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Stroke Oriented Controller Design for Dual-stage Actuator of Head Positioning Control System in Hard Disk Drives
8th IFAC Symposium on Mechatronic Systems 8th IFAC Symposium on Mechatronic Systems Vienna, Sept. on 4-6, 2019 8th IFACAustria, Symposium Systems online at www.sciencedirect.com Vienna, Austria, Sept. 4-6,Mechatronic 2019 Available 8th IFACAustria, Symposium Systems Vienna, Sept. on 4-6,Mechatronic 2019 Vienna, Austria, Sept. 4-6, 2019
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IFAC PapersOnLine 52-15 (2019) 573–578
Stroke Oriented Controller Design for Stroke Oriented Controller Design for Stroke Oriented Controller Design for Dual-stage Actuator of Head Positioning Stroke Oriented Controller Design for Dual-stage Actuator of Head Positioning Dual-stage Actuator of Head Positioning Control System in Hard Disk Drives Dual-stage Actuator of Head Positioning Control Control System System in in Hard Hard Disk Disk Drives Drives Control System in Hard Disk Drives Shota Yabui ∗∗ Takenori Atsumi ∗∗ Tsuyoshi Inoue ∗∗∗ ∗∗ ∗∗∗
Shota Yabui ∗ Takenori Atsumi ∗∗ Tsuyoshi Inoue ∗∗∗ Shota Yabui ∗ Takenori Atsumi ∗∗ Tsuyoshi Inoue ∗∗∗ Shota Yabui Takenori Atsumi Tsuyoshi (e-mail: Inoue ∗ University, ∗ Nagoya University, Nagoya, Nagoya, 464-8603, 464-8603, Japan Japan (e-mail: ∗ Nagoya e-mail:[email protected]). Nagoya University, Nagoya, 464-8603, Japan (e-mail: ∗∗ ∗ Nagoya e-mail:[email protected]). University, Nagoya, 464-8603, Japan (e-mail: of e-mail:[email protected]). ∗∗ Chiba Institute of Technology, Technology, Narashino, Narashino, 275-0016 275-0016 Japan Japan ∗∗ Chiba Institute e-mail:[email protected]). (e-mail:[email protected]). Chiba Institute of Technology, Narashino, 275-0016 Japan (e-mail:[email protected]). ∗∗∗∗∗ Chiba Institute of Technology, Narashino, 275-0016 Japan University, Nagoya, 464-8603, Japan (e-mail: (e-mail:[email protected]). ∗∗∗ Nagoya University, Nagoya, 464-8603, Japan (e-mail: ∗∗∗ Nagoya (e-mail:[email protected]). Nagoyae-mail:[email protected]). University, Nagoya, 464-8603, Japan (e-mail: ∗∗∗ Nagoyae-mail:[email protected]). University, Nagoya, 464-8603, Japan (e-mail: e-mail:[email protected]). e-mail:[email protected]). Abstract: Abstract: In In this this research, research, we we have have proposed proposed aa stroke-oriented stroke-oriented controller controller design design for for head head Abstract: In this research, we have proposed a stroke-oriented controller design foraa voice head positioning control system of hard disk drives (HDDs). A dual-stage actuator composed of positioning control system of hard disk drives (HDDs). A dual-stage actuator composed of voice Abstract: In this research, weisdisk have proposed athestroke-oriented controller design fora voice head coil motor and a piezo actuator widely used in head positioning system. The decoupling positioning control system of hard drives (HDDs). A dual-stage actuator composed of coil motor and a piezo actuator isdisk widely used in the A head positioning system. The decoupling positioning control system of hard drives (HDDs). dual-stage actuator composed of a voice filter design which decouples the interaction of each the actuator is a representative controller coil motor and a piezo actuator is widely used in the head positioning system. The decoupling filter designand which decouples theisinteraction of in each the actuator is a representative controller coil a piezo actuator widely used the head positioning system. The decoupling design for the dual-stage actuator. However, is necessary for the loop related to filtermotor design which decouples the interaction ofit each the actuator is a feedback representative controller design for the dual-stage actuator. However, it is necessary for the feedback loop related to filter design which decouples the interaction oflow each the actuator isdue a feedback representative controller design for the dual-stage actuator. However, it is necessary for the loop related to the piezo actuator to increase the gain in the frequency range to design constraints. It the piezo actuator to increase the gain in the low frequency range duefeedback to designloop constraints. It design for the dual-stage actuator. However, it is necessary for the related to can lead to increase a required stroke of the piezo actuator. The proposed controller design can the piezo actuator to increase the gain in the low frequency range due to design constraints. It can lead to increasetoa increase requiredthe stroke ofinthe piezo actuator. The proposed controller design can the piezo actuator gain the low frequency range due to design constraints. It decrease the required stroke of the piezo actuator by utilizing the interaction of each the actuator. can lead to increase a required stroke of the piezo actuator. The proposed controller design can decrease the requiredastroke of the piezoofactuator byactuator. utilizing The the interaction of each thedesign actuator. can lead to increase required stroke the piezo proposed controller can To confirm effectiveness the proposed controller design aa simulation was decrease thethe required stroke of the piezo actuator by utilizing the interaction of each theperformed actuator. To confirm effectiveness the proposed controller design method, method, simulation was decrease thethe required stroke vibrations. of the piezoAs actuator by utilizing the interaction ofthe each theperformed actuator. To compensate confirm the effectiveness the proposed controller design method, a simulation was performed to for external the results, it was confirmed that required stroke to compensate for external vibrations. As the results, it was confirmed that the required stroke To confirm the effectiveness the proposed controller design method, a simulation was performed of the piezo actuator can be reduced by about 65%, while the stability and positioning accuracy to compensate for external vibrations. As the results, it was confirmed that the required stroke of the piezo actuator can be reduced by about 65%, while the stability and positioning accuracy to the compensate for external vibrations. As the results, itaswas confirmed thatpositioning the required stroke of head positioning control system is almost same the that of decoupling filter design. piezo actuator can be reduced by about 65%, while stability and accuracy of the piezo head positioning control system isabout almost same as the that of decoupling filter design. of the actuator can be reduced by 65%, while the stability and positioning accuracy of the head positioning control system is almost same as the that of decoupling filter design. © the 2019,head IFACpositioning (International Federation of Automatic by of Elsevier Ltd. Allfilter rightsdesign. reserved. of control system is almost Control) same asHosting the that decoupling Keywords: Keywords: Hard Hard disk disk drives, drives, Positioning Positioning control, control, Stroke-oriented Stroke-oriented design, design, Dual-stage Dual-stage actuator. actuator. Keywords: Hard disk drives, Positioning control, Stroke-oriented design, Dual-stage actuator. Keywords: Hard disk drives, Positioning control, Stroke-oriented design, Dual-stage actuator. 1. decouple 1. INTRODUCTION INTRODUCTION decouple the the interaction interaction in in the the control control system. system. It It can can be be a a 1. INTRODUCTION decouple the interaction in the control system. Itinfluences can be a constraint in control system design. One of the constraint in control system design. One of the influences 1. INTRODUCTION decouple the inthe the control system. canpiezo be a in interaction control system design. One of the of the constraint constraint is that that required stroke ofItinfluences the The key key technology technology of of the the high high information information society society is is InIn- constraint of the is the design. required stroke of the piezo constraint in control system One of the influences The the constraint is that the required stroke of the piezo actuator can increase. increase. The key technology the high information societyto In- of ternet of (IoT) (2017). It actuator can ternet of things things (IoT)ofBettiol Bettiol (2017). It is is necessary necessary toisconconof the constraint is that the required stroke of the piezo can increase. The key technology the high information society In- actuator ternet of things (IoT)ofBettiol (2017). It is necessary toisconstruct an environment that can exchange a large amount In this research, research, we have have proposed proposed the the stroke-oriented stroke-oriented actuator can increase. struct anthings environment that can exchange a large amount In this we ternet of (IoT) Bettiol (2017). It is necessary to construct an data environment that can Many exchange a large amount In of digital digital on the the Internet. Internet. Internet companies this research, we the have proposed theof stroke-oriented controller design for control system the dual-stage dual-stage of data on Many Internet companies design for control system the struct an data environment that can exchange a large amount controller of digital on the Internet companies In this research, we the have proposed theof build data servers to Internet. store theMany digital data SPECTRA controller design for the control system of stroke-oriented the in dual-stage actuator. The decouple filter is not employed the build data servers to store the