Optimal control issues related to the hard disk drive servo systems

OPTIMAL CONTROL ISSUES RELATED TO THE HARD DISK DRIVE SERVO SYSTEMS ZHONGMING LI DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2000 OPTIMAL CONTROL ISSUES RELATED TO THE HARD DISK DRIVE SERVO SYSTEMS BY ZHONGMING LI A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY NATIONAL UNIVERSITY OF SINGAPORE 2000 Acknowledgments I would like to express my greatest gratitude and sincere thanks to my supervisors, Professor Ben. M. Chen, Dr. Guoxiao Guo and Professor T. H. Lee, for their invaluable supervision and support to my study in National University of Singapore. It is simply impossible for me to finish this thesis without their kind patience, tremendous encouragement and enlightening discussions. I would also like to thank Mr. Kexiu Liu, Mr. Xinmin Liu, Mr. Weilu Wang, Mr. Daowei Wu, Mr. Qi Hao and other postgraduate students in Department of Electrical Engineering of National University of Singapore and Data Storage Institute. They have shared with me a lot of invaluable ideas and knowledge, while their friendship has brought much joy during my period of postgraduate research. I am also thankful to the National University of Singapore for providing the research scholarship to support my Ph.D. study. Finally, I want to thank my wife, Zhang Ye, and my parents for their endless love, support and encouragement. i Summary The magnetic hard disk drive (HDD) as an important data-storage medium has seen a 100% annual growth rate of areal density in the past few years. This trend has been supported by the steady increase of the track density, which is measured by track-per-inch ( or TPI) and data density. The improved servo control, compared with other ways of increasing the track density such as reducing the vibration via thicker and alternative disk, fluid dynamic bearing spindle motors, higher bandwidth or dual stage actuators, multi-sensing technology and etc., is the most cost-effective way. Thus to improve the servo design in the hard disk drives is the first choice and last band aid, for supporting the TPI growth. This thesis presents some new control design methods for HDD servo systems. We have studied the robust and perfect tracking (RPT) design in both the continuoustime and discrete-time domains. Also the H2 optimal control has been studied to achieve the highest tracking accuracy. All the different designs have been applied to two kinds of hard disk drive servo systems, namely the single-stage actuator system, in which the voice coil motor (VCM) has been be used in virtually all commercial disk drives until now, and dual-stage actuator system, in which a secondary milli or micro actuator rides piggyback on top of the VCM and works as a fine positioning actuator. The dual stage servo is regarded as the key technology to support the TPI growth breakthrough in the future. Robust and Perfect Tracking Control, a newly-developed control design method, is the first control method we considered. In RPT design, we cast the overall HDD servo system design into a RPT design framework. A first order dynamic measurement feedback controller is then designed to achieve the robust and perfect tracking for any step reference. Our controller is theoretically capable of making ii the Lp -norm of the resulting tracking error with ≤ p < ∞ arbitrarily small in the face of external disturbances and initial conditions. Some trade-offs are then made in order for the RPT controller to be implementable using the existing hardware setup and to meet physical constraints such as sampling rate and the saturation of control in the system. The implementation results of the RPT controller are compared with those of a PID controller. The results show that our servo system is simpler and yet has faster seeking times, lower overshoot and higher accuracy. Later the RPT design is applied to the dual-stage actuator hard disk drives. We considered two different control strategies in the dual-stage actuator hard disk drives. One is to apply robust and perfect tracking to VCM actuator and the conventional PID design to the micro-actuator. Another design is to apply the robust and perfect tracking to the micro-actuator, and conventional design to VCM loop. These two control designs both show higher performances than the singlestage actuator system. The emphasis of the second half of this thesis is the application of H2 optimal control to investigate the performance limit for track following operation, which is traditionally evaluated as Track Mis-registration (TMR) or equivalently Track Per-Inch (TPI). Through analysis, we established that minimizing the closed-loop H2 norm considering the noise and disturbance models can minimize the TMR. Therefore an H2 control approach by solving the AREs for the non-regular H2 optimal control problem, is applied towards the minimization of the TMR. Both single-stage actuator case and dual-stage actuator are considered and the numerical examples for these cases are studied. The control designs are compared with the conventional PID control as well. Furthermore, to deal with the control saturation due to the limited displacement range of the secondary stage actuator, we also studied the H2 optimal control design with the PQ method together. Compared iii with existing design methods, the proposed methods not need the tedious controller parameter tuning, and the optimal tracking performance is guaranteed by the design method. Although the control designs were tested only on a dual-stage servo loop with the piezo-electrically actuated suspension, the method is generic, and should be applicable to other types of dual stage actuators such as MEMS based actuated slider and actuated head without much glitch. iv Contents Acknowledgments i Summary ii Introduction 1.1 Background and Motivations . . . . . . . . . . . . . . . . . . . . . . 