Tài liệu High Speed Precision Motion Control doc

High-Speed
Precision
Motion Control
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
Boca Raton London New York
Edited by
Takashi Yamaguchi
Mitsuo Hirata
Chee Khiang Pang
High-Speed
Precision
Motion Control
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Contents
List of Figures xi
List of Tables xvii
Preface xix
About the Editors xxi
List of Contributors xxiii
Nomenclature xxv
1 Introduction 1
Takashi Yamaguchi
1.1 Concept of High-Speed Precision Motion Control . . . . . . . 1
1.2 HardDiskDrives(HDDs) 4
Bibliography 9

2 System Modeling and Identification 11
Hiroshi Uchida, Takashi Yamaguchi, and Hidehiko Numasato
2.1 HDDServoSystems 11
2.1.1 InsideanHDD 12
2.1.2 Generation of Servo Position Signal . . . . . . . . . . 13
2.2 TMRBudgetDesign 16
2.3 ModelingofHDD 22
2.3.1 Introduction 22
2.3.2 PlantComponents 22
2.3.3 Modeling of Mechanical Dynamics . . . . . . . . . . . 24
2.4 ModelingofDisturbancesandPES 32
2.4.1 DisturbancesandPES 32
2.4.2 Decomposition of Steady-State PES . . . . . . . . . . 34
2.4.2.1 RROandNRRO 34
2.4.2.2 Frequency Spectrum of NRRO . . . . . . . . 36
2.4.2.3 Decomposition of NRRO . . . . . . . . . . . 37
2.4.3 Decomposition of Transient Response . . . . . . . . . 40
Bibliography 46
v
vi
3 Basic Approach to High-Speed Precision Motion Control 49
Atsushi Okuyama, Takashi Yamaguchi, Takeyori Hara, and Mitsuo Hirata
3.1 Introduction to Mode Switching Control (MSC) . . . . . . . 50
3.2 Track-Seeking: Fast Access Servo Control . . . . . . . . . . . 51
3.2.1 Two-Degrees-of-Freedom (TDOF) Control . . . . . . . 51
3.2.1.1 Advantages of TDOF Control . . . . . . . . 51
3.2.1.2 Structure of TDOF Control . . . . . . . . . . 53
3.2.1.3 Zero-Phase Error Tracking Control (ZPETC) 53
3.2.1.4 Reference Trajectory . . . . . . . . . . . . . 55
3.2.2 Access Servo Control Considering Saturation . . . . . 58

3.2.2.1 Basic Structure of Access Servo Control . . . 59
3.2.2.2 Reference Velocity Trajectory . . . . . . . . . 61
3.2.2.3 Proximate Time-Optimal Servomechanism
(PTOS) 62
3.3 Track-Settling: Initial Value Compensation (IVC) . . . . . . 63
3.3.1 ConceptofIVC 63
3.3.1.1 Initialization of Controller State Variable . . 64
3.3.1.2 Design of Mode Switching Condition . . . . . 64
3.3.2 IVCDesignMethod 65
3.3.3 Optimal Design of Mode Switching Condition . . . . . 72
3.4 Track-Following: Single- and Multi-Rate Control . . . . . . . 76
3.4.1 Single-RateControl 76
3.4.1.1 Introduction 76
3.4.1.2 Lead Compensator and PI Controller . . . . 77
3.4.1.3 NotchFilter 82
3.4.1.4 Observer State Feedback Control . . . . . . . 85
3.4.1.5 Pole Placement Technique . . . . . . . . . . 89
3.4.1.6 OptimalControlDesign 93
3.4.2 Multi-RateControl 94
3.4.2.1 Introduction 94
3.4.2.2 Problem Formulation . . . . . . . . . . . . . 95
3.4.2.3 Multi-RateObserver 97
3.5 Episode: Development of IVC Design Method in Industry . . 99
Bibliography 101
4 Ultra-Fast Motion Control 107
Mitsuo Hirata and Hiroshi Fujimoto
4.1 Vibration-MinimizedTrajectoryDesign 107
4.1.1 Introduction 107
4.1.2 Final State Control (FSC) Theory . . . . . . . . . . . 108
4.1.3 Vibration Minimized Trajectory Design Based on Final

StateControl 109
4.1.4 Application to Track-Seeking Control in HDDs . . . . 113
4.2 PerfectTrackingControl(PTC) 120
4.2.1 Introduction 120
vii
4.2.2 PTCTheory 121
4.2.3 Vibration Suppression Using PTC . . . . . . . . . . . 123
4.2.3.1 WithMPVT 123
4.2.3.2 With Parallel Realization . . . . . . . . . . . 124
4.2.3.3 With Modified Controllable Canonical Real-
ization 125
4.2.4 SimulationsandExperiments 126
4.2.4.1 Simulations Using Nominal Model . . . . . . 126
4.2.4.2 ExperimentsonHDDs 130
Bibliography 134
5 Ultra-Precise Position Control 137
Takenori Atsumi, Mituso Hirata, Hiroshi Fujimoto, and Nobutaka Bando
5.1 Phase-Stable Design for High Servo Bandwidth . . . . . . . . 138
5.1.1 ModelingofControlledObject 139
5.1.2 Controller Design Based on Vector Locus . . . . . . . 139
5.1.2.1 Relationship between Vector Locus and
Sensitivity Transfer Function . . . . . . . . . 142
5.1.2.2 Vector Locus of Controlled Object . . . . . . 142
5.1.3 ControllerDesign 145
5.1.3.1 Case 1: Gain-Stable Design for All Mechanical
ResonantModes 145
5.1.3.2 Case 2: Phase-Stable Design for Primary
Mechanical Resonant Mode . . . . . . . . . . 146
5.1.3.3 Case 3: Phase-Stable Design for All Mechani-
calResonantModes 150