digital data SPECTRA actuator. The decouple filter is not employed in the proproof digital data on the Many Internet companies build data servers to Internet. store the digital data SPECTRA controller design for thefilter control system of control the in dual-stage (2017). The main industrial products in the data server actuator. The decouple is not employed the proposed method. Although the design of the system (2017). The main industrial products in the data server posed method. Although the design of the control system build data servers to store the digital data SPECTRA (2017). industrial dataa server actuator. The decouple filter is not employed the proare hard hardThe diskmain drives (HDDs)products capable in of the storing large posed method. Although the design of theofcontrol system becomes complicated, the design freedom theincontroller controller are disk drives (HDDs) capable of storing a server large becomes complicated, the design freedom ofcontrol the (2017). main industrial products in the data are hardThe disk drives (HDDs) capable of storing a large posed method. Although the design of the system amount of digital data Yamato (2016). In the progress of becomes complicated, the design freedom of the controller design is is increased. increased. The The design design freedom freedom is is utilized utilized to to amount ofdisk digital data(HDDs) Yamatocapable (2016). of In storing the progress of design are hard drives aoflarge amount digital data Yamato In capacity the progress of design becomesiscomplicated, the design freedom ofactuator. theutilized controller IoT, theofdemand demand for the the large (2016). recording the increased. The design freedom is to decrease the required stroke of the piezo The IoT, the for large recording capacity of the decrease the required stroke of the piezo actuator. The amount ofdemand digital data Yamato (2016). In by the progress of design is increased. The design freedom is utilized to IoT, the for the recording HDD in data is increasing year the required stroke of the piezo time domain domain simulation was performed performed to actuator. verify the theThe efHDD in the the data server server is large increasing year capacity by year. year. of the decrease simulation was to verify efIoT, the demand for theis large recording HDD in the data server increasing year capacity by year. of the time decrease theof required stroke of the piezo actuator. The time domain simulation was performed to verify the effectiveness the proposed controller design method. In To increase the recording capacity of ofyear the by HDD, the popo- fectiveness of simulation the proposed controller design method. In HDD in the the datarecording server is increasing year.the timesimulations, domain wassystem performed to verify the efTo increase capacity the HDD, fectiveness of thethe proposed controller design method. In the control was operated to comTo increase the recording capacity of the HDD, the positioning accuracy of the head positioning control system the simulations, the control system wasdesign operated to comsitioning accuracy of the head positioning control system fectiveness theexternal proposed controller method. In simulations, the control system was operated to compensate for ofthe the vibration which is measured measured in To increase the recording capacity of theamount HDD, the po- the sitioning accuracy of head positioning control system must be improved improved forthe writing the large large of data pensate for external vibration which is in the simulations, the control system was operated to commust be for writing the amount of data pensate for the external vibration which is measured in an environment assuming the data server. As the results, sitioning accuracy of the head positioning control system must improved for writing the currently large amount of data on the thebe disk Yamaguchi (2012). The The required po- an environment the data server. Asmeasured the results, pensate the assuming external vibration which is in on disk Yamaguchi (2012). required poenvironment assuming therequired data server. Asofthe we have for confirmed that the the stroke theresults, piezo must improved fornanometer-order. writing The the currently large amount of data on thebe disk Yamaguchi (2012). currently required po- an sitioning accuracy is The HDD realizes we have confirmed that required stroke of the piezo an environment assuming the data server. As the results, sitioning accuracy is nanometer-order. The HDD realizes we have confirmed that the required stroke of the piezo actuator can be decreased by about 65% with comparison on the disk Yamaguchi (2012). The currently required po- actuator can be decreased by about 65% with comparison sitioning accuracy is nanometer-order. The HDD realizes high precision positioning control actuator high precision positioning control by by a a dual-stage dual-stage actuator we the havedecouple confirmed that the required stroke the can be decreased by abouteven 65% withofcomparison to controller design, though the piezo posisitioning accuracy is nanometer-order. The HDD realizes high precision positioning control by a adual-stage actuator using a voice coil motor (VCM) and piezo actuator in actuator to the decouple controller design, even though the posiactuator can be decreased by about 65% with comparison using a voice coil motor (VCM) and a piezo actuator in to the decouple controller design, even though the positioning accuracy and stability were almost equivalent in high precision positioning control by a dual-stage actuator using a voice coil motor (VCM) and Decouple a piezo actuator in tioning accuracy and stability were almost equivalent in the head head positioning control system. controller to thecontroller decouple controller design, even though the posithe positioning control system. Decouple controller tioning accuracy and stability were almost equivalent in both design. using a voice coil motor (VCM) and a piezo actuator in the head positioning control system. Decouple controller design which which decouples decouples the the interaction interaction of of each each actuator actuator is is both controller tioning accuracydesign. and stability were almost equivalent in design the head positioning control system. controller design which decouples the interaction of each actuator is both controller design. representative controller design methodDecouple Kobayashi (2004); both controller design. representative controller design method Kobayashi (2004); design which decouples the interaction of each actuator is 2. DUAL-STAGE DUAL-STAGE ACTUATOR ACTUATOR IN IN THE THE HEAD HEAD representative controller designIn method Kobayashi (2004);a Ito (2018); (2018); Bashash Bashash (2018). this design design method, 2. Ito (2018). In this method, a representative controller design method Kobayashi (2004); 2. DUAL-STAGE ACTUATOR IN THE HEAD POSITIONING CONTROL SYSTEM OF HDDS Ito (2018); Bashash (2018). In this design method, a feedback loop for each actuator can be dealt with as POSITIONING CONTROL SYSTEM OF HDDS feedback loop for each actuator can design be dealt with asa 2. DUAL-STAGE ACTUATOR IN THE Ito independent (2018); Bashash (2018). InTherefore, this method, POSITIONING CONTROL SYSTEM OFHEAD HDDS feedback loop for each actuator can be dealt with as an control system. the controller an independent control the controller SYSTEMdata OF HDDS feedback for each system. actuatorTherefore, can dealt withIt as an independent control system. Therefore, the controller ThePOSITIONING magnetic head head CONTROL for reading/writing reading/writing on aa disk disk design andloop performance evaluation are be manageable. is The magnetic for data on design and performance evaluation are manageable. It is an independent control system. Therefore, the controller magnetic head for reading/writing data on a disk design and performance evaluation are manageable. It is The is driven by the dual-stage actuator using the VCM and adopted for the controller design of the dual-stage actuis driven by thehead dual-stage actuator usingdata the VCM and adopted forperformance the controller design ofare themanageable. dual-stage actuThe magnetic for overview reading/writing on a disk designin and evaluation It is is driven by the dual-stage actuator using thepositioning VCM and adopted for themanufacturers controller design of the dual-stage actuthe piezo actuator. The of the head ator major HGST (2017). However, it piezo by actuator. The overview of the head ator in major manufacturers HGST (2017). However, it the is driven theisdual-stage actuator using thepositioning VCM and adopted for the controllerfilter, design of the dual-stage actupiezo actuator. The overview of the head positioning ator in major However, it the control system shown in Fig.1. Fig.1. The positioning control is necessary to employ called a filter control system is shown in The positioning control is necessary to manufacturers employ a a filter,HGST called (2017). a decouple decouple filter to to the piezo actuator. The overview of the head positioning ator in major manufacturers HGST (2017). However, it control is necessary to employ a filter, called a decouple filter to control system is shown in Fig.1. The positioning system shown in Fig.1. The positioning control is2405-8963 necessary to employ a filter, called a decouple filter to control © 2019, IFAC (International Federation of Automatic Control) Hosting by ElsevierisLtd. All rights reserved.
