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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