5.1.3.4 Comparison of Control Performances . . . . 150
5.2 Robust Control Using H
∞
ControlTheory 155
5.2.1 Introduction 155
5.2.2 Mathematical Representation of Plant Uncertainties . 156
5.2.2.1 Multiplicative Uncertainty . . . . . . . . . . 156
5.2.2.2 AdditiveUncertainty 157
5.2.3 Robust Stability Problem . . . . . . . . . . . . . . . . 157
5.2.4 H
∞
ControlTheory 159
5.2.5 Various H
∞
ControlProblems 161
5.2.5.1 Sensitivity Minimization Problem . . . . . . 161
5.2.5.2 Mixed Sensitivity Problem . . . . . . . . . . 162
5.2.6 Application of H
∞
ControltoHDDs 162
5.3 Multi-Rate H
∞
Control 169
5.3.1 Multi-Rate Discrete-Time H
∞
Control 169
5.3.2 Multi-Rate Sampled-Data H
∞
Control 171
5.4 RepetitiveControl 177

5.4.1 Introduction 177
5.4.2 Repetitive Perfect Tracking Control (RPTC) . . . . . 179
viii
5.4.2.1 Discrete-Time Plant Model with Multi-Rate
Hold 179
5.4.2.2 DesignofPTC 181
5.4.3 DesignofRPTC 182
5.4.4 Applications to RRO Rejection in HDDs . . . . . . . . 184
5.4.5 ExperimentsonRPTC 187
5.5 Acceleration Feedforward Control (AFC) . . . . . . . . . . . 192
5.5.1 Introduction 192
5.5.2 NecessityforAFC 196
5.5.3 TypesofAFC 198
5.5.3.1 Constant-TypeAFC 199
5.5.3.2 Filter-TypeAFC 200
5.5.3.3 Transfer Function-Type AFC . . . . . . . . . 200
5.5.3.4 Adaptive Identification-Type AFC . . . . . . 202
5.5.4 Performance Evaluation for AFC . . . . . . . . . . . . 205
5.5.5 ApplicationsofAFC 205
5.5.5.1 ApplicationtoVehicles 209
5.5.5.2 Application to Industrial Robots . . . . . . . 209
Bibliography 209
6 Control Design for Consumer Electronics 213
Mitsuo Hirata, Shinji Takakura, and Atsushi Okuyama
6.1 Control System Design for Energy Efficiency . . . . . . . . . 213
6.1.1 InterlacingController 214
6.1.2 Short-Track Seeking Using TDOF Control with IVC . 217
6.2 Controller Design for Low Acoustic Noise Seek . . . . . . . . 222
6.2.1 Short-Span Seek Control for Low Acoustic Noise . . . 222
6.2.2 Long-Span Seek Control for Low Acoustic Noise . . . 231

6.3 Servo Control Design Based on SRS Analysis . . . . . . . . . 243
6.3.1 SeekingNoise 243
6.3.2 Concept and Procedure of SRS Analysis . . . . . . . . 243
6.3.3 ModelsforSRSAnalysis 244
6.3.4 ExamplesofSRSAnalyses 246
6.3.5 Acoustic Noise Reduction Based on SRS Analysis . . . 249
Bibliography 256
7 HDD Benchmark Problem 259
Mitsuo Hirata
7.1 Public Release of the HDD Benchmark Problem . . . . . . . 259
7.2 PlantModel 261
7.3 DisturbanceModel 264
7.3.1 ForceDisturbance 265
7.3.2 FlutterDisturbance 265
7.3.3 RRO 267
7.3.4 MeasurementNoise 268
ix
7.4 Overview of the HDD Benchmark Problem Version 3 . . . . 269
7.5 ExampleofControllerDesign 272
7.5.1 Track-Following Control Problem . . . . . . . . . . . . 273
7.5.2 Track-Seeking Control Problem . . . . . . . . . . . . . 274
Bibliography 280
Index 283
List of Figures
1.1 SchematicapparatusofacommercialHDD 5
1.2 TrendofarealdensitiesofHDDs 6
2.1 BasicstructureinanHDD. 12
2.2 Read back signal (top) and servo pattern (bottom). . . . . . . 14
2.3 PES generation using burst signals read from the servo burst
pattern. 15