Copyright © 2019 IFAC 1445 Copyright © under 2019 IFAC 1445Control. Peer review responsibility of International Federation of Automatic Copyright © 2019 IFAC 1445 10.1016/j.ifacol.2019.11.737 Copyright © 2019 IFAC 1445
2019 IFAC MECHATRONICS 574 Vienna, Austria, Sept. 4-6, 2019
Disk
Shota Yabui et al. / IFAC PapersOnLine 52-15 (2019) 573–578
Table 2. Parameters of P pzt(s)
Spindle motor Magnetic head
i 1 2 3 4 5 6 7 8 9
Piezo actuator Position sensor
A/D converter
Power amplifier
D/A converter
VCM
Servo Controller for VCM and piezo actuator
Fig. 1. Schematic of an HDD head positioning control system Table 1. Parameters of P vcm i 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
ωvcm−i [rad/s] 0 5300 × 2π 6100 × 2π 6500 × 2π 8050 × 2π 9600 × 2π 14800 × 2π 17400 × 2π 21000 × 2π 26000 × 2π 26600 × 2π 29000 × 2π 32200 × 2π 38300 × 2π 43300 × 2π 44800 × 2π
αvcm−i 1.00 -1.00 0.10 -0.10 0.04 -0.70 -0.20 -1.00 3.00 -3.20 2.10 -1.50 2.00 -0.20 0.30 -0.50
ζvcm−i 0 0.02 0.04 0.02 0.01 0.03 0.01 0.02 0.02 0.012 0.007 0.01 0.03 0.01 0.01 0.01
7 ∑
αvcm−i (1) 2 s2 + 2ζvcm−i ωvcm−i + ωvcm−i
7 ∑
αpzt−i 2 s2 + 2ζpzt−i ωpzt−i + ωpzt−i
i=1
PP ZT (s) = κpzt
i=1
αpzt−i 0.007 0.012 0.015 0.01 0.10 0.20 0,40 1.50 1.30
ζpzt−i 0.02 0.02 0.025 0.007 0.01 0.01 0.009 0.007 0.04
the data server. The external vibration is measured by the experimental system assuming the data server as shown in Fig.3. The amplitude spectrum of the vibration is shown in Fig.4. 3. DECOUPLE CONTROLLER DESIGN FOR HEAD POSITIONING SYSTEM
system is composed of the VCM, the piezo actuator, magnetic heads, disks, and a spindle motor. The position signal on the disks is read by the magnetic head, and the position signal are input to the digital signal processor (DSP) which the control algorithm is written. The control systems for the VCM and the piezo actuator are designed based on frequency transfer functions of the actuators. PV CM (s) is a plant which a transfer function from the current to the magnetic head position. PP ZT (s) is a plant which a transfer function from the voltage to the magnetic head position. Here, s is the Laplace operator. PV CM (s) and PP ZT (s) are expressed as following equations (1), equation (2) defined as the previous study Atsumi (2018). PV CM (s) = κvcm
ωpzt−i [rad/s] 6560 × 2π 8050 × 2π 9200 × 2π 12900 × 2π 15500 × 2π 17200 × 2π 18050 × 2π 27100 × 2π 39500 × 2π
(2)
The parameters of these equations are shown in Table 1 anf Table 2. The frequency responses of the transfer functions PV CM (s) and PP ZT (s) are shown in Fig.2. From Fig.2, it can be seen that there are the peaks due to mechanical resonances larger than 5 kHz. The control system must compensate for the mechanical resonance to stable the control system. Furthermore, it must also compensate for the forced excitation caused by the external vibration. In this study, we focus on the external vibrations caused by server fans or an adjacent HDD in the HDD stored in
The decouple controller design is the representative design method in the head positioning control system of the dual-stage actuator. The block diagram of the decouple controller design is shown in Fig.5. Where, r(k) is reference signal，e(k) is position error signal，yV CM (t)is displacement of the VCM，yP ZT (t) is displacement of the piezo actuator, and d(t) is the external vibration. Ts is sampling time, k is sample number which is count number in the control system，and t is continuous time. z is 1-sample delay operator. H is a zero-order hold (ZOH), and K is a sampler. A sampling time of H and S are 11.575 us. CV CM (z) is a feedback controller which is a transfer function from e(k) to control signal for the VCM. CP ZT (z) is a feedback controller which is a transfer function from e(k) to control signal for the piezo actuator. z −1 is the one sample delay operator. D(z) is a decouple filter which decouples the interaction of the VCM and piezo actuator in the control system. The input of D(z) is the output of CP ZT (z), and the output of D(z) is add to the input of CV CM (z). The positioning accuracy of the control system is usually evaluated by using a sensitivity function. The sensitivity function of the decouple controller design is expressed as following equation. Sdecouple (z) = 1 (3) 1 + LP ZT (z) + LV CM (z)(1 + D(z)CP ZT (z)) PV CM (z) and PP ZT (z) are transfer functions PV CM (s) and PP ZT (s) discretized by the sampling time Ts for the calculation of the sensitivity function. LV CM (z) = PV CM (z)CV CM (z) is open loop related to the VCM. LP ZT (z) = PP ZT (z)CP ZT (z) is open loop related to the piezo actuator. In the decouple controller design, the decouple filter is designed to match the characteristics of the piezo actuator, that is, D(z) = PP ZT (z). Then, the characteristics of the control system can be decoupled between LV CM (z) and LP ZT (z). The sensitivity function is rewritten as following equation. 1
1
(4) 1 + LV CM (z) 1 + LP ZT (z) The sensitivity function SV CM (z) of the feedback loop related to the VCM and the sensitivity function SP ZT (z)
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Sdecouple (z) =
2019 IFAC MECHATRONICS Vienna, Austria, Sept. 4-6, 2019
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Gain [dB]
Gain [dB]
-50 -100 -150 103
104
40 20 0 -20 -40
103
103
104
Frequency [Hz] Phase [deg]
Phase [deg]
Frequency [Hz] 180 90 0 -90 -180
575
104
180 90 0 -90 -180
103
Frequency [Hz]
104
Frequency [Hz]
(a) Transfer characteristics of PV CM (s)
(b) Transfer characteristics of PP ZT (s)
Fig. 2. Frequency responses of plant
Fig. 5. Block diagram of the decouple controller design in head positioning system of HDD
Gain [dB]
Fig. 3. Experimental system for measuring the external vibrations
CVCM
D
CPZT
103
-200
104
Frequency [Hz] 180
Phase [deg]
Amplitude spectrum [dB]
-150
40 20 0 -20 -40 -60 -80
-250 Experimental data After averaging process of the experimental data
-300
90 0 -90 -180 103
104
Frequency [Hz]
103
104
Fig. 6. Frequency responses of controller in the decouple controller design
Frequency [Hz]
Fig. 4. Experimental results of external vibrations in the experimental system of the feedback loop related to the piezo actuator. The sensitivity functions SV CM (z) and SP ZT (z) are expressed as SV CM (z) = 1+LV 1CM (z) , SP ZT (z) = 1+LP1ZT (z) . Equation.(4) can be rewritten as following equation. Sdecouple (z) = SV CM (z)SP ZT (z)
(5)
The sensitivity function Sdecouple (z) is equivalent to the product of the sensitivity functions SV CM (z) and SP ZT (z). The feedback loop related to the VCM and the piezo actuator are independent. Therefore, the con-
trol system of the dual-stage actuator is equivalent to a form in which two feedback loops are connected in series. The controllers CV CM (z) and CP ZT (z) can be designed independently. The controllers CV CM (z) and CP ZT (z) were designed as the previous study Atsumi (2018). The frequency responses of the controllers CV CM (z)，D(z) and CP ZT (z) are shown in Fig,6. The frequency responses of the open loops LV CM (z), LV CM (z) and the whole open loop Ldecouple = LV CM (z)LV CM (z) are shown in Fig.7 and the vector loci of the open loops are shown in Fig.8. The frequency responses of the sensitivity functions SV CM (z), SP ZT (z) and Sdecouple (z) are shown in Fig.9.
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Gain [dB]
20 0 -20 -40 -60
LVCM LPZT Ldecouple
10
3
10
4
Frequency [Hz] Phase [deg]
180 90 0
Fig. 10. Block diagram of proposed design in head positioning system of HDD
-90 -180 10
3
10
4
Frequency [Hz]
Fig. 7. Frequency responses of the open loop in the decouple controller design
The control system can be designed as single-input-singleoutput system. The controller design and the performance evaluation are manageable. On the other hand, the control system must employ the decouple filter D(z) = PP ZT (z), and the both feedback loop must be stabilized. These can be constraint for the controller design.
4
4. STROKE ORIENTED CONTROLLER DESIGN FOR HEAD POSITIONING SYSTEM
3
Imag part
2
In this paper, we propose a controller design method to reduce the required stroke of the piezo actuator. The block diagram of the control system is shown in Fig.10. The control system is designed to be mutually interfere with each feedback loop without using the decouple filter. The sensitivity function of the control system is expressed as following equation.
