Tài liệu High Speed Precision Motion Control doc

High-Speed Precision Motion Control High-Speed Precision Motion Control Edited by Takashi Yamaguchi Mitsuo Hirata Chee Khiang Pang Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business MATLAB® is a trademark of The MathWorks, Inc and is used with permission The MathWorks does not warrant the accuracy of the text or exercises in this book This book’s use or discussion of MATLAB® software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB® software CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2012 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S Government works Printed in the United States of America on acid-free paper Version Date: 20111026 International Standard Book Number: 978-1-4398-6726-6 (Hardback) This book contains information obtained from authentic and highly regarded sources Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint Except as permitted under U.S Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400 CCC is a not-for-profit organization that provides licenses and registration for a variety of users For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Contents List of Figures xi List of Tables xvii Preface xix About the Editors xxi List of Contributors xxiii Nomenclature xxv Introduction Takashi Yamaguchi 1.1 Concept of High-Speed Precision Motion Control 1.2 Hard Disk Drives (HDDs) Bibliography System Modeling and Identification Hiroshi Uchida, Takashi Yamaguchi, and Hidehiko Numasato 2.1 HDD Servo Systems 2.1.1 Inside an HDD 2.1.2 Generation of Servo Position Signal 2.2 TMR Budget Design 2.3 Modeling of HDD 2.3.1 Introduction 2.3.2 Plant Components 2.3.3 Modeling of Mechanical Dynamics 2.4 Modeling of Disturbances and PES 2.4.1 Disturbances and PES 2.4.2 Decomposition of Steady-State PES 2.4.2.1 RRO and NRRO 2.4.2.2 Frequency Spectrum of NRRO 2.4.2.3 Decomposition of NRRO 2.4.3 Decomposition of Transient Response Bibliography 1 11 11 12 13 16 22 22 22 24 32 32 34 34 36 37 40 46 v vi 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 Concept of IVC 63 3.3.1.1 Initialization of Controller State Variable 64 3.3.1.2 Design of Mode Switching Condition 64 3.3.2 IVC Design Method 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-Rate Control 76 3.4.1.1 Introduction 76 3.4.1.2 Lead Compensator and PI Controller 77 3.4.1.3 Notch Filter 82 3.4.1.4 Observer State Feedback Control 85 3.4.1.5 Pole Placement Technique 89 3.4.1.6 Optimal Control Design 93 3.4.2 Multi-Rate Control 94 3.4.2.1 Introduction 94 3.4.2.2 Problem Formulation 95 3.4.2.3 Multi-Rate Observer 97 3.5 Episode: Development of IVC Design Method in Industry 99 Bibliography 101 Ultra-Fast Motion Control 107 Mitsuo Hirata and Hiroshi Fujimoto 4.1 Vibration-Minimized Trajectory Design 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 State Control 109 4.1.4 Application to Track-Seeking Control in HDDs 113 4.2 Perfect Tracking Control (PTC) 120 4.2.1 Introduction 120 vii 4.2.2 4.2.3 PTC Theory Vibration Suppression Using PTC 4.2.3.1 With MPVT 4.2.3.2 With Parallel Realization 4.2.3.3 With Modified Controllable Canonical Realization 4.2.4 Simulations and Experiments 4.2.4.1 Simulations Using Nominal Model 4.2.4.2 Experiments on HDDs Bibliography 121 123 123 124 125 126 126 130 134 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 Modeling of Controlled Object 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 Controller Design 145 5.1.3.1 Case 1: Gain-Stable Design for All Mechanical Resonant Modes 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 Mechanical Resonant Modes 150 5.1.3.4 Comparison of Control Performances 150 5.2 Robust Control Using H∞ Control Theory 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 Additive Uncertainty 157 5.2.3 Robust Stability Problem 157 5.2.4 H∞ Control Theory 159 5.2.5 Various H∞ Control Problems 161 5.2.5.1 Sensitivity Minimization Problem 161 5.2.5.2 Mixed Sensitivity Problem 162 5.2.6 Application of H∞ Control to HDDs 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 Repetitive Control 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 5.4.2.2 Design of PTC 5.4.3 Design of RPTC 5.4.4 Applications to RRO Rejection in HDDs 5.4.5 Experiments on RPTC 5.5 Acceleration Feedforward Control (AFC) 5.5.1 Introduction 5.5.2 Necessity for AFC 5.5.3 Types of AFC 5.5.3.1 Constant-Type AFC 5.5.3.2 Filter-Type AFC 5.5.3.3 Transfer Function-Type AFC 5.5.3.4 Adaptive Identification-Type AFC 5.5.4 Performance Evaluation for AFC 5.5.5 Applications of AFC 5.5.5.1 Application to Vehicles 5.5.5.2 Application to Industrial Robots Bibliography Control Design