2.4 w − wTMR and w − rTMR. 16
2.5 Basic design flow of HDD head-positioning system. . . . . . . 17
2.6 Errorfactorduringpositionsignalwriting. 19
2.7 Errorfactorofpositionsignal 19
2.8 Error factor of position signal fluctuation during data read-
ing/writing 20
2.9 Error factor of head vibration during data reading/writing. . 20
2.10 Error factor of tracking error during data reading/writing. . . 21
2.11Plantblockdiagram 22
2.12 Head-positioning mechanisms in HDDs. . . . . . . . . . . . . 24
2.13 Measured actuator dynamics and rigid body model. . . . . . 25
2.14 Modeling of actuator dynamics using the Σ-type model. . . . 27
2.15 Modeling of actuator dynamics using the Π-type model. . . . 28
2.16 Weighting function used for Π-typemodeling 29
2.17 Block diagram of head-positioning control system. . . . . . . 32
2.18TimetraceofPES 35
2.19RROspectrum 35
2.20NRRO. 36
2.21NRROupto4kHz. 37
2.22Baselineoftotalnoise 38
2.23MechanicalvibrationsinNRRO. 38
2.24PESnoiseinNRRO 39
2.25TorquenoiseinNRRO. 39
2.26Exampleofsettlingresponse. 43
2.27Residualmodesinsettlingresponse. 43
2.28 Response of mode at 2445 Hz. . . . . . . . . . . . . . . . . . . 44
2.29 Response of mode at 3306 Hz. . . . . . . . . . . . . . . . . . . 44
2.30 Response of mode at 713 Hz. . . . . . . . . . . . . . . . . . . 45
xi
xii List of Figures

3.1 A block diagram of a servo control system in an HDD. . . . . 50
3.2 UnityfeedbackODOFcontrolsystem 52
3.3 Filter-type expression of TDOF control system. . . . . . . . . 52
3.4 Feedforward type expression of TDOF control system. . . . . 53
3.5 Frequencyresponseofplant 56
3.6 Frequencyresponseofinversemodel 56
3.7 Frequency response of inverse model with two look ahead steps. 57
3.8 Frequency response from reference trajectory to plant output. 57
3.9 Augmentedsystem 58
3.10Minimumjerktrajectory. 59
3.11 Basic structure of access servo control for HDD. . . . . . . . . 60
3.12 Block diagram of velocity servo control system. . . . . . . . . 60
3.13 Example of reference velocity trajectory. . . . . . . . . . . . . 62
3.14BasicstructureofPTOS. 63
3.15 Transient response by pole-zero cancellation. . . . . . . . . . 68
3.16 Simulated ideal impulse response of a first-order system. . . . 69
3.17 Transient response of IVC with feedforward input. . . . . . . 70
3.18 Transient response of IVC with feedforward input. . . . . . . 71
3.19Optimalmodeswitchingcondition 73
3.20Transientresponseofheadposition. 74
3.21 Transient response of current (experimental result). . . . . . . 75
3.22 Time-domain waveform of head movement in HDDs. . . . . . 76
3.23 Block diagram of a control system. . . . . . . . . . . . . . . . 77
3.24 Bode plot of lead compensator and PI controller. . . . . . . . 78
3.25 Sensitivity functions with two different control bandwidths il-
lustratingthewaterbedeffect 79
3.26 Time responses of step reference and disturbance. . . . . . . . 82
3.27 Frequency responses of open-loop and sensitivity transfer func-
tions 83
3.28PESspectra. 84

3.29 Notch filter and effects of discretization using bilinear transfor-
mation. 84
3.30Bodeplotsofmulti-stagenotchfilters 85
3.31 Frequency responses of the perturbed open-loop model. . . . 86
3.32 Block diagram of observer-based state feedback control. . . . 86
3.33 Frequency responses of full-order and reduced-order plant mod-
els 88
3.34 Pole-zero map and damping ratio on the z-plane 90
3.35 Time responses of step reference and disturbance using state
feedback(upper)andestimator(lower). 91
3.36 Frequency responses of open-loop and sensitivity transfer func-
tions using state feedback (upper) and estimator (lower). . . . 92
3.37PESspectra. 92
3.38 Root locus using the Kalman filter design. . . . . . . . . . . . 93
3.39RootlocususingtheLQRdesign 94
List of Figures xiii
3.40 Input and output signals of the multi-rate system. . . . . . . 96
4.1 AugmentedsystemforSMARTtrajectory 109
4.2 Augmented system with a discrete-time integrator. . . . . . . 110
4.3 Frequencyresponseofplant 114
4.4 Control inputs u(t) andtheirfrequencyspectra 115
4.5 Displacement profile for two-track seek. . . . . . . . . . . . . 116
4.6 Block diagram of TDOF system for implementation of proposed
feedforward input. . . . . . . . . . . . . . . . . . . . . . . . . 116
4.7 Headpositionsfortwo-trackseekcontrol. 117
4.8 Head positions for two-track seek control (magnified). . . . . 118
4.9 Power spectrum densities of tracking error. . . . . . . . . . . 119
4.10Multi-ratehold 122
4.11 Vibration suppression PTC by MPVT. . . . . . . . . . . . . . 123
4.12 Vibration suppression PTC by parallel realization. . . . . . . 125