1 0 -1 LVCM
-2
L
-3 -4 -4
PZT
Ldecouple
-2
0
2
4
Spropose (z) =
Real part
Fig. 8. Nyquist diagram of the open loop in the decouple controller design
20
Gain [dB]
10 0 -10 -20 S VCM S PZT
-30
S decouple
-40
103
104
Frequency [Hz]
Fig. 9. Frequency responses of sensitivity function in the decouple controller design
1 1 + LV CM (z) + LP ZT (z)
(6)
The denominator of equation (6) indicates that the terms related to the VCM and the piezo actuator are interfered in the characteristics of the sensitivity function. The controller design and the performance evaluation can be more complicated than the decouple controller design. On the other hand, the control system does not need to employ the decouple filter D(z). Furthermore, as long as the stability of the whole control system is ensured, it is not necessary to ensure stability for each feedback loop. The design freedom of the proposed controller design is higher than the decouple controller design. The controllers were designed to decrease the required stroke of the piezo actuator by taking advantage of the design freedom. The frequency responses of the controllers CV CM (z) and CP ZT (z) are shown in Fig.11. The frequency responses of the open loops LV CM (z), LP ZT (z) and the whole feedback loop Lpropose (z) = LV CM (z) + LV CM (z) are shown in Fig.12. The vector loci of the open loops are shown in Fig.13. The zero-crossing frequency of the open loop LV CM (z) is about 5.5kHz as shown in Fig.12. The zero-crossing frequency is more than three times for that of the decouple filter design. The zero-crossing frequency of the open loop LV CM (z) is increased greatly, the feedback loop related to the VCM is unstable as shown in Fig.13. However, the whole feedback loop can be stabilized by the feedback loop related to the piezo actuator. Actually, the vector locus of the Lpropose (z) is stable as shown in Fig.13. In this design, the VCM mainly drives to compensate for the external vibrations in the low frequency and the piezo
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4
20 0
3
-20 -40
CVCM
-60
CPZT
2
Imag part
Gain [dB]
577
-80 3
4
10
10
Frequency [Hz]
1 0 -1
Phase [deg]
180
LVCM
-2
90
L
-3
0
-4 -4
-90 -180 3
10
Frequency [Hz]
Fig. 11. Frequency responses of controller in the proposed controller design
0
2
4
Fig. 13. Nyquist diagram of the open loop in the proposed controller design 20
20 0 -20 -40 -60
LVCM LPZT
Gain [dB]
Gain [dB]
-2
Real part
4
10
PZT
Lpropose
Lpropose
103
104
Frequency [Hz]
0
-20
Phase [deg]
180
-40
90
S proposed S decouple
0
-60
-90
103
-180 10
3
10
104
Frequency [Hz]
4
Frequency [Hz]
Fig. 14. Frequency responses of Spropose and Sdecouple
In the decouple controller design, the feedback loop related to the VCM and the feedback loop related to the piezo actuator must be stable. The gain of CV CM (z) can’t be increased in the low frequency range, because it leads to decrease the stability margin. As a result, the gain of CP ZT (z) must be increased to decrease the gain of the sensitivity function Sdecouple (z) in the low frequency range. It leads to increase the required stroke of the piezo actuator. Therefore, there is trade-off between the design freedom and the manageable design: the feedback loop can be handled independently as shown in equation 5.
20
Gain [dB]
actuator mainly drives to stabilize the whole feedback loop in the high frequency.
0 -20 -40
Ldecouple Lpropose
-60 3
4
10
10
Frequency [Hz] 180
Phase [deg]
Fig. 12. Frequency responses of the open loop in the proposed controller design
90 0 -90 3
4
10
10
Frequency [Hz]
Fig. 15. Frequency responses of Lpropose and Ldecouple The frequency responses of the sensitivity function Spropose (z) is shown in Fig.14. For comparison, the sensitivity function peaks in the frequency responses of P P ZT (s) as shown in Sdecouple (z) is also shown in Fig.14. Although the open Fig.2. Therefore, the negative impact for the robustness loop characteristics of LV CM (z) and LP ZT (z) are different isn’t much greater in the proposed controller design. between the decouple filter design and the proposed controller design, the shape of the frequency response of the 5. PERFORMANCE COMPARISON IN REAL-TIME sensitivity functions Spropose is almost same as that of the SIMULATION decouple filter design Sdecouple . The frequency responses of these open loop are shown in Fig.15. In the frequency responses, the gain of Lcouple is larger than that of Ldecouple The performance comparison between the proposed condesign around 10kHz. The robustness in the proposed con- troller design and the decouple controller designs is shown trol design is lower than that of the decoupling controller in this section. First, the gain margin, the phase margin design around 10kHz. The gain characteristic is dominant and the maximum gain of the sensitivity function are from LP ZT in Lcouple as shown in Fig.12. There is no large shown in Table.3. 1449
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Table 3. Stability of the control system
-180 S
Phase margin 57.3 deg 50.9 deg
Max gain of S 5.7dB 5.0dB
Amplitude spectrum [dB]
Decouple Proposed
Gain margin 7.7dB 9.1dB
-180
Amplitude spectrum [dB]
S proposed S decouple
-200
-220
-220
-240
103
104
Frequency [Hz]
Fig. 17. Amplitude spectrum of the displacement of the piezo actuator yP ZT (t) 103
104
Frequency [Hz]
Fig. 16. Amplitude spectrum of the position error signal e(k) Table 4. Comparison: e(k) and uP ZT (k) Decouple Proposed
-200
-260
-240
-260
proposed
S decouple
sigma of e(k) 2.68nm 2.67nm
performed to verify the effectiveness. As the results, the required stroke of piezo actuator commonly used in the dual-stage actuator was decreased by about 65%. The stability of the control system and the positioning accuracy are almost same level of the decouple controller design which is representative controller design method in the head positioning system of HDD.
sigma of uP ZT (k) 4.42nm 1.53nm
ACKNOWLEDGEMENTS
The both controller design satisfy the stability criterion Mamun (2017): Gain margin ≥ 6dB, Phase margin ≥40deg. The max gain of the sensitivity function is same value in both the design methods. The phase margin of the proposed controller design is less than that of the decouple controller design. The phase margins are calculated at zero-cross frequency of Ldecouple and Lpropose which is about 3kHz. There are no mechanical resonances in both plant PV CM (s) and PP ZT (s) at the frequency. Therefore, decreasing of the phase margin doesn’t impact for the stability of the control system. Real-time simulation using MATLAB/Simulink which compensated for the external vibration as shown in Fig.4 was demonstrated to evaluate these performances. The amplitude spectrum of the position error sigma e(k) is shown in Fig.16 and the displacement of the piezo actuator yP ZT (t) is shown in Fig.17. The positioning accuracy for the both design method is almost same as shown in Fig.16. On the other hand, the displacement of the piezo actuator yP ZT (t) is decreased by the proposed controller design in the low frequency (less than 1.5kHz). The sigma of the position error signal e(k) and the displacement of the yP ZT (t) is shown in Table.4. From Table.4, the sigma of the position error signal e(k) is almost same value, and the sigma of the displacement of the yP ZT (t) is decreased by about 65%. It means that the required stroke of the piezo actuator is about 35% compared with the decouple controller design. 6. CONCLUSION In this paper, we have proposed the stroke oriented controller design in the head positioning control system of HDD using the dual-stage actuator. The time domain simulation assuming the data server environment was
This work was supported by JSPS KAKENHI Grant Number JP18K13714. REFERENCES Atusmi T. Two-degree-of-freedom control scheme for flying-height and tracking-position controls with thermal actuators in HDDs. Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.12, No.1, 15pages, 2018. Bashash, S. and Shariat S. Performance enhancement of hard disk drives through data-driven control design and population clustering. Precision Engineering, Available online 17 December 2018 Bettiol M., Capestro M. and Di Maria (2017). Industry 4.0: the strategic role of marketing. , URL: www.economia.unipd.it/sites/economia.unipd.it/files/ 20170213.pdf HGST (2017). TECH BRIEF: HGST Micro Actuator. TB02-HGST-Mico-Actuator-EN-US-0917-0, URL: https://www.westerndigital.com/. Ito J and Atsumi T. Controller Design Method for Dual-StageActuator System of HDDs by using RBode Plot. Proceedings of the 4th IEEJ International Workshop on Sensing, Actuation, Motion Control, and Optimization, TT6–3, 2018. Kobayashi M., Nakagawa S. and Numasato H. Adaptive Control of Dual-Stage Actuator for Hard Disk Drives. Proceeding of the 2004 American Control Conference, pp. 523-528, 2004. Mamun A A., Guo G. and Bi C. Hard Disk Drive: Mechatronics and Control. CRC Press, 2017. Mamun A A., Guo G. and Bi C. Digital Data Storage Outlook 2017. , URL: https://spectralogic.com/wp-content/uploads/whitepaper-digital-data-storage-outlook-2017-v3.pdf. Yamaguchi T., Hirata M. and Pang C.K. High-speed precision motion control. CRC Press, 2012. Yamato Y. Cloud Storage Application Area of HDD-SSD Hybrid Storage, Distributed Storage, and HDD Storage. IEEJ TRANSACTIONS on Electrical and Electronic Engineering, Vol. 11, pp. 674-675, 2016.
