Download Track following control

Robust track-following
control for dual-stage
servo systems in HDDs
Ryozo Nagamune
Division of Optimization & Systems Theory
Royal Institute of Technology, Sweden
(Joint work with R. Horowitz and his students at UC Berkeley)
Seminar at Department of Mechanical Engineering,
University of British Columbia
February 3rd, 2006
Outline
• Track following control in HDDs
• Worst-case H2 performance minimization
• Design techniques
– Multirate control
– Robust control
(Mixed H2/H1, Mixed H2/m, Robust H2)
• Examples
• Conclusions
Track following control
Goal: Control the R/W head to
follow the data track
in a highly accurate manner
Data track
Servo sector
Inputs : Voice Coil Motor (VCM)
+ mini/micro-actuator
Measurements :
Position Error Signal (PES)
+ other sensor signals
Dual-stage &
multi-sensing system VCM
Read/Write
head
www.westerndigital.com
Dual-stage multi-sensing control
Variations
VCM
Microactuator
Fixed sampling rate
Dual-stage multisensing system
PES
:
Sensor signals
(PZT-sensor etc)
Disturbances (track runout, windage,
measurement noise, etc.)
Control features
1. Multivariable control
2. Possibly multirate control
3. Robust control
4. Optimal control
Conventional methods
• PQ method
• Sensitivity decoupling
Robust control theory
Outline
• Track following control in HDDs
• Worst-case H2 performance minimization
• Design techniques
– Multirate control
– Robust control
(Mixed H2/H1, Mixed H2/m, Robust H2)
• Examples
• Conclusions
Worst-case H2 minimization
Uncertainty
Parametric uncertainties in
Dynamic uncertainty
: PES etc.
Dual-stage
multi-sens.
system
Measurements
: Disturbances
(runout, windage, noise)
Control inputs
Design K s.t.
Controller
K
Optimality
Multirate Multivariable
S : Multirate sampler, H : Multirate hold
Robustness
: map from w to z
: robustly stabilizing controller set
Outline
• Track following control in HDDs
• Worst-case H2 performance minimization
• Design techniques
Control for LTI systems
– Multirate control
– Robust control
(Mixed H2/H1, Mixed H2/m, Robust H2)
• Examples
• Conclusions
Outline
• Track following control in HDDs
• Worst-case H2 performance minimization
• Design techniques
– Multirate control
– Robust control
(Mixed H2/H1, Mixed H2/m, Robust H2)
• Examples
• Conclusions
Mixed H2/H1 synthesis
(Scherer, Oliveira, etc)
Dynamic uncertainty
Original formulation
Performance : Nominal
Stability : Dynamic uncertainty
Nominal
We solve a convex optimization problem.
K
Advantage :
Computationally inexpensive
Disadvantage :
Insufficient robustness conditions
Mixed H2/m synthesis
(Packard, Doyle, Young, etc)
Dynamic & parametric
uncertainties
Original formulation
Performance : Nominal
Stability : Dynamic & parametric
Nominal
K
We combine a mixed H2/H1
technique with D-K iterations.
Advantage :
Guaranteed robust stability
Disadvantage :
No robust performance
Robust H2 synthesis
(Kanev, Scherer, Paganini, etc)
Original formulation
Parametric uncertainties
Performance : Robust
Stability : Parametric uncertainties
Nominal
K
We solve a series of convex
optimization problems.
Advantage :
Robust performance
Disadvantage :
Computationally expensive
No dynamic uncertainty
Outline
• Track following control in HDDs
• Worst-case H2 performance minimization
• Design techniques
– Multirate control
– Robust control
(Mixed H2/H1, Mixed H2/m, Robust H2)
• Examples
• Conclusions
Example 1: Setting
Position Error Signal (PES)
Noise
Read/write
head
Airflow
Track runout
Microactuator
(MA)
Slider
Vibration signal
Noise
Two inputs
Relative position error signal
VCM
Noise
Three outputs
Sampling/hold rates twice
faster than that of PES
Example 1 : Block diagram
Dynamic uncertainty
Parametric uncertainty
VCM dynamics
Gvcm
Gc
Gma
Input
Output
Disturbance
Microactuator
dynamics
Runout model
Example 1 : Simulation result
200 enumerations of parametric variations
Design method
RMS value of PES (nm)
degK
(before
Nominal
reduction)
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/m
5.31
5.88
8 (13)
Robust H2
5.93
6.47
9 (11)
Example 2 : Setting
(with R. de Callafon at UC San Diego)
PZT-actuated suspension
Frequency responses for
36 dual-stage systems
10
Inputs :
uV (VCM)
uPZT (PZT-actuator)
Measurement :
yLDV (Head position)
magnitude
10
5
0
uV to yLDV
10
2
10
3
10
4
4
10
2
uPZT to yLDV
10
0
10
2
10
3
10
frequency [Hz]
4
10
Example2 : Modeling
d1
10
uV
uPZT
10
d3I
magnitude
d2I
E-block
Suspension
modes
PZT-driver
yLDV
5
0
uV to yLDV
10
2
10
3
10
4
4
10
2
10
uPZT to yLDV
0
10
2
10
3
10
frequency [Hz]
Experiment
Sampled models
uV to yLDV
Experiment
Sampled models
uPZT to yLDV
4
10
Example 2 : Controller design
runout
 Robust H2 synthesis
+
 Single-rate controller
 deg K = 13
K
-
uV
uPZT
plant
yLDV
PES
Amplitude plots of sensitivity functions (from runout to PES)
Simulation
Experiment
Outline
• Track following control in HDDs
• Worst-case H2 performance minimization
• Design techniques
– Multirate control
– Robust control
(Mixed H2/H1, Mixed H2/m, Robust H2)
• Examples
• Conclusions
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/m
Robust H2
General dual-stage multi-sensing systems
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