4.13 Vibration suppression PTC with canonical form. . . . . . . . 126
4.14Frequencyresponsesofnominalplant. 127
4.15Simulationofnominalmodel. 129
4.16 Control input. . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.17 Frequency responses of detailed model and modified trajectory. 131
4.18Experimentalresults(envelop) 132
5.1 Frequency response of mechanical characteristics of the head-
positioningsysteminHDDs. 140
5.2 Frequency response of controlled object P
d
[z] 141
5.3 Gain of sensitivity transfer function in the Nyquist diagram. . 143
5.4 Vector loci of mechanical system and controlled object. . . . . 144
5.5 Frequency responses of controllers in case 1. . . . . . . . . . . 146
5.6 Open-loop transfer function L[z] incase1 147
5.7 Frequency responses of controllers in case 2. . . . . . . . . . . 148
5.8 Open-loop transfer function L[z] incase2 149
5.9 Frequency responses of controllers in case 3. . . . . . . . . . . 151
5.10 Open-loop transfer function L[z] incase3 152
5.11 Gains of frequency responses of the sensitivity transfer func-
tions 153
5.12 Gains of frequency responses of the complementary sensitivity
transferfunctions. 154
5.13Smallgaintheorem. 157
5.14 Robust stabilization for multiplicative uncertainties. . . . . . 158
5.15 Robust stabilization for multiplicative uncertainty. . . . . . . 159
5.16Generalizedplant. 160
5.17Mixedsensitivityproblem 163
5.18Frequencyresponseofplant 164
5.19 Frequency responses of Δ

m
and w
m
. 165
5.20Track-followingcontrolsystem. 165
xiv List of Figures
5.21Generalizedplants 166
5.22 Magnitude response of H
∞
controller. 167
5.23Timeresponses 168
5.24 Generalized plant for multi-rate discrete-time H
∞
controller
design 169
5.25 Frequency responses of W
t
and Δ
m
. 170
5.26Liftedgeneralizedplant 171
5.27 Position Error Signals (PES) and control inputs. . . . . . . . 172
5.28 Single-rate and multi-rate sampled-data H
∞
control problem. 173
5.29 Generalized plant for multi-rate sampled-data H
∞
control
problem 174
5.30 Frequency responses of weighting functions. . . . . . . . . . . 175

5.31 Polyphase representation of multi-rate controller. . . . . . . . 176
5.32 Frequency responses of multi-rate and single-rate sampled-data
controllers. 177
5.33 PES and control inputs. . . . . . . . . . . . . . . . . . . . . . 178
5.34Multi-ratehold 180
5.35BlockdiagramofRPTC 181
5.36PSGforasecond-ordersystem 182
5.37FF-RPTCalgorithm 183
5.38 Simulation of PES using the FF-RPTC and nominal plant with
k
p
=1.0k
pn
and L =0μs 185
5.39 Frequency responses of sensitivity transfer functions S[z] and
T [z] 186
5.40 Simulation with small variation (k
p
=1.1k
pn
and L =
43.26 μs). 188
5.41FFTofsimulationresults 189
5.42 Simulation with big variation (k
p
=1.4k
pn
and L =43.26 μs). 190
5.43 Frequency response of Q-filter with γ =2 191
5.44FFTspectraofRROsignals. 193

5.45FFTspectraofNRROsignals. 194
5.46Timeresponses 195
5.47 Block diagram with feedforward input. . . . . . . . . . . . . . 197
5.48 Block diagram of an HDD subjected to external vibrations. . 197
5.49 Block diagram of an HDD considering torque disturbance. . . 198
5.50 Block diagram of constant-type AFC. . . . . . . . . . . . . . 199
5.51 Block diagram of filter-type AFC with PCF. . . . . . . . . . . 200
5.52 Block diagram of transfer function-type AFC for transfer func-
tioncalculation 201
5.53 Block diagram for transfer function calculation using transfer
function-typeAFC 201
5.54 Block diagram of adaptive identification-type AFC. . . . . . . 202
5.55 Block diagram of adaptive identification-type AFC using RLS
andgradientmethod. 203
5.56 Experimental setup with shaker for verification of AFC. . . . 205
List of Figures xv
5.57 Time series of PES with and without proposed AFC. . . . . . 206
5.58 Frequency spectrum of PES without AFC. . . . . . . . . . . . 207
5.59FrequencyspectrumofPESwithAFC. 208
6.1 Track-followingcontrolsystem. 214
6.2 Parallel representation of controller C
d
[z] 215
6.3 Parallel representation of controller with down-samplers. . . . 215
6.4 Multi-rateinterlacingcontroller. 216
6.5 Comparison of track-following performance. . . . . . . . . . . 217
6.6 ODOFcontrolsystem 218
6.7 Improvement of step response by initial value compensation. . 221
6.8 ConventionalTDOFcontrolsystem. 223
6.9 N-DelayTDOFcontrolsystem 223