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Stroke Oriented Controller Design for Stroke Oriented Controller Design for Stroke Oriented Controller Design for Dual-stage Actuator of Head Positioning Stroke Oriented Controller Design for Dual-stage Actuator of Head Positioning Dual-stage Actuator of Head Positioning Control System in Hard Disk Drives Dual-stage Actuator of Head Positioning Control Control System System in in Hard Hard Disk Disk Drives Drives Control System in Hard Disk Drives Shota Yabui ∗∗ Takenori Atsumi ∗∗ Tsuyoshi Inoue ∗∗∗ ∗∗ ∗∗∗
Shota Yabui ∗ Takenori Atsumi ∗∗ Tsuyoshi Inoue ∗∗∗ Shota Yabui ∗ Takenori Atsumi ∗∗ Tsuyoshi Inoue ∗∗∗ Shota Yabui Takenori Atsumi Tsuyoshi (e-mail: Inoue ∗ University, ∗ Nagoya University, Nagoya, Nagoya, 464-8603, 464-8603, Japan Japan (e-mail: ∗ Nagoya e-mail:[email protected]). Nagoya University, Nagoya, 464-8603, Japan (e-mail: ∗∗ ∗ Nagoya e-mail:[email protected]). University, Nagoya, 464-8603, Japan (e-mail: of e-mail:[email protected]). ∗∗ Chiba Institute of Technology, Technology, Narashino, Narashino, 275-0016 275-0016 Japan Japan ∗∗ Chiba Institute e-mail:[email protected]). (e-mail:[email protected]). Chiba Institute of Technology, Narashino, 275-0016 Japan (e-mail:[email protected]). ∗∗∗∗∗ Chiba Institute of Technology, Narashino, 275-0016 Japan University, Nagoya, 464-8603, Japan (e-mail: (e-mail:[email protected]). ∗∗∗ Nagoya University, Nagoya, 464-8603, Japan (e-mail: ∗∗∗ Nagoya (e-mail:[email protected]). Nagoyae-mail:[email protected]). University, Nagoya, 464-8603, Japan (e-mail: ∗∗∗ Nagoyae-mail:[email protected]). University, Nagoya, 464-8603, Japan (e-mail: e-mail:[email protected]). e-mail:[email protected]). Abstract: Abstract: In In this this research, research, we we have have proposed proposed aa stroke-oriented stroke-oriented controller controller design design for for head head Abstract: In this research, we have proposed a stroke-oriented controller design foraa voice head positioning control system of hard disk drives (HDDs). A dual-stage actuator composed of positioning control system of hard disk drives (HDDs). A dual-stage actuator composed of voice Abstract: In this research, weisdisk have proposed athestroke-oriented controller design fora voice head coil motor and a piezo actuator widely used in head positioning system. The decoupling positioning control system of hard drives (HDDs). A dual-stage actuator composed of coil motor and a piezo actuator isdisk widely used in the A head positioning system. The decoupling positioning control system of hard drives (HDDs). dual-stage actuator composed of a voice filter design which decouples the interaction of each the actuator is a representative controller coil motor and a piezo actuator is widely used in the head positioning system. The decoupling filter designand which decouples theisinteraction of in each the actuator is a representative controller coil a piezo actuator widely used the head positioning system. The decoupling design for the dual-stage actuator. However, is necessary for the loop related to filtermotor design which decouples the interaction ofit each the actuator is a feedback representative controller design for the dual-stage actuator. However, it is necessary for the feedback loop related to filter design which decouples the interaction oflow each the actuator isdue a feedback representative controller design for the dual-stage actuator. However, it is necessary for the loop related to the piezo actuator to increase the gain in the frequency range to design constraints. It the piezo actuator to increase the gain in the low frequency range duefeedback to designloop constraints. It design for the dual-stage actuator. However, it is necessary for the related to can lead to increase a required stroke of the piezo actuator. The proposed controller design can the piezo actuator to increase the gain in the low frequency range due to design constraints. It can lead to increasetoa increase requiredthe stroke ofinthe piezo actuator. The proposed controller design can the piezo actuator gain the low frequency range due to design constraints. It decrease the required stroke of the piezo actuator by utilizing the interaction of each the actuator. can lead to increase a required stroke of the piezo actuator. The proposed controller design can decrease the requiredastroke of the piezoofactuator byactuator. utilizing The the interaction of each thedesign actuator. can lead to increase required stroke the piezo proposed controller can To confirm effectiveness the proposed controller design aa simulation was decrease thethe required stroke of the piezo actuator by utilizing the interaction of each theperformed actuator. To confirm effectiveness the proposed controller design method, method, simulation was decrease thethe required stroke vibrations. of the piezoAs actuator by utilizing the interaction ofthe each theperformed actuator. To compensate confirm the effectiveness the proposed controller design method, a simulation was performed to for external the results, it was confirmed that required stroke to compensate for external vibrations. As the results, it was confirmed that the required stroke To confirm the effectiveness the proposed controller design method, a simulation was performed of the piezo actuator can be reduced by about 65%, while the stability and positioning accuracy to compensate for external vibrations. As the results, it was confirmed that the required stroke of the piezo actuator can be reduced by about 65%, while the stability and positioning accuracy to the compensate for external vibrations. As the results, itaswas confirmed thatpositioning the required stroke of head positioning control system is almost same the that of decoupling filter design. piezo actuator can be reduced by about 65%, while stability and accuracy of the piezo head positioning control system isabout almost same as the that of decoupling filter design. of the actuator can be reduced by 65%, while the stability and positioning accuracy of the head positioning control system is almost same as the that of decoupling filter design. © the 2019,head IFACpositioning (International Federation of Automatic by of Elsevier Ltd. Allfilter rightsdesign. reserved. of control system is almost Control) same asHosting the that decoupling Keywords: Keywords: Hard Hard disk disk drives, drives, Positioning Positioning control, control, Stroke-oriented Stroke-oriented design, design, Dual-stage Dual-stage actuator. actuator. Keywords: Hard disk drives, Positioning control, Stroke-oriented design, Dual-stage actuator. Keywords: Hard disk drives, Positioning control, Stroke-oriented design, Dual-stage actuator. 1. decouple 1. INTRODUCTION INTRODUCTION decouple the the interaction interaction in in the the control control system. system. It It can can be be a a 1. INTRODUCTION decouple the interaction in the control system. Itinfluences can be a constraint in control system design. One of the constraint in control system design. One of the influences 1. INTRODUCTION decouple the inthe the control system. canpiezo be a in interaction control system design. One of the of the constraint constraint is that that required stroke ofItinfluences the The key key technology technology of of the the high high information information society society is is InIn- constraint of the is the design. required stroke of the piezo constraint in control system One of the influences The the constraint is that the required stroke of the piezo actuator can increase. increase. The key technology the high information societyto In- of ternet of (IoT) (2017). It actuator can ternet of things things (IoT)ofBettiol Bettiol (2017). It is is necessary necessary toisconconof the constraint is that the required stroke of the piezo can increase. The key technology the high information society In- actuator ternet of things (IoT)ofBettiol (2017). It is necessary toisconstruct an environment that can exchange a large amount In this research, research, we have have proposed proposed the the stroke-oriented stroke-oriented actuator can increase. struct anthings environment that can exchange a large amount In this we ternet of (IoT) Bettiol (2017). It is necessary to construct an data environment that can Many exchange a large amount In of digital digital on the the Internet. Internet. Internet companies this research, we the have proposed theof stroke-oriented controller design for control system the dual-stage dual-stage of data on Many Internet companies design for control system the struct an data environment that can exchange a large amount controller of digital on the Internet companies In this research, we the have proposed theof build data servers to Internet. store theMany digital data SPECTRA controller design for the control system of stroke-oriented the in dual-stage actuator. The decouple filter is not employed the build data servers to store the digital data SPECTRA actuator. The decouple filter is not employed in the proproof digital data on the Many Internet companies build data servers to Internet. store the digital data SPECTRA controller design for thefilter control system of control the in dual-stage (2017). The