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Advances in Industrial Control
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Other titles published in this Series:
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Robust Autonomous Guidance
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Dynamic Modelling of Gas Turbines
Gennady G. Kulikov and Haydn A. Thompson (Eds.)
ControlofFuelCellPowerSystems
Jay T. Pukrushpan, Anna G. Stefanopoulou and Huei Peng
Fuzzy Logic, Identification and Predictive Control
Jairo Espinosa, Joos Vandewalle and Vincent Wertz
Optimal Real-time Control of Sewer Networks
Magdalene Marinaki and Markos Papageorgiou
Process Modelling for Control
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Computational Intelligence in Time Series Forecasting
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Modelling and Control of mini-Flying Machines
Pedro Castillo, Rogelio Lozano and Alejandro Dzul
Rudder and Fin Ship Roll Stabilization
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Measurement, Control, and Communication Using IEEE 1588
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Piezoelectric Transducers for Vibration Control and Damping

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Ben M. Chen, PhD
Department of Electrical and Computer
Engineering
National University of Singapore
4 Engineering Drive 3
Singapore 117576
Kemao Peng, PhD
Department of Electrical and Computer
Engineering
National University of Singapore
4 Engineering Drive 3
Singapore 117576
Tong H. Lee, PhD
Department of Electrical and Computer
Engineering
National University of Singapore
4 Engineering Drive 3
Singapore 117576
Venkatakrishnan Venkataramanan, PhD
Mechatronics and Recording Channel
Division
Data Storage Institute
DSI Building, 5 Engineering Drive 1
Singapore 117608
British Library Cataloguing in Publication Data
Hard disk drive servo systems. - 2nd ed. - (Advances in
industrial control)
1.Servomechanisms 2.Data disk drives - Design 3.Hard disks
(Computer science)

Advances in Industrial Control
Series Editors
Professor Michael J. Grimble, Professor of Industrial Systems and Director
Professor Michael A. Johnson, Professor (Emeritus) of Control Systems
and Deputy Director
Industrial Control Centre
Department of Electronic and Electrical Engineering
University of Strathclyde
Graham Hills Building
50 George Street
Glasgow G1 1QE
United Kingdom
Series Advisory Board
Professor E.F. Camacho
Escuela Superior de Ingenieros
UniversidaddeSevilla
Camino de los Descobrimientos s/n
41092 Sevilla
Spain
Professor S. Engell
Lehrstuhl für Anlagensteuerungstechnik
Fachbereich Chemietechnik
Universität Dortmund
44221 Dortmund
Germany
Professor G. Goodwin
Department of Electrical and Computer Engineering
The University of Newcastle
Callaghan
NSW 2308

Box 118
S-221 00 Lund
Sweden
Professor A. Ray
Pennsylvania State University
Department of Mechanical Engineering
0329 Reber Building
University Park
PA 16802
USA
Professor D.E. Seborg
Chemical Engineering
3335 Engineering II
University of California Santa Barbara
Santa Barbara
CA 93106
USA
Doctor K.K. Tan
Department of Electrical Engineering
National University of Singapore
4 Engineering Drive 3
Singapore 117576
Doctor I. Yamamoto
Technical Headquarters
Nagasaki Research & Development Center
Mitsubishi Heavy Industries Ltd
5-717-1, Fukahori-Machi
Nagasaki 851-0392
Japan
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followed by the control and applications content of the monograph. Hard disk drive
systems are beset by nonlinear effects arising from friction, high-frequency
mechanical resonances and actuator saturation so any control methods used have to
be able to deal with these physical problems. Furthermore, there are two
operational modes to contend with: track seeking and track following each with
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x Series Editors’ Foreword
different performance specifications. The type of control solution proposed by
Professor Chen and his co-authors emerges from the interplay between the desire
to mitigate the nonlinear effects and yet find a control strategy to unify the control
of the two operational modes. To reveal the strategy developed in this Foreword
would be like prematurely revealing the ending of a fascinating mystery story.
The monograph also has other valuable features: Chapter 3 contains succinct
presentations of five different control methods with formulas given for both
continuous and discrete forms. Two chapters on nonlinear control follow that
covering linear control techniques. These chapters review classical time-optimal
control and introduce the relatively new composite nonlinear feedback (CNF)
control method. Again, presentations are given in both the continuous-time and
discrete-time domains for completeness.
The second part of the monograph comprises five applications studies
presented over five chapters. Whilst the first three of these chapters test out the
control methods discussed in earlier chapters, the last two chapters introduce new
applications hardware into the hard disk drive servo system problem: microdrive
systems and piezoelectric actuators; nonlinear system effects are prominent in
these new hardware systems.
Overall, it is an excellent monograph that exemplifies the topicality of control
engineering problems today. Many lecturers will find invaluable material within
this monograph with which to enthuse and motivate a new generation of control
engineering students. Right at the end of this monograph, Professor Chen and his
co-authors have extracted a benchmark control design problem for a typical hard