6.10 N-Delay control inputs. . . . . . . . . . . . . . . . . . . . . . 225
6.11 Contour plot of J. 227
6.12 Frequency characteristics of 3-delay feedforward control input. 227
6.13 Frequency characteristics of 4-delay feedforward control input. 228
6.14Headpositions 229
6.15Acousticnoise. 230
6.16Model-followingcontrol 232
6.17 Frequency responses of VCM plant and model. . . . . . . . . 233
6.18VCMmodelinthemodelcontrolsystem. 233
6.19 VCM model used in the model-following control. . . . . . . . 234
6.20 Multi-rate model-following control system with sliding mode
control. 236
6.21 Frequency characteristics of S. 236
6.22Currentwaveforms 238
6.23FFTanalysisofcurrents. 239
6.24Velocityprofiles. 240
6.25Acousticnoise. 241
6.26Headpositions 242
6.27Seekingnoisegeneratingprocess 244
6.28Exampleofseekingnoise. 245
6.29ConceptofSRSanalysis 246
6.30 Frequency response of models for SRS analysis. . . . . . . . . 247
6.31ExamplesofSRSanalysis 248
6.32 Acoustic noise reduction based on SRS analysis. . . . . . . . . 249
6.33 Block diagram of short-span seeking control system based on
PTC 250
6.34 Trapezoid acceleration trajectory. . . . . . . . . . . . . . . . . 251
6.35SRSanalysisbeforeoptimization 252
6.36 Experimental results before optimization. . . . . . . . . . . . 253
6.37SRSanalysisafteroptimization 254

6.38 Experimental results after optimization. . . . . . . . . . . . . 255
6.39Effectsofdifferentweightingvalues. 256
xvi List of Figures
7.1 Block diagram of the HDD plant model. . . . . . . . . . . . . 261
7.2 Frequency response of the nominal model in Version 1. . . . . 263
7.3 Frequency response of the nominal model in Version 2. . . . . 264
7.4 Frequency responses of perturbed plants with the nominal
modelinVersion1 265
7.5 Frequency responses of perturbed plants with the nominal
modelinVersion2 266
7.6 Disturbancesandtheirsummingpoints. 266
7.7 Time response of y[k] with disturbances and sensor noise. . . 267
7.8 Spectra of y[k] with disturbances and sensor noise. . . . . . . 268
7.9 Block diagram of control system for track-following. . . . . . 273
7.10 Bode plots of PID controller and notch filter. . . . . . . . . . 274
7.11PESvssectornumber 275
7.12Trackingerrors 277
7.13 Time responses of feedforward inputs. . . . . . . . . . . . . . 278
7.14Track-seekingresponses 279
List of Tables
1.1 Short History of Servo Control Technologies Applied to HDDs 7
1.2 Short History of Precision Control Technologies Applied to
HDDs 8
2.1 Example of Mechanical Dynamics Modeling Using the Σ-Type
Model 27
2.2 Example of Mechanical Dynamics Modeling Using the Π-Type
Model 29
2.3 Transformation of Zeros from Σ-Type Model to Π-Type Model 30
2.4 ExampleofNRRODecomposition 40
4.1 ControlandSamplingPeriods 127

4.2 ExperimentalSeekTime 133
5.1 Parameters of P
c
(s). 139
5.2 ComparisonofControlPerformances 151
7.1 PlantParameters 261
7.2 Parameters of P
mech
inVersion1 262
7.3 Parameters of P
mech
inVersion2 262
7.4 Upper and Lower Bounds of Plant Parameters in Version 1 . 262
7.5 Upper and Lower Bounds of Plant Parameters in Version 2 . 262
7.6 FlutterDisturbance 267
7.7 ParametersofRRO 268
7.8 m-files 269
xvii
Preface
This book describes high-speed precision motion control technologies which
are developed and applied to hard disk drives (HDDs). The first feature of
this book is that all the editors and the authors are engineers and professors
who are directly engaged in the study and development of HDD servo control.
Each author describes the control technologies that he developed, and most of
these technologies have already been successfully applied to mass production
of HDDs. As the proposed methodologies have been verified on commercial
HDDs at the very least, these advanced control technologies can also be read-
ily applied to precision motion control of other mechatronic systems, e.g.,
scanners, micro-positioners, photocopiers, atomic force microscopes (AFMs),
etc.

The second feature of this book is that the control technologies are catego-
rized into high-speed servo control, precision control, and environment-friendly
control. As such, potential readers can easily find an appropriate control tech-
nology according to their domain of application. The control technologies de-
scribed in this book also range from fundamental classical control theories to
selected advanced topics such as multi-rate control.
Learning Outcomes
We expect this book to be useful to engineers, researchers, and students in
technical junior colleges and universities as well as postgraduate students in
various fields. Potential readers not working in the relevant fields can also
appreciate the literature therein even without prior knowledge and exposure,
and will still be able to apply the tool sets proposed to address realistic in-
dustrial problems. As such, engineers and managers are empowered with the
knowledge and know-how to make important decisions and policies. Besides,
this book can also be used to educate fellow researchers and the public about
the advantages of various control technologies.
Many universities have established programmes and courses in this field,
with much cross-faculty and inter-discipline research going on in this area
as well. This book can also serve as a textbook for an intermediate to ad-
vanced module as part of control engineering, sampled-data systems, mecha-
tronics, etc. We also hope that the book is concise enough to be used for
self-study, or as a recommended text, for a single advanced undergraduate or
postgraduate module on linear systems and digital control theory.
xix
xx Preface
Acknowledgements
We would like to express our gratitude to university professors researching
HDD servo control and HDD company engineers for their efforts in evolving
high-speed precision motion control technology. We have learned a lot through
various technical discussions and communications with all of them.