for Consumer Electronics Mitsuo Hirata, Shinji Takakura, and Atsushi Okuyama 6.1 Control System Design for Energy Efficiency 6.1.1 Interlacing Controller 6.1.2 Short-Track Seeking Using TDOF Control with IVC 6.2 Controller Design for Low Acoustic Noise Seek 6.2.1 Short-Span Seek Control for Low Acoustic Noise 6.2.2 Long-Span Seek Control for Low Acoustic Noise 6.3 Servo Control Design Based on SRS Analysis 6.3.1 Seeking Noise 6.3.2 Concept and Procedure of SRS Analysis 6.3.3 Models for SRS Analysis 6.3.4 Examples of SRS Analyses 6.3.5 Acoustic Noise Reduction Based on SRS Analysis Bibliography HDD Benchmark Problem Mitsuo Hirata 7.1 Public Release of the HDD Benchmark 7.2 Plant Model 7.3 Disturbance Model 7.3.1 Force Disturbance 7.3.2 Flutter Disturbance 7.3.3 RRO 7.3.4 Measurement Noise 179 181 182 184 187 192 192 196 198 199 200 200 202 205 205 209 209 209 213 213 214 217 222 222 231 243 243 243 244 246 249 256 259 Problem 259 261 264 265 265 267 268 ix 7.4 7.5 Overview of the HDD Benchmark Problem Version Example of Controller Design 7.5.1 Track-Following Control Problem 7.5.2 Track-Seeking Control Problem Bibliography Index 269 272 273 274 280 283 List of Figures 1.1 1.2 Schematic apparatus of a commercial HDD Trend of areal densities of HDDs 2.1 2.2 2.3 Basic structure in an HDD Read back signal (top) and servo pattern (bottom) PES generation using burst signals read from the servo burst pattern w − wT M R and w − rT M R Basic design flow of HDD head-positioning system Error factor during position signal writing Error factor of position signal Error factor of position signal fluctuation during data reading/writing Error factor of head vibration during data reading/writing Error factor of tracking error during data reading/writing Plant block diagram Head-positioning mechanisms in HDDs Measured actuator dynamics and rigid body model Modeling of actuator dynamics using the Σ-type model Modeling of actuator dynamics using the Π-type model Weighting function used for Π-type modeling Block diagram of head-positioning control system Time trace of PES RRO spectrum NRRO NRRO up to kHz Baseline of total noise Mechanical vibrations in NRRO PES noise in NRRO Torque noise in NRRO Example of settling response Residual modes in settling response Response of mode at 2445 Hz Response of mode at 3306 Hz Response of mode at 713 Hz 12 14 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.20 2.21 2.22 2.23 2.24 2.25 2.26 2.27 2.28 2.29 2.30 15 16 17 19 19 20 20 21 22 24 25 27 28 29 32 35 35 36 37 38 38 39 39 43 43 44 44 45 xi xii List of Figures 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18 3.19 3.20 3.21 3.22 3.23 3.24 3.25 3.26 3.27 3.28 3.29 3.30 3.31 3.32 3.33 3.34 3.35 3.36 3.37 3.38 3.39 A block diagram of a servo control system in an HDD Unity feedback ODOF control system Filter-type expression of TDOF control system Feedforward type expression of TDOF control system Frequency response of plant Frequency response of inverse model Frequency response of inverse model with two look ahead steps Frequency response from reference trajectory to plant output Augmented system Minimum jerk trajectory Basic structure of access servo control for HDD Block diagram of velocity servo control system Example of reference velocity trajectory Basic structure of PTOS Transient response by pole-zero cancellation Simulated ideal impulse response of a first-order system Transient response of IVC with feedforward input Transient response of IVC with feedforward input Optimal mode switching condition Transient response of head position Transient response of current (experimental result) Time-domain waveform of head movement in HDDs Block diagram of a control system Bode plot of lead compensator and PI controller Sensitivity functions with two different control bandwidths illustrating the waterbed effect Time responses of step reference and disturbance Frequency responses of open-loop and sensitivity transfer functions PES spectra Notch filter and effects of discretization using bilinear transformation Bode plots of multi-stage notch filters Frequency responses of the perturbed open-loop model Block diagram of observer-based state feedback control Frequency responses of full-order and reduced-order plant models Pole-zero map and damping ratio on the z-plane Time responses of step reference and disturbance using state feedback (upper) and estimator (lower) Frequency responses of open-loop and sensitivity transfer functions using state feedback (upper) and estimator (lower) PES spectra Root locus using the Kalman filter design Root locus using the LQR design 50 52 52 53 56 56 57 