Robust track-following control for dual-stage servo systems in HDDs

Ryozo NagamuneDivision of Optimization & Systems Theory

Royal Institute of Technology, Sweden

Seminar at Department of Mechanical Engineering, University of British Columbia

February 3rd, 2006

(Joint work with R. Horowitz and his students at UC Berkeley)

Outline

• Track following control in HDDs

• Worst-case H2 performance minimization

• Design techniques– Multirate control– Robust control

(Mixed H2/H1, Mixed H2/, Robust H2)

• Examples

• Conclusions

Track following control

www.westerndigital.com

Data track

Read/Write head

Goal: Control the R/W head to follow the data track in a highly accurate manner

Inputs : Voice Coil Motor (VCM)

+ mini/micro-actuator

Measurements : Position Error Signal (PES) + other sensor signals

VCM

Servo sector

Dual-stage & multi-sensing system

Robust control theory

Dual-stage multi-sensing control

Dual-stage multi-sensing system

PESVCM

Micro-actuator

Sensor signals (PZT-sensor etc)

Fixed sampling rate

:

Disturbances (track runout, windage, measurement noise, etc.)

Variations

1. Multivariable control

2. Possibly multirate control

4. Optimal control

3. Robust control

Control features Conventional methods• PQ method• Sensitivity decoupling

Outline

• Track following control in HDDs

• Worst-case H2 performance minimization

• Design techniques– Multirate control– Robust control

(Mixed H2/H1, Mixed H2/, Robust H2)

• Examples

• Conclusions

Dual-stage multi-sens. system

S : Multirate sampler, H : Multirate hold

K

: PES etc. : Disturbances (runout, windage, noise)

Multirate Multivariable

Design K s.t.Measurements Control inputs

RobustnessOptimality

: map from w to z

Controller

Uncertainty

: robustly stabilizing controller set

Parametric uncertainties in

Dynamic uncertainty

Worst-case H2 minimization

Outline

• Track following control in HDDs

• Worst-case H2 performance minimization

• Design techniques– Multirate control– Robust control

(Mixed H2/H1, Mixed H2/, Robust H2)

• Examples

• Conclusions

Control for LTI systems

Outline

• Track following control in HDDs

• Worst-case H2 performance minimization

• Design techniques– Multirate control– Robust control

(Mixed H2/H1, Mixed H2/, Robust H2)

• Examples

• Conclusions

Nominal

K

Dynamic uncertaintyOriginal formulation

Performance : Nominal Stability : Dynamic uncertainty

Advantage : Computationally inexpensive

Disadvantage : Insufficient robustness conditions

We solve a convex optimization problem.

Mixed H2/H1 synthesis(Scherer, Oliveira, etc)

Nominal

K

Dynamic & parametric uncertainties

Original formulation

Performance : Nominal Stability : Dynamic & parametric

Advantage : Guaranteed robust stability

Disadvantage : No robust performance

We combine a mixed H2/H1 technique with D-K iterations.

Mixed H2/ synthesis(Packard, Doyle, Young, etc)

Nominal

K

Parametric uncertaintiesOriginal formulation

Performance : Robust Stability : Parametric uncertainties

Advantage : Robust performanceDisadvantage : Computationally expensive No dynamic uncertainty

We solve a series of convex optimization problems.

Robust H2 synthesis(Kanev, Scherer, Paganini, etc)

Outline

• Track following control in HDDs

• Worst-case H2 performance minimization

• Design techniques– Multirate control– Robust control

(Mixed H2/H1, Mixed H2/, Robust H2)

• Examples

• Conclusions

VCMRelative position error signal

Position Error Signal (PES)

Vibration signal

Slider

Read/write head

Micro-actuator (MA)

Two inputsSampling/hold rates twice faster than that of PES

Noise

NoiseNoise

Airflow Track runout

Three outputs

Example 1: Setting

Example 1 : Block diagram

Gvcm

Gma

Gc

InputOutputDisturbance

Parametric uncertaintyDynamic uncertainty

VCM dynamics

Microactuator dynamics

Runout model

Example 1 : Simulation result

Design method RMS value of PES (nm) degK (befor

e reduction)Nominal Worst

PQ method 7.75 10.00 6

Sensitivity decoupling

7.11 8.35 6

Mixed H2/H1 6.57 7.82 8 (13)

Mixed H2/ 5.31 5.88 8 (13)

Robust H2 5.93 6.47 9 (11)

200 enumerations of parametric variations

Example 2 : Setting(with R. de Callafon at UC San Diego)

Inputs : uV (VCM) uP

ZT (PZT-actuator)

Measurement : yLDV (Head position)

102

103

104

100

105

102

103

104

100

102

104

mag

nitu

de

frequency [Hz]

Frequency responses for 36 dual-stage systems

uV to yLDV

uPZT to yLDV

PZT-actuated suspension

Example2 : Modeling

Suspension modes

E-block

PZT-driver

uV

yLDVuPZT

uV to yLDV uPZT to yLDV

Experiment Experiment

Sampled models Sampled models

102

103

104

100

105

102

103

104

100

102

104

mag

nitu

de

frequency [Hz]

uV to yLDV

uPZT to yLDV

Example 2 : Controller design

Simulation Experiment

Amplitude plots of sensitivity functions (from runout to PES)

Robust H2 synthesis

Single-rate controller

deg K = 13

runout

+-

PESplantK

-uV

uPZT yLDV

Outline

• Track following control in HDDs

• Worst-case H2 performance minimization

• Design techniques– Multirate control– Robust control

(Mixed H2/H1, Mixed H2/, Robust H2)

• Examples

• Conclusions

A multirate multivariable robust optimal track-following control in HDDs

Worst-case H2 minimization problem Design methods via convex optimization

Mixed H2/H1 Mixed H2/ Robust H2

General dual-stage multi-sensing systems

Conclusions

Future research topics

Sampled-data control • Inter-sampling behavior

Performance analysis tool• Degradation of track-following property

Multiple controller / Adaptive controller • Improvement of tracking precision

Probabilistic approach• More accurate uncertainty description

User-friendly software