We would like to take this opportunity to express our gratitude to CRC
Press for publishing this book. We would also like to acknowledge our loved
ones for their love, understanding, and encouragement throughout the entire
course of preparing this research monograph. This book was also made possible
with the help of our colleagues, collaborators, as well as students, research
staffs, and members of our research teams. This work was supported in part
by Singapore MOE AcRF Tier 1 Grant R-263-000-564-133.
Last, but not least, we would like to take a moment to send all our best
wishes to those who are affected, directly or indirectly, by the 2011 Eastern
Japan great earthquake disaster.
Takashi Yamaguchi
Mitsuo Hirata
Chee Khiang Pang
MATLAB
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About the Editors
Dr. Takashi Yamaguc hi graduated from the Tokyo Institute of Technol-
ogy with an M.S. in 1981. He joined the Mechanical Engineering Research
Laboratory (MERL), Hitachi Ltd., in 1981, and worked on research and de-
velopment of servo control of hard disk drives (HDDs) from 1987 to 2008. He
received his Dr Eng. in 1998, and the title of his dissertation was Study of

Head Positioning Servo Control for Hard Disk Drives.
Over the past thirty years, Dr. Yamaguchi’s main research interests and
areas have focused on motion control design, especially fast and precise po-
sitioning servo control design for HDDs. He has published 42 full papers, 26
articles and survey papers, 4 books as co-author, 71 presentations, and holds
28 US patents. Most of the publications are related to servo control of HDDs.
In 2008, he joined the Core Technology Research Center, Research & Devel-
opment Group, Ricoh Company Ltd., where he is currently a general manager
and an executive engineer. He is a fellow of the Japan Society of Mechanical
Engineers (JSME) and a senior member of the Institute of Electrical Engineers
in Japan (IEEJ).
He was a chief editor of Nanoscale Servo Control, TDU Press, 2007, which
was the first book in Japan regarding the modelling and the control of HDDs.
He was a guest editor for a special issue on “Servo Control for Data Storage
and Precision Systems,” Mechatronics, 2010.
Professor Mitsuo Hirata received his Ph.D. from Chiba University in 1996.
From 1996 to 2004, he was a research associate of electronics and mechanical
engineering at Chiba University. Currently, he is an associate professor of
electrical and electronic systems engineering at Utsunomiya University.
Prof. Hirata has extensive research experience in the design and implemen-
tation of advanced control algorithms for mechatronic systems. Some past re-
lated projects include high speed and high precision control of head actuators
of HDDs, semiconductor manufacturing systems (a collaboration with Canon
Inc.), Galvano scanner (a collaboration with Canon Inc.), and transmission of
vehicles (a collaboration with Nissan Motor Co., Ltd.), etc.
He was the co-author and editor of Nanoscale Servo Control, TDU Press,
2007, which was the first book in Japan regarding the modelling and the
control of HDDs. The book includes an HDD benchmark problem in the at-
tached CD-ROM, and he is the chair of a technical working group of the
HDD benchmark problem that can also be obtained from the following URL:

He has published
xxi
xxii About the Editors
many international refereed journals and conference papers relevant to the
scope of this book.
Professor Chee Khiang Pang, Justin, was born in Singapore in 1976. He
received B.Eng. (Hons.), M.Eng., and Ph.D. degrees in 2001, 2003, and 2007,
respectively, all in electrical and computer engineering, from the National
University of Singapore (NUS), working closely with A*STAR Data Storage
Institute (DSI), Singapore. In 2003, he was a visiting fellow in the School of
Information Technology and Electrical Engineering (ITEE), the University of
Queensland (UQ), St. Lucia, QLD, Australia, working on a probabilistic small
signal stability of large-scale interconnected power systems project funded by
the Electric Power Research Institute (EPRI), Palo Alto, California, USA.
From 2006 to 2008, he was a researcher (tenure) with Central Research Lab-
oratory, Hitachi Ltd., Kokubunji, Tokyo, Japan. In 2007, he was a visiting
academic in the School of ITEE, UQ, St. Lucia, QLD, Australia, and was in-
vited by IEEE Queensland Section to deliver a seminar. From 2008 to 2009, he
was a visiting research professor in the Automation & Robotics Research Insti-
tute (ARRI), the University of Texas at Arlington (UTA), Fort Worth, Texas,
USA. Currently, he is an assistant professor in the Department of Electrical
and Computer Engineering (ECE), NUS, Singapore. He is a faculty associate
with A*STAR DSI and a senior member of IEEE.
Prof. Pang is the author of Intelligent Diagnosis and Prognosis of Indus-
trial Networked Systems (CRC Press, 2011). In recent years, he served as
a guest editor for the International Journal of Systems Science, Journal of
Control Theory and Applications,andTransactions of the Institute of Mea-
surement and Control. He is currently serving as an associate editor for Trans-
actions of the Institute of Measurement and Control, on the editorial board
for International Journal of Computational Intelligence Research and Applica-