57 58 59 60 60 62 63 68 69 70 71 73 74 75 76 77 78 79 82 83 84 84 85 86 86 88 90 91 92 92 93 94 284 non-repeatable component, tracking error, 271 plant model, 255–257 plant parameters, 255 position error signal vs sector number, 269 proportional-integral-derivative controller, notch filter, Bode plots, 268 public release, 253–254 repeatable component, tracking error, 271 RRO parameters, 261 Bilinear transformation discretization using, 83 notch filter, effects of discretization using, 83 Burst signals read from servo burst pattern, PES generation, 14 C Canonical form, vibration suppression PTC, 121 Concept of high speed precision motion control, 1–4 Constant-type AFC, 194 Control, sampling periods, 125 Control design, consumer electronics, 207–250 acoustic noise, 237 acoustic noise seek, 216–231 long-span seek control, 225-231 short-span seek control, 216-225 controller with down-samplers, parallel representation, 209 energy efficiency, 207–216 interlacing controller, 208–211 short-track seeking using TDOF control, initial value compensation, 211–216 head positions, 238 model-following control, 225 Index multi-rate interlacing controller, 210 ODOF control system, 212 seeking noise, 239 servo control design, SRS analysis, 231–250 acoustic noise reduction, 243–250 seeking noise, 231 SRS analyses examples, 233–242 SRS analysis, 232 SRS analysis models, 232 sliding mode control, 229 SRS analysis, 240 track-following control system, 208 track-following performance, comparison, 211 trapezoid acceleration trajectory, 244 velocity profile, 236 weighting values, 250 Controller design, 266–273 track-following control problem, 267–268 track-seeking control problem, 268–273 Current with switching condition, transient response, 74 D Damping ratio pole-zero map, z-plane, 89 z-plane, 89 Data reading/writing head vibration during, error factor, 20 position signal fluctuation during, error factor, 20 tracking error during, error factor, 21 Design of mode switching condition, 64 Index Detailed model, modified trajectory, frequency responses, 128 Discrete-time integrator, augmented system, 107 Displacement profile, two tracks seek, 114 Disturbance, step reference, time responses, 81 Disturbance modeling, 34–45, 257–262 flutter disturbance, 259–260 force disturbance, 258–259 measurement noise, 262 RRO, 260–261 transient response decomposition, 40–45 E Electronics, consumer, control design, 213–258 acoustic noise, 237 acoustic noise seek, 216–231 long-span seek control, 225-231 short-span seek control, 216-225 controller with down-samplers, parallel representation, 209 energy efficiency, 207–216 interlacing controller, 208–211 short-track seeking using TDOF control, initial value compensation, 211–216 head positions, 238 model-following control, 225 multi-rate interlacing controller, 210 ODOF control system, 212 seeking noise, 239 servo control design, SRS analysis, 231–250 acoustic noise reduction, 243–250 seeking noise, 231 285 SRS analyses examples, 233–242 SRS analysis, 232 SRS analysis models, 232 sliding mode control, 229 SRS analysis, 240 track-following control system, 208 track-following performance, comparison, 211 trapezoid acceleration trajectory, 244 velocity profile, 236 weighting values, 250 Energy efficiency, 207–216 interlacing controller, 207–211 short-track seeking using TDOF control, initial value compensation, 211–216 Example of settling response, 43 Experimental seek time, 130 External vibrations, 193 F Fast access servo control, 51–62 access servo control considering saturation, 58–62 basic structure of access servo control, 58–60 proximate time-optimal servomechanism, 62 reference velocity trajectory, 60–61 two-degrees-of-freedom control, 51–58 advantages of TDOF control, 51–52 reference trajectory, 55–58 structure of TDOF control, 52–53 zero-phase error tracking control, 53–55 Feedforward control, acceleration, 191–204 286 adaptive identification-type, 197–200 application, 204 constant-type, 194–195 filter-type, 195 industrial robot application, 204 necessity for, 192–193 performance evaluation, 200–203 transfer function-type, 195–197 types, 193–200 vehicle application, 204 Feedforward input, 193 TDOF system for implementation, 114 time responses, 272 Feedforward repetitive perfect tracking control algorithm, 179 Feedforward type expression, TDOF control system, 53 Filter-type AFC with PCF, 196 Final state control theory, 106–107 First-order system, simulated ideal impulse response, 68 Flutter disturbance, 259–260 Frequency response detailed model, modified trajectory, 128 head-positioning system, 138 of inverse model, 56 two look ahead steps, 56 nominal