cmparisn f sensitivity functins. Ψ NRRO,measured (f i )= S(f i ) ( d (f i ) + P (f i ) d (f i ) )+ S(f i ) n(f i ), Ψ NRRO,true (f i )= S(f i ) ( d (f i ) + P (f i ) d (f i ) ) + T (f i ) n(f i ), that is, Ψ NRRO,true (f i )=S NRRO,measured S(f i ) n(f i ) + T (f i ) n(f i ). (7) Accrding t (7), the 3σ f true NRRO is btained as 6.4 nm, crrespnding t 395 ktpi based n % track width tlerance fr 3σ. The NRRO 3σ cmparisn and the achieved ktpi are summarized in Table II. IV. CONCLUSION A STW platfrm with multiple micractuatrs has been presented in this paper. Vibratin and nise analysis based n the measured PES revealed that the platfrm was disturbed by narrw-band vibratins. A generalized PLPF is prpsed Fig. 3. NRRO pwer spectrum with serv cntrl (reduced especially at 65 Hz, 8% reductin befre khz, 395 ktpi achieved). TABLE II 3σ COMPARISON OF NRRO AND ACHIEVED KTPI Measured True ktpi NRRO (nm) NRRO (nm) N cntrl Cntrl with PF Cntrl with PLPF t reject narrw-band vibratins in a brad frequency range while minimally degrade the system stability and distrt the sensitivity curve arund the disturbance frequency. The PLPF was applied t the STW serv system t reject narrw-band vibratins arund 65 Hz and the results shwed that a 6.4 nm 3σ value f the true PES NRRO is achieved, which is equivalent t 395 ktpi track density. REFERENCES [] R. Ehrlich and D. Curran Majr HDD TMR surces and prjected scaling with TPI, IEEE Trans. Magnetics, 35(), pp , 999. [] L. Fan, H. Ottesen, T. Reiley, and R. Wd, Magnetic recrding head psitining at very high track densities using a micractuatr-based tw-stage serv system, IEEE Trans. Industrial Electrn., 4(3), pp. -33, 995. [3] G. F. Franklin, J. D. Pwell, and A. Emami-Naeini, Feedback Cntrl f Dynamic Systems, 3rd ed., Reading, MA: Addisn-Wesley, 994. [4] G. Gu and J. Zhang, Feedfrward cntrl fr reducing disk-flutterinduced track misregistratin, IEEE Trans. Magnetics, 39(4), pp. 3-8, 3. [5] T. Hiran, L. Fan, T. Semba, W. Lee, J. Hng, S. Pattanaik, P. Webb, W. Juan, and S. Chan, High-bandwidth HDD tracking serv by a mving-slider micr-actuatr, IEEE Trans. Magnetics, 35(5), pp , 999. [6] L. Sievers and A. Fltw, Cmparisn and extensins f cntrl methds fr narrw-band disturbance rejectin, IEEE Trans. Signal Prcessing, 4(), pp , 99. [7] K. Takaishi and Y. Uematsu, Hard Disk Drive Serv Technlgy fr Media-Level Serv Track Writing, IEEE Trans. Magnetics, 39(), pp , 3. [8] D. Wu, G. Gu, and C. Chng, Midfrequencydisturbance suppressin via micr-actuatr in dual-stage HDDs, IEEE Trans. Magnetics, 38(5), pp. 89-9,. [9] J. Zheng, G. Gu, and Y. Wang, Identificatin and decentralized cntrl f a dual-actuatr hard disk drive systems, IEEE Trans. Magnetics, 4(9), pp. 55-5, 5. [] MicrE PA Psitiner- Installatin Guide and User s Manual, MicrE, Clrad. 34