tions, and on the conference editorial board for IEEE Control Systems Society
(CSS). He was listed in Marquis Who’s Who in the World,27
th
Edition, USA,
2010, and was the recipient of the Best Application Paper Award in the 8
th
Asian Control Conference (ASCC 2011), Kaohsiung, Taiwan, 2011.
List of Contributors
Hidehiko Numasato
Hitachi Global Storage Technologies Japan, Ltd.
Fujisawa, Kanagawa, Japan
Hiroshi Uchida
Hitachi Global Storage Technologies Japan, Ltd.
Fujisawa, Kanagawa, Japan
Shinji Takakura
Toshiba Corp.
Kawasaki, Kanagawa, Japan
T akeyori Hara
Toshiba Corp.
Ome, Tokyo, Japan
Dr. Nobutaka Bando
Japan Aerospace Exploration Agency
Sagamihara, Kanagawa, Japan
Dr. Takashi Yamaguchi
Ricoh Company Ltd.
Yokohama, Kanagawa, Japan
Dr. Takenori Atsumi
Hitachi, Ltd.
Fujisawa, Kanagawa, Japan
Prof. Atsushi Okuyama

Tokai University
Hiratsuka, Kanagawa, Japan
Prof. Hiroshi Fujimoto
The University of Tokyo
Kashiwa, Chiba, Japan
Prof. Mitsuo Hirata
Utsunomiya University
Utsunomiya, Tochigi, Japan
xxiii
Nomenclature
A/D Analog-to-Digital
AFC Acceleration Feedforward Control
AFM Atomic Force Microscopy
ARE Algebraic Riccati Equation
BER Bit Error Rate
CACSD Computer-Aided Control System Design
CD Compact Disc
CPU Central Processing Unit
D/A Digital-to-Analog
DFT Discrete Fourier Transform
DOF Degree-of-Freedom
DSP Digital Signal Processor
DVD Digital Versatile Disc
EMF Electro-Motive Force
FB-RPTC FeedBack Repetitive Perfect Tracking Control
FF-RPTC FeedForward Repetitive Perfect Tracking Control
FFSC Frequency-Shaped Final-State Control
FFT Fast Fourier Transform
FIR Finite Impulse Response
FIV Flow-Induced Vibration

FSC Final-State Control
HDD Hard Disk Drive
HGST Hitachi Global Storage Technologies
IDR Inter-Sample Disturbance Rejection
IEEJ Institute of Electrical Engineers of Japan
IIR Infinite Impulse Response
ISS Initial Shock Spectrum
IVC Initial Value Compensation
LCD Liquified Crystal Display
LMI Linear Matrix Inequality
LPF Low Pass Filter
LQG Linear Quadratic Gaussian
LQR Linear Quadratic Regulator
LTI Linear Time-Invariant
xxv
xxvi Nomenclature
MD Mini Disc
MIMO Multi-Input-Multi-Output
MPES Master Position Error Signal
MPVT Minimizing Primary Vibration Trajectory
MSC Mode Switching Control
NRRO Non-Repeatable Run-Out
ODOF One-Degree-of-Freedom
OTC Off-Track Capability
PCB Printed Circuit Board
PCF Phase Compensating Filter
PES Position Error Signal
PID Proportional–Integral–Derivative
PSG Periodic Signal Generator
PTC Perfect Tracking Control

PTOS Proximate Time-Optimal Servomechanism
R/W Read/Write
RLS Recursive Least Squares
rpm revolutions-per-minute
RPTC Repetitive Perfect Tracking Control
RRO Repeatable Run-Out
RSS Residual Shock Spectrum
SAM Servo Address Mark
SISO Single-Input–Single-Output
SP Sound Pressure
SPES Slave Position Error Signal
SQP Sequential Quadratic Programming
SRS Shock Response Spectrum
STW Servo Track-Writing
TDOF Two Degrees-of-Freedom
TMR Track Mis-Registration
TP Track Pitch
TPI Tracks-Per-Inch
VCM Voice Coil Motor
ZOH Zero Order Hold
ZPE Zero-Phase Error
ZPETC Zero-Phase Error Tracking Control
Chapter 1
Introduction
Takashi Yamaguchi
Ricoh Company Ltd.
1.1 Concept of High-Speed Precision Motion Control 1
1.2 Hard Disk Drives (HDDs) 4
Bibliography 8
1.1 Concept of High-Speed Precision Motion Control

