Ver. 1.0.8

Benchmark problem for magnetic-head
positioning control in HDD
User manual without MATLAB ver. (Windows PC)
Investigating R&D Committee on “Precision Servo Technology for High Value-Added Mechatronic System”
The Institute of Electrical Engineers of Japan1

Magnetic-head positioning control system in the benchmark problem••••

The control system has two actuators: VCM and PZT actuator.
The control variable is the magnetic-head position.
The PZT actuator has a stroke limitation (In this benchmark: 50 nm).
We focus on the track-following control.
Disk
Magnetic headVCM

PZT actuator（Micro-actuator）

2

The mechanical characteristics of the actuators and the example controllers aregiven in the following paper.
T. Atsumi and S. Yabui, “Quadruple-Stage Actuator System for Magnetic-Head Positioning System in HDDs,”
The IEEE Transactions on Industrial Electronics, Vol. 67, No. 11, pp. 9184-9194, (2020-11)

Frequency response of VCM

Frequency response of PZT actuator

3

Block diagram of magnetic-head positioning control system
Pcv : VCM in continuous-time system, Pcp : PZT actuator in continuous-time system

Cdv : Feedback controller for VCM, Cdp : Feedback controller for PZT actuator
Fmv : Multi-rate filter for VCM, Fmp : Multi-rate filter for PZT actuator
Ip : Interpolator, Hm : Multi-rate zero-order hold, S : Sampler

dp : Fan-induced vibration, df : Rotational vibration (RV), dRRO : Repeatable Run-Out (RRO)
yc : Head position in continuous time, yd : Head position in discrete time, ycp : Displacement of PZT actuator

Cdpr =0 +e−dRRO − +Cdv

Ip
Ip

Fmp
Fmv

Hmdf+HmydPcp+

Pcv

ycp
dp++++yc

S

The control system is MISO sampled-data control system with multi-rate filters.

4

Disturbances in the benchmark problem•dRRO：RRO（Repeatable Run-Out)
Oscillation of target tracks written on the disk. Note that it is regarded as noise.

•df：RV（Rotational vibration）
External vibration caused by other HDDs in a storage box.

•dp：Fan-induced vibration
External vibration caused by cooling fans in a storage box.
Cdp

r =0 +e−dRRO − +Cdv

Ip
Ip

Fmp
FmvHmdf+Hm

yd

Pcp+PcvS

ycp

dp++++

yc5

• Control system in the benchmark problem• How to use the benchmark problem• Example6• Control system in the benchmark problem• How to use the benchmark problem• Example

7Model of the controlled object⚫

Parameters of the nominal controlled object are shown in the following paper.
T. Atsumi and S. Yabui, “Quadruple-Stage Actuator System for Magnetic-Head Positioning System in HDDs,”
The IEEE Transactions on Industrial Electronics, Vol. 67, No. 11, pp. 9184-9194, (2020-11)

⚫
⚫
⚫
⚫

⚫

Sampling time: 1/(7200/60)/420 ≈ 1.9841 × 10−6 (7200rpm, 420 sector)
Number of multi rate: 2
Track pitch：482 kTPI (52.7 nm)
Controlled object has variations• Temperature dependencies of mechanical resonant frequencies➢ LT(Low temp.)：VCM: +4 % from nominal model, PZT actuator: +6 % from nominal model➢ RT(Room temp.)：Same as nominal models➢ HT(High temp.)： VCM: −4% from nominal model, PZT actuator: −6% from nominal model• Temperature dependencies of damping ratios➢ LT(Low temp.)：VCM: -20 % from nominal model, PZT actuator: -20 % from nominal model➢ RT(Room temp.)：Same as nominal models➢ HT(High temp.)： VCM: +20% from nominal model, PZT actuator: +20% from nominal mode
• PZT actuator’s gain
➢ ±5%
The number of cases for controlled objects: 9Case No.

123456789Temp.

LTRTHTLTRTHTLTRTHTPZT gain

NominalNominalNominalNominal +5%

Nominal +5%

Nominal +5%

Nominal −5%

Nominal −5%

Nominal −5%8Frequency responses of the controlled object for all casesCdp

r =0 +e−dRRO − +Cdv

Ip

Ip

Fmp
Fmv

Hmdf+

HmydPcp+Pcv

ycp

dp++++ycS
9

Disturbances in the benchmark problem• RV: Reproduced by the disturbance shown in the following paper
T. Atsumi and S. Yabui, “Quadruple-Stage Actuator System for Magnetic-Head Positioning System in HDDs,” TheIEEE Transactions on Industrial Electronics, Vol. 67, No. 11, pp. 9184-9194, (2020-11)• Fan-induced vibration: : Reproduced by the disturbance shown in the following paper
T. Eguchi, Y. Asai, K. Ichikawa, and M. Takada: ``Airborne and Structure-Borne Transmission of High Frequency FanVibration in a Storage Box'', Proceedings of the ASME 2017 Conference on Information Storage and Processing
Systems, Paper No. 5406 (2017)• RRO: Time-domain signal which has same amplitude for all frequencies except 0 Hz.
RV

Fan-induced vibe.