main industrial products in the data server actuator. The decouple is not employed the proposed method. Although the design of the system (2017). The main industrial products in the data server posed method. Although the design of the control system build data servers to store the digital data SPECTRA (2017). industrial dataa server actuator. The decouple filter is not employed the proare hard hardThe diskmain drives (HDDs)products capable in of the storing large posed method. Although the design of theofcontrol system becomes complicated, the design freedom theincontroller controller are disk drives (HDDs) capable of storing a server large becomes complicated, the design freedom ofcontrol the (2017). main industrial products in the data are hardThe disk drives (HDDs) capable of storing a large posed method. Although the design of the system amount of digital data Yamato (2016). In the progress of becomes complicated, the design freedom of the controller design is is increased. increased. The The design design freedom freedom is is utilized utilized to to amount ofdisk digital data(HDDs) Yamatocapable (2016). of In storing the progress of design are hard drives aoflarge amount digital data Yamato In capacity the progress of design becomesiscomplicated, the design freedom ofactuator. theutilized controller IoT, theofdemand demand for the the large (2016). recording the increased. The design freedom is to decrease the required stroke of the piezo The IoT, the for large recording capacity of the decrease the required stroke of the piezo actuator. The amount ofdemand digital data Yamato (2016). In by the progress of design is increased. The design freedom is utilized to IoT, the for the recording HDD in data is increasing year the required stroke of the piezo time domain domain simulation was performed performed to actuator. verify the theThe efHDD in the the data server server is large increasing year capacity by year. year. of the decrease simulation was to verify efIoT, the demand for theis large recording HDD in the data server increasing year capacity by year. of the time decrease theof required stroke of the piezo actuator. The time domain simulation was performed to verify the effectiveness the proposed controller design method. In To increase the recording capacity of ofyear the by HDD, the popo- fectiveness of simulation the proposed controller design method. In HDD in the the datarecording server is increasing year.the timesimulations, domain wassystem performed to verify the efTo increase capacity the HDD, fectiveness of thethe proposed controller design method. In the control was operated to comTo increase the recording capacity of the HDD, the positioning accuracy of the head positioning control system the simulations, the control system wasdesign operated to comsitioning accuracy of the head positioning control system fectiveness theexternal proposed controller method. In simulations, the control system was operated to compensate for ofthe the vibration which is measured measured in To increase the recording capacity of theamount HDD, the po- the sitioning accuracy of head positioning control system must be improved improved forthe writing the large large of data pensate for external vibration which is in the simulations, the control system was operated to commust be for writing the amount of data pensate for the external vibration which is measured in an environment assuming the data server. As the results, sitioning accuracy of the head positioning control system must improved for writing the currently large amount of data on the thebe disk Yamaguchi (2012). The The required po- an environment the data server. Asmeasured the results, pensate the assuming external vibration which is in on disk Yamaguchi (2012). required poenvironment assuming therequired data server. Asofthe we have for confirmed that the the stroke theresults, piezo must improved fornanometer-order. writing The the currently large amount of data on thebe disk Yamaguchi (2012). currently required po- an sitioning accuracy is The HDD realizes we have confirmed that required stroke of the piezo an environment assuming the data server. As the results, sitioning accuracy is nanometer-order. The HDD realizes we have confirmed that the required stroke of the piezo actuator can be decreased by about 65% with comparison on the disk Yamaguchi (2012). The currently required po- actuator can be decreased by about 65% with comparison sitioning accuracy is nanometer-order. The HDD realizes high precision positioning control actuator high precision positioning control by by a a dual-stage dual-stage actuator we the havedecouple confirmed that the required stroke the can be decreased by abouteven 65% withofcomparison to controller design, though the piezo posisitioning accuracy is nanometer-order. The HDD realizes high precision positioning control by a adual-stage actuator using a voice coil motor (VCM) and piezo actuator in actuator to the decouple controller design, even though the posiactuator can be decreased by about 65% with comparison using a voice coil motor (VCM) and a piezo actuator in to the decouple controller design, even though the positioning accuracy and stability were almost equivalent in high precision positioning control by a dual-stage actuator using a voice coil motor (VCM) and Decouple a piezo actuator in tioning accuracy and stability were almost equivalent in the head head positioning control system. controller to thecontroller decouple controller design, even though the posithe positioning control system. Decouple controller tioning accuracy and stability were almost equivalent in both design. using a voice coil motor (VCM) and a piezo actuator in the head positioning control system. Decouple controller design which which decouples decouples the the interaction interaction of of each each actuator actuator is is both controller tioning accuracydesign. and stability were almost equivalent in design the head positioning control system. controller design which decouples the interaction of each actuator is both controller design. representative controller design methodDecouple Kobayashi (2004); both controller design. representative controller design method Kobayashi (2004); design which decouples the interaction of each actuator is 2. DUAL-STAGE DUAL-STAGE ACTUATOR ACTUATOR IN IN THE THE HEAD HEAD representative controller designIn method Kobayashi (2004);a Ito (2018); (2018); Bashash Bashash (2018). this design design method, 2. Ito (2018). In this method, a representative controller design method Kobayashi (2004); 2. DUAL-STAGE ACTUATOR IN THE HEAD POSITIONING CONTROL SYSTEM OF HDDS Ito (2018); Bashash (2018). In this design method, a feedback loop for each actuator can be dealt with as POSITIONING CONTROL SYSTEM OF HDDS feedback loop for each actuator can design be dealt with asa 2. DUAL-STAGE ACTUATOR IN THE Ito independent (2018); Bashash (2018). InTherefore, this method, POSITIONING CONTROL SYSTEM OFHEAD HDDS feedback loop for each actuator can be dealt with as an control system. the controller an independent control the controller SYSTEMdata OF HDDS feedback for each system. actuatorTherefore, can dealt withIt as an independent control system. Therefore, the controller ThePOSITIONING magnetic head head CONTROL for reading/writing reading/writing on aa disk disk design andloop performance evaluation are be manageable. is The magnetic for data on design and performance evaluation are manageable. It is an independent control system. Therefore, the controller magnetic head for reading/writing data on a disk design and performance evaluation are manageable. It is The is driven by the dual-stage actuator using the VCM and adopted for the controller design of the dual-stage actuis driven by thehead dual-stage actuator usingdata the VCM and adopted forperformance the controller design ofare themanageable. dual-stage actuThe magnetic for overview reading/writing on a disk designin and evaluation It is is driven by the dual-stage actuator using thepositioning VCM and adopted for themanufacturers controller design of the dual-stage actuthe piezo actuator. The of the head ator major HGST (2017). However, it piezo by actuator. The overview of the head ator in major manufacturers HGST (2017). However, it the is driven theisdual-stage actuator using thepositioning VCM and adopted for the controllerfilter, design of the dual-stage actupiezo actuator. The overview of the head positioning ator in major However, it the control system shown in Fig.1. Fig.1. The positioning control is necessary to employ called a filter control system is shown in The positioning control is necessary to manufacturers employ a a filter,HGST called (2017). a decouple decouple filter to to the piezo actuator. The overview of the head positioning ator in major manufacturers HGST (2017). However, it control is necessary to employ a filter, called a decouple filter to control system is shown in Fig.1. The positioning system shown in Fig.1. The positioning control is2405-8963 necessary to employ a filter, called a decouple filter to control © 2019, IFAC (International Federation of Automatic Control) Hosting by ElsevierisLtd. All rights reserved.