First of all, it is important to define the title of this book “High-Speed
Precision Motion Control.” For accurate servo-positioning of mechanical ac-
tuators in realistic engineering systems, high quality motion is required to
achieve both high speed and high precision positioning. As such, the typical
four control systems design phases are:
1. design of reference trajectory;
2. design of controller to track the reference trajectory;
3. design of transient or settling controller to minimize the tracking error
caused by various unmodeled dynamics or unpredicted plant fluctua-
tions; and
4. design of controller to suppress external disturbances to ensure the con-
trolled object remains on the target position.
To be more specific, the word “precision” must also be properly defined. A
well-known metric for precision is the ratio between accuracy (or resolution)
and stroke (or range). For high-performance positioning systems, ultra-high
precision is usually in the order of magnitudes of 10
−6
to 10
−7
or less.
Many devices and equipment require high-speed precision motion control
in industrial engineering systems. For example, the Hard Disk Drive (HDD)
is one such unique device that requires high-speed precision motion control of
the magnetic Read/Write (R/W) heads to perform read and write operations
of user data on the magnetic disks.
The technologies required to achieve high-speed and precise positioning
depend on whether the controlled variables such as position can be directly
1
2
detected. In the case where the controlled variables can be directly detected,

the control methodology is known as full closed-loop control. Otherwise, it is
known as semi closed-loop or open-loop control. In the latter (which is a more
popular method in industries due to the difficulty in selecting suitable sensors
to detect the controlled variables), design efforts to achieve high precision are
focused on keeping the operating conditions constant so that the controlled
variables are not affected by unobservable external disturbances.
In the case of full closed-loop control, disturbances and plant dynamics
as well as their fluctuations are included in the servo control loop, which
causes the control system design to be much more challenging. However, once
a satisfactory control loop can be designed, this method essentially has the
potential to achieve the required precise positioning, since the errors between
the reference and the controlled variables due to disturbances or fluctuations
can be detected and minimized accordingly. From the viewpoint of control
systems design, the full closed-loop control design methodology is more ideal
and preferred. The head-positioning servo control of the R/W head in an HDD
is one of full closed-loop control, since the control variable, i.e., the position
error between the R/W head and the written data track, can be measured or
detected directly. Traditionally, there have been many setbacks when designing
controllers in order to realize the advantage of full closed-loop control in the
history of HDD development. Subsequently, a positioning accuracy of several
nanometers can be achieved under normal operating conditions in today’s
HDDs.
The detailed features of high-speed precision motion control described in
this book are as follows:
1. Control systems design based on the four control systems de-
sign phases
It is important to design the correct handover from high-speed mo-
tion control to precision motion control. Currently, many industrial con-
trollers used in various engineering disciplines have two or more control
modes, and a supervisory controller is commonly employed to switch be-

tween the tracking mode to the positioning mode in order to accomplish
a given command such as moving and settling the controlled object to
the target position. Each control mode is also usually designed to opti-
mally meet the local performance index. For example, the performance
index may be minimum time in the tracking mode, while disturbance
suppression capability may be the performance index in the positioning
mode. In Chapter 3, fundamental controller designs based on classical
control theories and their extensions are described, including the entire
structure of the proposed Mode Switching Control (MSC) framework.
In Chapter 4, several ultra-fast motion control design methods based on
advanced control theories are described, and several ultra-precise posi-
tion control designs based on advanced control theories are discussed in
Chapter 5.
Introduction 3
2. Control systems design considering control input saturation
When the distance from the current location to the desired target is suf-
ficiently large, a maximum control input which saturates the power am-
plifier during acceleration is effective in shortening the actuation time.
In this case, the design issue is how to track the controlled object on the
reference trajectory precisely during deceleration, i.e., after releasing the
control input of the power amplifier from saturation during acceleration
(see Chapter 3.2.2).
3. Control systems design considering vibration characteristics
One of the factors which deteriorates high-speed precision positioning
is the vibration of the controlled object whose modes are easily excited
by external disturbances or control input. This is especially true in the
case of full closed-loop control, which takes into account all the vibration
modes including those above the sampling frequency. It is also desirable
to design the reference trajectory and its tracking control so as not to
excite the vibration modes during actuation (see Chapters 3.4.1, 4.1,

5.1, and 5.2).
4. Control systems design considering di s turbance suppression
capabilities
One of the most important indices in precise motion control design is the
improvement in disturbance suppression capabilities. This generalizes to
the demand for high servo bandwidth control and advanced sensor fu-
sion techniques to detect disturbances so that corresponding disturbance
rejection control methods can be used to suppress the detected external
disturbances (see Chapters 5.1, 5.4, and 5.5).
5. Sampling frequency selection for signal detection
It is desirable to detect controlled variables directly for precision motion
control. The quality of the detected signals, such as noise level, resolution
of the detected signal, and linearity, etc., are important performance
measures. Moreover, as the sampling frequency of detected signals affects
servo control performance, it is also necessary to develop control design
methods to improve servo control performance using a specific sampling
frequency (see Chapters 3.4.2, 4.2, 5.3).
6. Influences on environment
With the current environmental concerns for sustainability and energy
efficiencies, it is important to take into account environment factors such
as power consumption and noise. A couple of approaches to design con-
trollers with less influence and impact on the environment are included
(see Chapters 6.1, 6.2, and 6.3).
The six items mentioned above are the main features of high-speed pre-
cision motion control covered in this book. The applications of these con-
trol systems design methodologies cover many industrial applications such as