model in version 1, 257 nominal model in version 2, 258 nominal plant, 124 perturbed plants with nominal model version 1, 259 version 2, 260 plant, 56, 112, 160 from reference trajectory to plant output, 55 FSC theory See Final state control theory Index Full-order, reduced-order plant models, frequency responses, 87 G Generation, servo position signal, 13–15 H H∞ control theory, 152–164 application, 159–164 H∞ control problems, 158–159 mixed sensitivity problem, 158–159 sensitivity minimization problem, 158 plant uncertainties, mathematical representation, 153–154 additive uncertainty, 154 multiplicative uncertainty, 153 robust stability problem, 154–155 Hard disk drive benchmark problem, 253–273 block diagram, hard disk drive plant model, 255 bounds, plant parameters version 1, 255 version 2, 256 control system for track-following, 267–268 controller design, 266–273 track-following control problem, 267–268 track-seeking control problem, 268–273 disturbance model, 257–262 flutter disturbance, 259–260 force disturbance, 258–259 measurement noise, 262 RRO, 260–261 disturbances, summing points, 260 Index feedforward inputs, time responses, 272 flutter disturbance, 259–260 frequency response nominal model in version 1, 257 nominal model in version 2, 258 frequency response perturbed plants with nominal model version 1, 259 version 2, 260 hard disk drive benchmark problem version 3, 262–266 non-repeatable component, tracking error, 271 plant model, 255–257 plant parameters, 255 position error signal vs sector number, 269 proportional-integral-derivative controller, notch filter, Bode plots, 268 public release, 253–254 repeatable component, tracking error, 271 RRO parameters, 261 Hard disk drive modeling, 22–32 mechanical dynamics modeling, 24–32 plant components, 22–23 Hard disk drive servo systems, 11–15 inside hard disk drive, 11–13 servo position signal generation, 13–15 Hard disk drives, 4–8 head-positioning mechanisms in, 24 history of precision control technologies, history of servo control technologies, structure, 12 Head position 287 control system, block diagram of, 33 hard disk drives, time-domain waveform, 75 mechanisms in, system modeling, identification, 24 with switching condition, transient response, 73 system, hard disk drive design flow, 17 two track seek control, 115–116 Head vibration during, error factor, 20 High servo bandwidth, phase-stable design, 136–152 controlled object modeling, 137 controller design, 143–152 control performances comparison, 148–152 gain-stable design, 143–144 mechanical resonant modes, 144–148 vector locus, controller design based on, 137–142 controlled object vector locus, 140–142 sensitivity transfer function, 140 High-speed precision motion control, 49–100 access servo control, hard disk drive, structure, 60 access servo control for hard disk drive, structure, 60 augmented system, 58 bilinear transformation discretization using, 83 notch filter, effects of discretization using, 83 concept, 1–4 control system, block diagram, 76 current with switching condition, experimental transient response, 74 288 Index damping ratio pole-zero map, z-plane, 89 z-plane, 89 design method, development in industry, 98–100 disturbance, step reference, time responses, 81 fast access servo control, 51–62 access servo control considering saturation, 58–62 basic structure of access servo control, 58–60 proximate time-optimal servomechanism, 62 reference trajectory, 55–58 reference velocity trajectory, 60–61 structure of TDOF control, 52–53 two-degrees-of-freedom control, 51–58 zero-phase error tracking control, 53–55 feedforward type expression, TDOF control system, 53 first-order system, simulated ideal impulse response, 68 frequency response of inverse model, 56 of plant, 56 from reference trajectory to plant output, 57 frequency response of inverse model, look ahead steps, 56 full-order, reduced-order plant models, frequency responses, 87 head movement in hard disk drives, time-domain waveform, 75 head position with switching condition, transient response, 73 initial value compensation, 63–75 concept of initial value compensation, 63–64 design method, 64–70 design of mode switching condition, 64 initialization of controller state variable, 63–64 optimal design of mode switching condition, 71–75 input, output signals, multi-rate system, 95 inverse model, frequency response of, 56 Kalman filter design, root locus using, 92 lead compensator, PI controller, Bode plot, 77 look ahead steps, frequency response of inverse model, 56 LQR design, root locus using, 93 minimum jerk trajectory, 59 mode switching control, 50 multi-rate control