Copyright © 2019 IFAC 1445 Copyright © under 2019 IFAC 1445Control. Peer review responsibility of International Federation of Automatic Copyright © 2019 IFAC 1445 10.1016/j.ifacol.2019.11.737 Copyright © 2019 IFAC 1445
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Table 2. Parameters of P pzt(s)
Spindle motor Magnetic head
i 1 2 3 4 5 6 7 8 9
Piezo actuator Position sensor
A/D converter
Power amplifier
D/A converter
VCM
Servo Controller for VCM and piezo actuator
Fig. 1. Schematic of an HDD head positioning control system Table 1. Parameters of P vcm i 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
ωvcm−i [rad/s] 0 5300 × 2π 6100 × 2π 6500 × 2π 8050 × 2π 9600 × 2π 14800 × 2π 17400 × 2π 21000 × 2π 26000 × 2π 26600 × 2π 29000 × 2π 32200 × 2π 38300 × 2π 43300 × 2π 44800 × 2π
αvcm−i 1.00 -1.00 0.10 -0.10 0.04 -0.70 -0.20 -1.00 3.00 -3.20 2.10 -1.50 2.00 -0.20 0.30 -0.50
ζvcm−i 0 0.02 0.04 0.02 0.01 0.03 0.01 0.02 0.02 0.012 0.007 0.01 0.03 0.01 0.01 0.01
7 ∑
αvcm−i (1) 2 s2 + 2ζvcm−i ωvcm−i + ωvcm−i
7 ∑
αpzt−i 2 s2 + 2ζpzt−i ωpzt−i + ωpzt−i
i=1
PP ZT (s) = κpzt
i=1
αpzt−i 0.007 0.012 0.015 0.01 0.10 0.20 0,40 1.50 1.30
ζpzt−i 0.02 0.02 0.025 0.007 0.01 0.01 0.009 0.007 0.04
the data server. The external vibration is measured by the experimental system assuming the data server as shown in Fig.3. The amplitude spectrum of the vibration is shown in Fig.4. 3. DECOUPLE CONTROLLER DESIGN FOR HEAD POSITIONING SYSTEM
system is composed of the VCM, the piezo actuator, magnetic heads, disks, and a spindle motor. The position signal on the disks is read by the magnetic head, and the position signal are input to the digital signal processor (DSP) which the control algorithm is written. The control systems for the VCM and the piezo actuator are designed based on frequency transfer functions of the actuators. PV CM (s) is a plant which a transfer function from the current to the magnetic head position. PP ZT (s) is a plant which a transfer function from the voltage to the magnetic head position. Here, s is the Laplace operator. PV CM (s) and PP ZT (s) are expressed as following equations (1), equation (2) defined as the previous study Atsumi (2018). PV CM (s) = κvcm
ωpzt−i [rad/s] 6560 × 2π 8050 × 2π 9200 × 2π 12900 × 2π 15500 × 2π 17200 × 2π 18050 × 2π 27100 × 2π 39500 × 2π
(2)
The parameters of these equations are shown in Table 1 anf Table 2. The frequency responses of the transfer functions PV CM (s) and PP ZT (s) are shown in Fig.2. From Fig.2, it can be seen that there are the peaks due to mechanical resonances larger than 5 kHz. The control system must compensate for the mechanical resonance to stable the control system. Furthermore, it must also compensate for the forced excitation caused by the external vibration. In this study, we focus on the external vibrations caused by server fans or an adjacent HDD in the HDD stored in
The decouple controller design is the representative design method in the head positioning control system of the dual-stage actuator. The block diagram of the decouple controller design is shown in Fig.5. Where, r(k) is reference signal，e(k) is position error signal，yV CM (t)is displacement of the VCM，yP ZT (t) is displacement of the piezo actuator, and d(t) is the external vibration. Ts is sampling time, k is sample number which is count number in the control system，and t is continuous time. z is 1-sample delay operator. H is a zero-order hold (ZOH), and K is a sampler. A sampling time of H and S are 11.575 us. CV CM (z) is a feedback controller which is a transfer function from e(k) to control signal for the VCM. CP ZT (z) is a feedback controller which is a transfer function from e(k) to control signal for the piezo actuator. z −1 is the one sample delay operator. D(z) is a decouple filter which decouples the interaction of the VCM and piezo actuator in the control system. The input of D(z) is the output of CP ZT (z), and the output of D(z) is add to the input of CV CM (z). The positioning accuracy of the control system is usually evaluated by using a sensitivity function. The sensitivity function of the decouple controller design is expressed as following equation. Sdecouple (z) = 1 (3) 1 + LP ZT (z) + LV CM (z)(1 + D(z)CP ZT (z)) PV CM (z) and PP ZT (z) are transfer functions PV CM (s) and PP ZT (s) discretized by the sampling time Ts for the calculation of the sensitivity function. LV CM (z) = PV CM (z)CV CM (z) is open loop related to the VCM. LP ZT (z) = PP ZT (z)CP ZT (z) is open loop related to the piezo actuator. In the decouple controller design, the decouple filter is designed to match the characteristics of the piezo actuator, that is, D(z) = PP ZT (z). Then, the characteristics of the control system can be decoupled between LV CM (z) and LP ZT (z). The sensitivity function is rewritten as following equation. 1
1
(4) 1 + LV CM (z) 1 + LP ZT (z) The sensitivity function SV CM (z) of the feedback loop related to the VCM and the sensitivity function SP ZT (z)
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Sdecouple (z) =
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Gain [dB]
Gain [dB]
-50 -100 -150 103
104
40 20 0 -20 -40
103
103
104
Frequency [Hz] Phase [deg]
Phase [deg]
Frequency [Hz] 180 90 0 -90 -180
575
104
180 90 0 -90 -180
103
Frequency [Hz]
104
Frequency [Hz]
(a) Transfer characteristics of PV CM (s)
(b) Transfer characteristics of PP ZT (s)
Fig. 2. Frequency responses of plant
Fig. 5. Block diagram of the decouple controller design in head positioning system of HDD
Gain [dB]
Fig. 3. Experimental system for measuring the external vibrations
CVCM
D
CPZT
103
-200
104
Frequency [Hz] 180
Phase [deg]
Amplitude spectrum [dB]
-150
40 20 0 -20 -40 -60 -80
-250 Experimental data After averaging process of the experimental data
-300
90 0 -90 -180 103
104
Frequency [Hz]
103
104
Fig. 6. Frequency responses of controller in the decouple controller design
Frequency [Hz]
Fig. 4. Experimental results of external vibrations in the experimental system of the feedback loop related to the piezo actuator. The sensitivity functions SV CM (z) and SP ZT (z) are expressed as SV CM (z) = 1+LV 1CM (z) , SP ZT (z) = 1+LP1ZT (z) . Equation.(4) can be rewritten as following equation. Sdecouple (z) = SV CM (z)SP ZT (z)
(5)
The sensitivity function Sdecouple (z) is equivalent to the product of the sensitivity functions SV CM (z) and SP ZT (z). The feedback loop related to the VCM and the piezo actuator are independent. Therefore, the con-
trol system of the dual-stage actuator is equivalent to a form in which two feedback loops are connected in series. The controllers CV CM (z) and CP ZT (z) can be designed independently. The controllers CV CM (z) and CP ZT (z) were designed as the previous study Atsumi (2018). The frequency responses of the controllers CV CM (z)，D(z) and CP ZT (z) are shown in Fig,6. The frequency responses of the open loops LV CM (z), LV CM (z) and the whole open loop Ldecouple = LV CM (z)LV CM (z) are shown in Fig.7 and the vector loci of the open loops are shown in Fig.8. The frequency responses of the sensitivity functions SV CM (z), SP ZT (z) and Sdecouple (z) are shown in Fig.9.
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Gain [dB]
20 0 -20 -40 -60
LVCM LPZT Ldecouple
10
3
10
4
Frequency [Hz] Phase [deg]
180 90 0
Fig. 10. Block diagram of proposed design in head positioning system of HDD
-90 -180 10
3
10
4
Frequency [Hz]
Fig. 7. Frequency responses of the open loop in the decouple controller design
The control system can be designed as single-input-singleoutput system. The controller design and the performance evaluation are manageable. On the other hand, the control system must employ the decouple filter D(z) = PP ZT (z), and the both feedback loop must be stabilized. These can be constraint for the controller design.
4
4. STROKE ORIENTED CONTROLLER DESIGN FOR HEAD POSITIONING SYSTEM
3
Imag part
2
In this paper, we propose a controller design method to reduce the required stroke of the piezo actuator. The block diagram of the control system is shown in Fig.10. The control system is designed to be mutually interfere with each feedback loop without using the decouple filter. The sensitivity function of the control system is expressed as following equation.