The scope of this second edition remains the same. It is to provide a systematic
treatment on the design of modern HDD servo systems. We particularly focus on the
applications of some newly developed control theories, namely the robust and per-
fect tracking (RPT) control, and the composite nonlinear feedback (CNF) control.
Emphasis is made on HDD servo systems with either a single-stage voice-coil-motor
(VCM) actuator or a dual-stage actuator in which an additional microactuator is at-
tached to a conventional VCM actuator to provide faster response and hence higher
bandwidth in the track-following stage. New design considerations and techniques,
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xii Preface
which have drastically improved the overall performance of our HDD servo systems,
are introduced in this new edition. We also take this opportunity to extend the CNF
control technique to systems with external disturbances and to include a comprehen-
sive modeling and compensation of friction and nonlinearities as well as a complete
servo system design of a microdrive.
The intended audience of this book includes practicing engineers in hard disk
and CD-ROM drive industries and researchers in areas related to servo systems and
engineering. An appropriate background for this monograph would be some senior
level and/or first-year graduate level courses in linear systems and multivariable con-
trol. Some knowledge of control techniques for systems with actuator nonlinearities
would certainly be helpful.
We have the benefit of the collaboration of several coworkers, from whom we
have learned a great deal. Many of the results presented in this monograph are the
results of our collaboration. Among these coworkers are Professor Chang C. Hang
of the National University of Singapore, Dr Siri Weerasooriya, Dr Tony Huang, Mr
Wei Guo and Dr Guoxiao Guo of the Data Storage Institute of Singapore. We are
indebted to them for their contributions.
The authors of this monograph are particularly thankful to Guoyang Cheng for
his help in proofreading the whole manuscript. The first two authors would also like
to thank their current and former graduate students, especially Yi Guo, Xiaoping

1.2.2 Trends in Advances of HDD Systems ................... 8
1.3 Overview of HDD Servo Systems ............................. 9
1.3.1 Mechanical Structure of an HDD . . . .................... 9
1.3.2 Issues on Control System Design . . . .................... 11
1.4 Implementation Setup....................................... 17
1.5 Preview of Each Chapter . ................................... 18
2 System Modeling and Identification .............................. 21
2.1 Introduction . . ............................................. 21
2.2 Time-domain Methods . . . ................................... 22
2.2.1 Impulse Response Analysis . . . ......................... 22
2.2.2 Step Response Analysis . .............................. 24
2.3 Frequency-domain Methods . . . . .............................. 26
2.3.1 Prediction Error Identification Approach . . ............... 26
2.3.2 Least Square Estimation Method . . . .................... 29
2.4 Physical Effect Approach with Monte Carlo Estimations .......... 32
2.4.1 Structural Analysis of Physical Effects . . . ............... 32
2.4.2 Monte Carlo Estimations . ............................. 33
2.4.3 Verification and Validation . . . ......................... 33
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xiv Contents
3 Linear Systems and Control ..................................... 37
3.1 Introduction . . ............................................. 37
3.2 Structural Decomposition of Linear Systems.................... 38
3.2.1 Interpretation . ....................................... 41
3.2.2 Properties . . ........................................ 43
3.3 PID Control . . ............................................. 47
3.3.1 Selection of Design Parameters ........................ 47
3.3.2 Sensitivity Functions . . . .............................. 48
3.4
Optimal Control ........................................ 49