multi-rate control, 93–98 multi-rate observer, 96–98 problem formulation, 94–96 single-rate control, 75–93 multi-rate system, input, output signals, 95 multi-stage notch filters, Bode plots, 84 notch filter bilinear transformation, discretization, 83 effects of discretization using, bilinear transformation, 83 notch filters, multi-stage, Bode plots, 84 observer-based state feedback control, 85 open-loop Index sensitivity transfer functions, state feedback, 91 state feedback, frequency responses, 91 open loop, sensitivity transfer functions, frequency responses, 82 optimal mode switching condition, 72 perturbed open-loop model, frequency responses, 85 PI controller Bode plot, 77 lead compensator, Bode plot, 77 plant frequency response, 56 pole-zero cancellation, transient response, IVC, 67 pole-zero map damping ratio, z-plane, 89 damping ratio on z-plane, 89 z-plane, 89 position error signal spectra, 82 PTOS structure, 62 reduced-order, full-order plant models, frequency responses, 87 reduced-order plant models, frequency responses, 87 reference trajectory to plant output, frequency response, 57 reference velocity trajectory, 61 root locus Kalman filter design, 92 LQR design, 93 sensitivity functions with control bandwidths, waterbed effect, 78 sensitivity transfer, open loop functions, frequency responses, 82 sensitivity transfer functions open-loop, state feedback, 91 289 state feedback, frequency responses, 91 servo control system, hard disk drive, 50 single-rate, multi-rate control, 75–99 single-rate control lead compensator, PI controller, 76–80 notch filter, 80–84 observer state feedback control, 84–88 optimal control design, 92–93 pole placement technique, 88–91 state feedback disturbance using, 90 open-loop, sensitivity transfer functions, frequency responses, 91 state feedback control block diagram, 85 observer-based, block diagram, 85 step reference disturbance, time responses, 81 disturbance time responses, state feedback, 90 switching condition, optimal mode, 72 TDOF control system feedforward type expression, 53 filter-type expression, 52 time-domain waveform, head movement in hard disk drives, 75 time responses, step reference, disturbance, 81 track-following, 75–98 track-seeking, 51–62 track-setting, 63–75 transient response with IVC, pole-zero cancellation, 67 290 transient response without IVC, 67 unity feedback ODOF control system, 52 velocity servo control system, block diagram, 60 waterbed effect, 78 z-plane, 89 pole-zero map, damping ratio, 89 History of precision control technologies, hard disk drives, History of servo control technologies, hard disk drives, I Initial value compensation, 63–75 concept of initial value compensation, 63–64 design of mode switching condition, 64 initialization of controller state variable, 63–64 design method, 64–70 development in industry, 98–100 optimal design of mode switching condition, 71–75 Initialization of controller state variable, 63–64 Input, output signals, multi-rate system, 95 Inside hard disk drive, 11–13 Inverse model, frequency response of, 56 IVC See Initial value compensation K Kalman filter, 92 L Lead compensator, PI controller, Bode plot, 77 Lifted generalized plant, 167 Index Look ahead steps, frequency response of inverse model, 56 LQR design, root locus using, 93 M Measured actuator dynamics, 25 Mechanical dynamics modeling, system modeling, identification, hard disk drive modeling, 24–32 Mechanical vibrations in NRRO, 38 Minimizing primary vibration trajectory, 121, 130 Minimum jerk trajectory, 59 Mixed sensitivity problem, 159 Modeling, identification of system, 11–45 data reading/writing head vibration during, error factor, 20 position signal fluctuation during, error factor, 20 tracking error during, error factor, 21 disturbances modeling, 32–45 transient response decomposition, 40-45 example of settling response, 43 hard disk drive modeling, 22–32 mechanical dynamics modeling, 24–32 plant components, 22–23 hard disk drive servo systems, 11–15 inside hard disk drive, 11–13 servo position signal generation, 13–15 hard disk drive structure, 12 hard disk drives, head-positioning mechanisms in, 24 head-positioning control system, block diagram of, 33 Index head-positioning system, hard disk drive design flow, 17 measured actuator dynamics, 25 mechanical vibrations in NRRO, 38 non-repeatable runout, 36 non-repeatable runout decomposition, 40 plant block diagram, 22 position error signal, time trace of, 35 position error signal generation, burst signals read from servo burst pattern, 14 position error signal modeling, 32–45 position error signal noise in non-repeatable runout, 39 