1 0 -1 LVCM
-2
L
-3 -4 -4
PZT
Ldecouple
-2
0
2
4
Spropose (z) =
Real part
Fig. 8. Nyquist diagram of the open loop in the decouple controller design
20
Gain [dB]
10 0 -10 -20 S VCM S PZT
-30
S decouple
-40
103
104
Frequency [Hz]
Fig. 9. Frequency responses of sensitivity function in the decouple controller design
1 1 + LV CM (z) + LP ZT (z)
(6)
The denominator of equation (6) indicates that the terms related to the VCM and the piezo actuator are interfered in the characteristics of the sensitivity function. The controller design and the performance evaluation can be more complicated than the decouple controller design. On the other hand, the control system does not need to employ the decouple filter D(z). Furthermore, as long as the stability of the whole control system is ensured, it is not necessary to ensure stability for each feedback loop. The design freedom of the proposed controller design is higher than the decouple controller design. The controllers were designed to decrease the required stroke of the piezo actuator by taking advantage of the design freedom. The frequency responses of the controllers CV CM (z) and CP ZT (z) are shown in Fig.11. The frequency responses of the open loops LV CM (z), LP ZT (z) and the whole feedback loop Lpropose (z) = LV CM (z) + LV CM (z) are shown in Fig.12. The vector loci of the open loops are shown in Fig.13. The zero-crossing frequency of the open loop LV CM (z) is about 5.5kHz as shown in Fig.12. The zero-crossing frequency is more than three times for that of the decouple filter design. The zero-crossing frequency of the open loop LV CM (z) is increased greatly, the feedback loop related to the VCM is unstable as shown in Fig.13. However, the whole feedback loop can be stabilized by the feedback loop related to the piezo actuator. Actually, the vector locus of the Lpropose (z) is stable as shown in Fig.13. In this design, the VCM mainly drives to compensate for the external vibrations in the low frequency and the piezo
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4
20 0
3
-20 -40
CVCM
-60
CPZT
2
Imag part
Gain [dB]
577
-80 3
4
10
10
Frequency [Hz]
1 0 -1
Phase [deg]
180
LVCM
-2
90
L
-3
0
-4 -4
-90 -180 3
10
Frequency [Hz]
Fig. 11. Frequency responses of controller in the proposed controller design
0
2
4
Fig. 13. Nyquist diagram of the open loop in the proposed controller design 20
20 0 -20 -40 -60
LVCM LPZT
Gain [dB]
Gain [dB]
-2
Real part
4
10
PZT
Lpropose
Lpropose
103
104
Frequency [Hz]
0
-20
Phase [deg]
180
-40
90
S proposed S decouple
0
-60
-90
103
-180 10
3
10
104
Frequency [Hz]
4
Frequency [Hz]
Fig. 14. Frequency responses of Spropose and Sdecouple
In the decouple controller design, the feedback loop related to the VCM and the feedback loop related to the piezo actuator must be stable. The gain of CV CM (z) can’t be increased in the low frequency range, because it leads to decrease the stability margin. As a result, the gain of CP ZT (z) must be increased to decrease the gain of the sensitivity function Sdecouple (z) in the low frequency range. It leads to increase the required stroke of the piezo actuator. Therefore, there is trade-off between the design freedom and the manageable design: the feedback loop can be handled independently as shown in equation 5.
20
Gain [dB]
actuator mainly drives to stabilize the whole feedback loop in the high frequency.
0 -20 -40
Ldecouple Lpropose
-60 3
4
10
10
Frequency [Hz] 180
Phase [deg]
Fig. 12. Frequency responses of the open loop in the proposed controller design
90 0 -90 3
4
10
10
Frequency [Hz]
Fig. 15. Frequency responses of Lpropose and Ldecouple The frequency responses of the sensitivity function Spropose (z) is shown in Fig.14. For comparison, the sensitivity function peaks in the frequency responses of P P ZT (s) as shown in Sdecouple (z) is also shown in Fig.14. Although the open Fig.2. Therefore, the negative impact for the robustness loop characteristics of LV CM (z) and LP ZT (z) are different isn’t much greater in the proposed controller design. between the decouple filter design and the proposed controller design, the shape of the frequency response of the 5. PERFORMANCE COMPARISON IN REAL-TIME sensitivity functions Spropose is almost same as that of the SIMULATION decouple filter design Sdecouple . The frequency responses of these open loop are shown in Fig.15. In the frequency responses, the gain of Lcouple is larger than that of Ldecouple The performance comparison between the proposed condesign around 10kHz. The robustness in the proposed con- troller design and the decouple controller designs is shown trol design is lower than that of the decoupling controller in this section. First, the gain margin, the phase margin design around 10kHz. The gain characteristic is dominant and the maximum gain of the sensitivity function are from LP ZT in Lcouple as shown in Fig.12. There is no large shown in Table.3. 1449
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Table 3. Stability of the control system
-180 S
Phase margin 57.3 deg 50.9 deg
Max gain of S 5.7dB 5.0dB
Amplitude spectrum [dB]
Decouple Proposed
Gain margin 7.7dB 9.1dB
-180
Amplitude spectrum [dB]
S proposed S decouple
-200
-220
-220
-240
103
104
Frequency [Hz]
Fig. 17. Amplitude spectrum of the displacement of the piezo actuator yP ZT (t) 103
104
Frequency [Hz]
Fig. 16. Amplitude spectrum of the position error signal e(k) Table 4. Comparison: e(k) and uP ZT (k) Decouple Proposed
-200
-260
-240
-260
proposed
S decouple
sigma of e(k) 2.68nm 2.67nm
performed to verify the effectiveness. As the results, the required stroke of piezo actuator commonly used in the dual-stage actuator was decreased by about 65%. The stability of the control system and the positioning accuracy are almost same level of the decouple controller design which is representative controller design method in the head positioning system of HDD.
sigma of uP ZT (k) 4.42nm 1.53nm
ACKNOWLEDGEMENTS
The both controller design satisfy the stability criterion Mamun (2017): Gain margin ≥ 6dB, Phase margin ≥40deg. The max gain of the sensitivity function is same value in both the design methods. The phase margin of the proposed controller design is less than that of the decouple controller design. The phase margins are calculated at zero-cross frequency of Ldecouple and Lpropose which is about 3kHz. There are no mechanical resonances in both plant PV CM (s) and PP ZT (s) at the frequency. Therefore, decreasing of the phase margin doesn’t impact for the stability of the control system. Real-time simulation using MATLAB/Simulink which compensated for the external vibration as shown in Fig.4 was demonstrated to evaluate these performances. The amplitude spectrum of the position error sigma e(k) is shown in Fig.16 and the displacement of the piezo actuator yP ZT (t) is shown in Fig.17. The positioning accuracy for the both design method is almost same as shown in Fig.16. On the other hand, the displacement of the piezo actuator yP ZT (t) is decreased by the proposed controller design in the low frequency (less than 1.5kHz). The sigma of the position error signal e(k) and the displacement of the yP ZT (t) is shown in Table.4. From Table.4, the sigma of the position error signal e(k) is almost same value, and the sigma of the displacement of the yP ZT (t) is decreased by about 65%. It means that the required stroke of the piezo actuator is about 35% compared with the decouple controller design. 6. CONCLUSION In this paper, we have proposed the stroke oriented controller design in the head positioning control system of HDD using the dual-stage actuator. The time domain simulation assuming the data server environment was
This work was supported by JSPS KAKENHI Grant Number JP18K13714. REFERENCES Atusmi T. Two-degree-of-freedom control scheme for flying-height and tracking-position controls with thermal actuators in HDDs. Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.12, No.1, 15pages, 2018. Bashash, S. and Shariat S. Performance enhancement of hard disk drives through data-driven control design and population clustering. Precision Engineering, Available online 17 December 2018 Bettiol M., Capestro M. and Di Maria (2017). Industry 4.0: the strategic role of marketing. , URL: www.economia.unipd.it/sites/economia.unipd.it/files/ 20170213.pdf HGST (2017). TECH BRIEF: HGST Micro Actuator. TB02-HGST-Mico-Actuator-EN-US-0917-0, URL: https://www.westerndigital.com/. Ito J and Atsumi T. Controller Design Method for Dual-StageActuator System of HDDs by using RBode Plot. Proceedings of the 4th IEEJ International Workshop on Sensing, Actuation, Motion Control, and Optimization, TT6–3, 2018. Kobayashi M., Nakagawa S. and Numasato H. Adaptive Control of Dual-Stage Actuator for Hard Disk Drives. Proceeding of the 2004 American Control Conference, pp. 523-528, 2004. Mamun A A., Guo G. and Bi C. Hard Disk Drive: Mechatronics and Control. CRC Press, 2017. Mamun A A., Guo G. and Bi C. Digital Data Storage Outlook 2017. , URL: https://spectralogic.com/wp-content/uploads/whitepaper-digital-data-storage-outlook-2017-v3.pdf. Yamaguchi T., Hirata M. and Pang C.K. High-speed precision motion control. CRC Press, 2012. Yamato Y. Cloud Storage Application Area of HDD-SSD Hybrid Storage, Distributed Storage, and HDD Storage. IEEJ TRANSACTIONS on Electrical and Electronic Engineering, Vol. 11, pp. 674-675, 2016.
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