5.3 Discrete-time Systems . . . ................................... 142
5.3.1 Systems without External Disturbances . . . ............... 142
5.3.2 Systems with External Disturbances .................... 151
5.3.3 Selection of Nonlinear Feedback Parameters . . . .......... 158
5.3.4 An Illustrative Example . .............................. 161
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Contents xv
5.4 Can We Beat Time-optimal Control? . ......................... 162
5.5 CNF Control Software Toolkit . . .............................. 164
5.5.1 Software Framework and User Guide ................... 166
5.5.2 An Illustrative Example . .............................. 172
Part II HDD Servo Systems Design
6 Track Following of a Single-stage Actuator ........................ 179
6.1 Introduction . . ............................................. 179
6.2 VCM Actuator Model . . . . ................................... 180
6.3 Track-following Controller Design . . . ......................... 181
6.4 Simulation and Implementation Results ........................ 188
6.4.1 Track-following Test . . . .............................. 188
6.4.2 Frequency-domain Test . .............................. 191
6.4.3 Runout Disturbance Test .............................. 191
6.4.4 Position Error Signal Test ............................. 198
7 Track Seeking of a Single-stage Actuator ......................... 201
7.1 Introduction . . ............................................. 201
7.2 Track Seeking with PTOS Control . . . ......................... 202
7.3 Track-seeking with MSC . ................................... 203
7.4 Track Seeking with CNF Control ............................. 205
7.5 Simulation and Implementation Results ........................ 206
7.5.1 Track-seeking Test ................................... 206
7.5.2 Frequency-domain Test . .............................. 209
8 Dual-stage Actuated Servo Systems .............................. 217

the set of real numbers
the entire complex plane
the set of complex numbers inside the unit circle
the set of complex numbers outside the unit circle
the unit circle in the complex plane
the open left-half complex plane
the open right-half complex plane
the imaginary axis in the complex plane
an identity matrix
an identity matrix of dimension
the transpose of
H
the complex conjugate transpose of
Im the range space of
Ker the null space of
the Moore–Penrose (pseudo) inverse of
the set of eigenvalues of
the maximum eigenvalue of
the maximum singular value of
the usual 2-norm of a matrix
the -norm of a stable system or
the -norm of a signal or
the set of all functions whose norms are finite
the -norm of a signal or
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xviii Notation
the set of all functions whose -norms are finite
the -norm of a stable system or
dim the dimension of a subspace
the orthogonal complement of a subspace of

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1
Introduction
1.1 Introduction
Hard disk drives (HDDs) provide an important data-storage medium for computers
and other data-processing systems. In most commercial HDDs, rotating disks coated
with a thin magnetic layer or recording medium are written with data that are ar-
ranged in concentric circles or tracks. Data are read or written with a read/write
(R/W) head, which consists of a small horseshoe-shaped electromagnet. Figure 1.1
shows a simple illustration of a typical hard disk servo system with a voice-coil-
motor (VCM) actuator.
The two main functions of the R/W head-positioning servomechanism in disk
drives are track seeking and track following. Track seeking moves the R/W head
from the present track to a specified destination track in minimum time using a
bounded control effort. Track following maintains the head as close as possible to
the destination track center while information is being read from or written to the
disk. Track density is the reciprocal of the track width. It is suggested that, on a disk
surface, tracks should be written as closely spaced as possible so that we can maxi-
mize the usage of the disk surface. This means an increase in the track density, which
subsequently means a more stringent requirement on the allowable variations of the
position of the heads from the true track center.
The prevalent trend in hard disk design is towards smaller hard disks with in-
creasingly larger capacities. This implies that the track width has to be smaller,
which leads to lower error tolerance in the positioning of the head. The controller
for track following has to achieve tighter regulation in the control of the servomech-
anism. Basically, the servo system of an HDD can be divided into three stages, i.e. the
track-seeking, track-settling and track-following stages (see Figure 1.2 for a detailed
illustration). Current HDDs use a combination of classical control techniques, such
as the proximate time-optimal control technique in the track-seeking stage, and lead-
lag compensators, proportional-integral-derivative (PID) compensators in the track-