position signal error factor, 20 position signal writing, error factor during, 19 read back signal, 13 and servo pattern, 13 residual modes in settling response, 43 rigid body model, 25 RRO spectrum, 35 servo pattern, 13 steady-state PES decomposition, 34–40 non-repeatable runout, 34–36 non-repeatable runout decomposition, 36–40 non-repeatable runout frequency spectrum, 36 RRO, 34–36 torque noise in non-repeatable runout, 39 total noise baseline, 38 track mis-registration budget design, 15–21 MPVT See Minimizing primary vibration trajectory 291 Multi-rate, single-rate sampled-data-controllers, frequency responses, 172 Multi-rate control multi-rate control, 93–98 multi-rate observer, 96–98 problem formulation, 94–96 single-rate control, 75–93 lead compensator, PI controller, 76–80 notch filter, 80–84 observer state feedback control, 84–88 optimal control design, 92–93 pole placement technique, 88–91 Multi-rate controller, polyphase representation, 172 Multi-rate H∞ control, 165–174 discrete-time H∞ control, 165–167 sampled-data H∞ control, 167–174 Multi-rate hold, 119, 175 Multi-rate system, input, output signals, 95 Multi-stage notch filters, Bode plots, 84 Multiplicative uncertainty, robust stabilization, 155, 156 N Non-repeatable component, tracking error, 271 Non-repeatable runout decomposition, 40 system modeling and identification, 40 frequency spectrum, 36 signals, fast Fourier transform spectra, 189 system modeling and identification, steady-state PES decomposition, 34–38 Notch filter 292 bilinear transformation, discretization using, 83 effects of discretization using, bilinear transformation, 83 multi-stage, Bode plots, 84 Nyquist diagram, 141 O Observer-based state feedback control, block diagram, 85 Open loop sensitivity transfer functions frequency responses, 82 state feedback, 91 state feedback, frequency responses, 91 Optimal design of mode switching condition, 71–75 Optimal mode switching condition, 72 P Parallel realization, 122 vibration suppression PTC, 121 Perfect tracking control, 118–130 experiments, 124–130 on hard disk drives, 128–130 simulations, 124–130 using nominal model, 125–128 theory, 119–120 vibration suppression using, 121–124 with minimizing primary vibration trajectory, 121–122 with modified controllable canonical realization, 123–124 with parallel realization, 122–123 Perturbed open-loop model, frequency responses, 85 PES See Position error signal Phase-stable design, high servo bandwidth, 136–152 Index controlled object modeling, 137 controller design, 143–152 control performances comparison, 148–152 gain-stable design, 143–144 mechanical resonant modes, 144–148 vector locus, controller design based on, 137–142 controlled object vector locus, 140–142 sensitivity transfer function, 140 Plant block diagram, 22 Plant components hard disk drive modeling, 22–23 system modeling, identification, hard disk drive modeling, 22–23 Plant frequency response, 56 Plant model, 255–257 Plant parameters, 255 Pole-zero cancellation, 67 transient response with IVC, 65 Pole-zero map damping ratio on z-plane, 89 z-plane, 89 Position error signal control inputs, 173 generation using burst signals read from servo burst pattern, 14 generation using servo burst pattern signals, 14 modeling, 32–45 noise in non-repeatable runout, 39 spectra, 82, 91 vs sector number, 269 Position signal error factor, 19 system modeling and identification, 19 Position signal fluctuation during, error factor, 20 Index Position signal writing, error factor during, 19 system modeling and identification, 19 Power spectrum densities, tracking error, 117 Precision control technologies history, Proportional-integral-derivative controller, notch filter, Bode plots, 268 Proximate time-optional servo mechanism structure, 61 PTC See Perfect tracking control Public release, 253–254 Q Q-filter, 185, 187, 191 R Read back signal, 13 and servo pattern, 13 servo pattern, system modeling, identification, 13 top, servo pattern, 13 Reduced-order plant models, frequency responses, 87 Reference trajectory, plant output, frequency response, 55 Reference velocity, trajectory, 60 Repeatable component, tracking error, 271 Repeatable run-out parameters, 261 signals, fast Fourier transform spectra, 189 spectrum, 35 system modeling and identification, steady-state position error signal decomposition, 32–34 Repetitive control, 174–191 discrete-time plant model, multi-rate hold, 175–176 experiments, 185–191 293 PTC design, 176–178 repetitive perfect tracking control, 175–178 repetitive perfect tracking control design, 178–180 RRO rejection, hard disk drives, 180–185 Repetitive perfect tracking control, 