RRO

10

• Control system in the benchmark problem• How to use the benchmark problem• Example

11

Setting
Step 1. Download and install the Windows version of the MATLAB Runtime for R2022afrom the following link on the MathWorks website:
https://www.mathworks.com/products/compiler/mcr/index.html
Step 2. Download the EXE files from the following website:
http://www2.iee.or.jp/~dmec/committee/DMEC1005/dsa_HDD_bench_e.html

Step 3. Unzip the “HDDBenchmarkProblem.zip”.

12UsageStep 1. Define the state-space matrixes of your designed controllers as follows.
➢ Cdv : A_Cd_vcm.txt, B_Cd_vcm.txt, C_Cd_vcm.txt, D_Cd_vcm.txt➢ Cdp : A_Cd_pzt.txt, B_Cd_pzt.txt, C_Cd_pzt.txt, D_Cd_pzt.txt➢ Fmv : A_Fm_vcm.txt, B_Fm_vcm.txt, C_Fm_vcm.txt, D_Fm_vcm.txt➢ Fmp : A_Fm_pzt.txt, B_Fm_pzt.txt, C_Fm_pzt.txt, D_Fm_pzt.txt

Step 2. Execute “Simulation_trackfollow” which shows simulation results of the control system.
Step 3. Execute “Plot_control_system” which shows frequency responses of the control system.

As an example, the unzipped folder includes controllers in the following paper (Dual: VCM + Micro.).
T. Atsumi and S. Yabui, “Quadruple-Stage Actuator System for Magnetic-Head Positioning System in HDDs”, The IEEE Transactions on IndustrialElectronics, Vol. 67, No. 11, pp. 9184-9194, (2020-11)

13

Validation of control system➢ We evaluate the worst case of 3𝜎 (three times of STD) value of yc insteady state response for one second.
➢ Maximum value of |ycp| must be smaller than 50 nm.

Cdpr =0 +e−dRRO − +Cdv

Ip
Ip

Fmp
Fmv

Hmdf+

Hmyd

Pcp+

Pcv

ycp
dp++++ycS14

• Control system in the benchmark problem• How to use the benchmark problem• Example

15

Results of “Simulation_trackfollow” with the example controller

Cdp

r =0 +e−dRRO − +Cdv

Figure 3: dRRO

Figure 2: Amplitude spectrum of dp

Figure 1: Amplitude spectrum of df

Ip

Ip

Fmp
Fmv

Hmdf+

Hmyd

Pcp+

Pcv
Sycp

dp++++

yc16

Results of “Simulation_trackfollow” with the example controller (Cont.)
Figure 4: ycp

Cdp

r =0 +e−dRRO − +

Cdv

Ip

Ip

Figure 5: Max of |ycp|

Fmp
Fmv

Hmdf+

Hmyd

Pcp+

Pcv
Sycp

dp++++

yc17

Results of “Simulation_trackfollow” with the example controller (Cont.)
Figure 6: yc

Figure 7: Amplitude spectrum of yc

Cdp

r =0 +e−dRRO − +Cdv

Ip

Ip

Fmp
Fmv

Hmdf+

Hmyd

Figure 8: 3𝜎 values ofPcp+

Pcv
Syc [% of Track width]ycp

dp++++yc18

Results of “Plot_control_system” with the example controller
Figure 9: Pcv

Cdp

r =0 +e−dRRO − +Cdv

Figure 10: Pcp

Ip

Ip

Fmp
Fmv

Hmdf+

HmydPcp+Pcv
Sycp

dp++++yc19

Results of “Plot_control_system” with the example controller (Cont.)
Figure 11: Multi-rate filters

Cdp

r =0 +e−dRRO − +Cdv

Ip

Ip

Fmp
Fmv

Hmdf+

Hmyd

Pcp+PcvSycp

dp++++yc20

Results of “Plot_control_system” with the example controller (Cont.)
Figure 12: Bode plot for udv → yd

Cdp

r =0 +e−dRRO − +

Cdv

udp
udv

Ip

Ip

Fmp
Fmv

Figure 13: Bode plot for udp → yd

Hmdf+

HmydPcp+Pcv
Sycp

dp++++

yc21

Results of “Plot_control_system” with the example controller (Cont.)
Figure 14 : Feedback controller for VCM

Cdp

r+e−dRRO − +Cdv

Ip
Ip

Fmp
Fmv

Figure 15 : Feedback controller for PZT actuator

Hmdf+

Hmyd

Pcp+PcvSycp
dp++++

yc22

Results of “Plot_control_system” with the example controller (Cont.)
Figure 17: Nyquist plot for e → yd

Figure 16: Bode plot for e → yd

Cdp

r =0 +e−dRRO − +Cdv

Ip

Ip

Fmp
FmvHmdf+

Hmyd

Pcp+PcvSycp

dp++++yc23

Results of “Plot_control_system” with the example controller (Cont.)
Figure 18: Gain Bode plot for dp → yd

Cdp

r =0 +e−dRRO − +Cdv

Ip

Ip

Fmp
Fmv

Hmdf+

Hmyd

Pcp+PcvS

ycp

dp++++yc24

END
Benchmark problem for magnetic-head positioning control in HDD
User manual without MATLAB ver. (Windows PC)

Investigating R&D Committee on “Precision Servo Technology for High Value-Added Mechatronic System”
The Institute of Electrical Engineers of Japan