175–178 Residual modes in settling response, 43 Rigid body model, 25 system modeling and identification, 25 Rigid perfect tracking control, 129 Root locus Kalman filter design, 92 LQR design, 93 RPTC See Repetitive perfect tracking control RRO See Repeatable run-out S Schematic apparatus, commercial hard disk drive, Second order system, PSG, 177 Sensitivity functions with control bandwidths, waterbed effect, 78 Sensitivity transfer functions open-loop, state feedback, 91 state feedback, frequency responses, 91 open loop functions, frequency responses, 82 Servo burst pattern signals, position error signal generation, 14 Servo control design, shock response spectrum analysis, 231–250 acoustic noise reduction, 243–250 analysis, 232 examples, 233–242 models, 232–233 294 seeking noise, 231 Servo control system, hard disk drive, 50 Servo control technologies history, Servo pattern, 13 system modeling and identification, 13 Shaker for verification of AFC, 201 Simulations, 124–130 using nominal model, 125–128 Single-rate, multi-rate control, 75–98 Small gain theorem, 154 SMART trajectory, augmented system, 107 State feedback disturbance using, 90 open-loop, sensitivity transfer functions, 91 State feedback control block diagram, 85 observer-based, block diagram, 85 Steady-state PES decomposition, 34–40 non-repeatable runout, 34–36 decomposition, 36–40 frequency spectrum, 36 repeatable run-out, 34–36 system modeling and identification, 34–40 Step reference, disturbance time responses, 81 state feedback, 90 Summing points, 260 Switching condition, optimal mode, 72 System modeling, identification, 11–45 data reading/writing head vibration during, error factor, 20 position signal fluctuation during, error factor, 20 tracking error during, error factor, 21 Index disturbances modeling, 32–45 transient response decomposition, 40–45 example of settling response, 43 hard disk drive, 24 head-positioning mechanisms, 24 structure, 12 hard disk drive head-positioning mechanisms, 24 hard disk drive modeling, 22–32 mechanical dynamics modeling, 24–32 plant components, 22–23 hard disk drive servo systems, 11–15 inside hard disk drive, 11–15 servo position signal generation, 13–15 hard disk drive structure, 12 head-positioning control system, 33 block diagram, 33 head-positioning system, hard disk drive design flow, 17 measured actuator dynamics, 25 mechanical vibrations in NRRO, 38 non-repeatable runout, 36 decomposition, 40 plant block diagram, 22 position error signal, time trace, 35 position error signal generation using burst signals read from servo burst pattern, 14 position error signal modeling, 32–45 position error signal noise in non-repeatable runout, 39 position signal error factor, 20 position signal writing, error factor, 19 read back signal, 13 Index and servo pattern, 13 repeatable run-out spectrum, 35 residual modes in settling response, 43 rigid body model, 25 servo pattern, 13 steady-state PES decomposition, 34–40 non-repeatable runout, 34–36 non-repeatable runout decomposition, 36–40 non-repeatable runout frequency spectrum, 36 repeatable run-out, 34–36 RRO, 34–36 torque noise in non-repeatable runout, 39 total noise baseline, 38 track mis-registration budget design, 15–21 295 Track-seeking control in hard disk drives, 111–117 Tracking error, power spectrum densities, 117 Tracking error during, error factor, 21 Transfer function calculation, transfer function-type AFC, 196 Transfer function-type AFC, transfer function calculation, 196 Transient response decomposition, disturbances modeling, 40–45 Transient response with IVC, pole-zero cancellation, 67 Transient response without IVC, 67 Trend, areal densities of hard disk drives, Two-degrees-of-freedom control, 51–58 advantages of TDOF control, 51–52 feedforward type expression, 53 filter-type expression, 52 implementation of feedforward input, 114 reference trajectory, 55–58 structure of TDOF control, 52–53 zero-phase error tracking control, 53–55 T TDOF control See Two-degrees-of-freedom control Time-domain waveform, head movement in hard disk drives, 75 Time responses, 165, 195 step reference, disturbance, 80 Time responses of step reference, 90 Time trace of, system modeling and identification, PES, 35 U Torque disturbance, hard disk drive, Ultra-fast motion control, 105–130 194 canonical form, 126, 129 Torque noise in non-repeatable vibration suppression PTC, runout, 39 124 Total noise baseline, 38 control, sampling periods, 125 system modeling and control input, 127 identification, 38 detailed model, modified Track-following control system, 161, trajectory, frequency 267 responses, 128 discrete-time integrator, Track mis-registration budget design, augmented system, 105 15–21 296 Index track-seeking control in hard displacement profile, two tracks disk drives, 111–117 seek, 114 experimental seek time, 130 Ultra-precise position control, feedforward input, TDOF 135–204 implementation system, 114 acceleration feedforward control, frequency response, 112 191–204 detailed model, modified adaptive identification-type, trajectory, 128 197–200 nominal plant, 124 application, 204 head positions, two track seek constant-type, 194–195 control, 115–116 filter-type, 195 minimizing primary vibration industrial robot application, trajectory, 121, 126 204 vibration suppression perfect necessity for, 192–193 tracking control, 121 performance evaluation, multi-rate hold, 119 200–203 parallel realization, 126 transfer function-type, vibration suppression PTC, 195–197 121 types, 193–200 perfect tracking control, 118–130 vehicle application, 204 experiments, 124–130 adaptive identification-type hard disk drives, 128–130 AFC, 197–200 modified controllable RLS gradient method, 199 canonical realization, constant-type AFC, 194–195 123–124 control performances nominal model, 125–128 comparison, 148–152 simulations, 124–130 external vibrations, 193 theory, 119–120 feedforward input, 193 vibration suppression using, feedforward repetitive perfect 121–124 tracking control algorithm, power spectrum densities, 179 tracking error, 117 filter-type AFC with PCF, 196 rigid PTC, 129 frequency response, SMART trajectory, augmented head-positioning system, system, 107 138 TDOF system, implementation frequency response of plant, 160 of feedforward input, 114 generalized plant, 157, 162 tracking error, power spectrum H∞ control theory, 152–164 densities, 117 additive uncertainty, 154 vibration-minimized trajectory application, 159–164 design, 105–117 control problems, 158–159 based on final state control, mixed sensitivity problem, 108–111 158–159 final state control theory, 106–107 multiplicative uncertainty, 153 Index plant uncertainties, mathematical representation, 153–154 robust stability problem, 154–155 sensitivity minimization problem, 158 lifted generalized plant, 167 mixed sensitivity problem, 159 multi-rate, single-rate sampled-data-controllers, frequency responses, 172 multi-rate controller, polyphase representation, 172 multi-rate H∞ control, 165–174 discrete-time H∞ control, 165–167 sampled-data H∞ control, 167–174 multi-rate hold, 175 multiplicative uncertainty, robust stabilization, 155, 156 non-repeatable runout signals, fast Fourier transform spectra, 189 Nyquist diagram, 141 phase-stable design, high servo bandwidth, 136–152 control performances comparison, 148–152 controlled object modeling, 137 controlled object vector locus, 140–142 controller design, 143–152 gain-stable design, 143–144 mechanical resonant modes, 144–148 sensitivity transfer function, 140 vector locus, controller design based on, 137–142 position error signals, control inputs, 168 297 repetitive control, 175–191 discrete-time plant model, multi-rate hold, 175–176 experiments, 185–191 PTC design, 176–178 repeatable run-out rejection, hard disk drives, 180–185 repetitive perfect tracking control, 175–178 repetitive perfect tracking control design, 178–180 repetitive perfect tracking control, 175–178 RRO signals, fast Fourier transform spectra, 188 second order system, PSG, 177 shaker for verification of AFC, 201 small gain theorem, 154 time responses, 164, 190 torque disturbance, hard disk drive, 194 track-following control system, 161 transfer function calculation, 197 transfer function-type AFC, 196 weighting functions, frequency responses, 171 Unity feedback ODOF control system, 52 V Velocity servo control system, block diagram, 60 Vibration-minimized trajectory design, 103–111 based on final state control, 106–109 final state control theory, 104–105 track-seeking control in hard disk drives, 109–111 Vibration suppression using, 121–124 298 Index with minimizing primary vibration trajectory, 121–122 with modified controllable canonical realization, 123–124 with parallel realization, 122–123 W Waterbed effect, 77–78 Weighting functions, frequency responses, 171 Z z-plane pole-zero map, damping ratio, 89 Zero-order hold, 54, 60, 62, 79, 108, 137 Zero-phase error tracking control, 53–55 ... 1.1 1.2 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... 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. .. from high- speed motion control to precision motion control Currently, many industrial controllers used in various engineering disciplines have two or more control modes, and a supervisory controller