1.2 Hard Disk Drive (HDD) Servo Mechanism . . . . . . . . . . . . . . 1.3 Contributions And Organizations of Thesis . . . . . . . . . . . . . . 12 Modeling And Identification of Hard Disk Drive Actuators 16 2.1 Steps of System Identification . . . . . . . . . . . . . . . . . . . . . 17 2.2 Dual-actuator Structure in Hard Disk Drives . . . . . . . . . . . . . 20 2.3 Modeling And Identification of Micro-actuator . . . . . . . . . . . . 21 2.4 The Micro-actuator Model . . . . . . . . . . . . . . . . . . . . . . . 24 2.5 Modeling And Identification of Voice Coil Motor . . . . . . . . . . . 26 2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 v Preliminary 33 3.1 Special Coordinate Basis (SCB) [100] . . . . . . . . . . . . . . . . . 33 3.1.1 Transformation of continuous-time system using SCB . . . . 34 3.1.2 Properties of Special Coordinate Basis . . . . . . . . . . . . 37 3.2 Robust and Perfect Tracking (RPT) Control . . . . . . . . . . . . . 39 3.2.1 State feedback Case: . . . . . . . . . . . . . . . . . . . . . . 42 3.2.2 Solutions to Measurement Feedback Case: . . . . . . . . . . 45 3.3 H2 Optimal Control . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.3.1 H2 Optimal Control Problem . . . . . . . . . . . . . . . . . 52 3.3.2 Infima of H2 optimal problem . . . . . . . . . . . . . . . . . 53 3.3.3 The Existence Conditions . . . . . . . . . . . . . . . . . . . 56 3.3.4 H2 Suboptimal State and Measurement Feedback Control . . 58 3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Robust and Perfect Tracking Control: Single-stage Actuator Case 60 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.2 Control System Design Using the RPT Approach . . . . . . . . . . 62 4.3 Implementation Results . . . . . . . . . . . . . . . . . . . . . . . . 73 4.3.1 Track Following Test . . . . . . . . . . . . . . . . . . . . . . 73 4.3.2 Position Error Signal Test . . . . . . . . . . . . . . . . . . . 75 vi 4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Robust and Perfect Tracking Control: Dual-stage Actuator Case 81 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.2 Control Structure of Dual-stage Actuator . . . . . . . . . . . . . . . 83 5.3 Robust and Perfect Tracking Control Design of Dual-stage Actuator (I) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 5.3.1 System Models . . . . . . . . . . . . . . . . . . . . . . . . . 84 5.3.2 Individual Servo Loop Controller Design . . . . . . . . . . . 87 5.3.3 Implementation Results . . . . . . . . . . . . . . . . . . . . 88 5.4 Robust and Perfect Tracking Control Design of Dual-stage Actuator (II) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.4.1 Robust and Perfect Tracking Control for Discrete-time Systems 92 5.4.2 RPT Design for Dual-stage Actuator . . . . . . . . . . . . . 97 5.4.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . 99 5.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . 103 H2 Optimal Control Towards The Highest TPI 105 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 6.2 TMR and H2 Optimal Control Problem . . . . . . . . . . . . . . . . 107 6.3 H2 Output Feedback Optimal Problem and Controller Design . . . 110 vii 6.3.1 Control Design for Regular Case . . . . . . . . . . . . . . . . 110 6.3.2 Control Design for Singular Case . . . . . . . . . . . . . . . 112 6.3.3 Optimal Control Design Procedure Summary 6.4 Single-Stage Actuator Case . . . . . . . . 113 . . . . . . . . . . . . . . . . . . . . . . 115 6.5 Dual-Stage Actuator Case . . . . . . . . . . . . . . . . . . . . . . . 120 6.6 Dual-stage Case: H2 Design Using PQ Method . . . . . . . . . . . . 124 6.7 Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 128 Conclusions and Suggestions 129 7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 7.2 Suggestions For Future Work . . . . . . . . . . . . . . . . . . . . . 131 Bibliography 133 A Author’s Publications 151 A.1 Journal Publications . . . . . . . . . . . . . . . . . . . . . . . . . . 151 A.2 Conference Publications . . . . . . . . . . . . . . . . . . . . . . . . 151 viii BIBLIOGRAPHY [32] T. 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Z. M. Li, G. X. Guo, B. M. Chen and T. H. Lee, “Optimal control design towards the hightest track-per-inch in hard disk drives”, Journal of Information Storage and Processing Systems (JISPS), Vol. 3, No. 1-2, pp. 27-41, April 2001. 2. T. B. Goh, Z. Li, B. M. Chen, T. H. Lee, and T. Huang, “Design and implementation of a hard disk drive servo system using robust and perfect tracking approach”, IEEE Trans. on Control Systems Technology, Vol. 9, No. 2, pp. 221-233, March 2001. . A.2 Conference Publications 1. Z. M. Li, K. X. Liu, B. M. Chen, and T. H. Lee, “Robust and Perfect Tracking Control Design of a Hard Disk Drive with a Dual-stage Actuator”, Proceedings of the 2001 American Control Conference, Arlington, Virginia, 151 APPENDIX A. AUTHOR’S PUBLICATIONS USA, pp. 3849-3854, June 2001. 2. Z. M. Li, G. X. Guo, B. M. Chen and T. H. Lee, “Optimal control design to achieve hightest track-per-inch in hard disk drives”, Presented at the 11th Annual Symposium on Information Storage and Processing Systems, Santa Clara, California, USA, June 2000. 3. T. B. Goh, Z. Li, B. M. Chen, T. H. Lee, and T. Huang, “Design and implementation of a hard disk drive servo system using robust and perfect tracking approach”, Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix, Arizona, USA, pp. 5247-5252, December 1999. 4. T. B. Goh, Z. M. Li, Ben M. Chen, and T. H. Lee, “Control design for a dual-stage actuator in hard disk drives”, Proceedings of the 1999 IEEE Hong Kong Symposium on Robotics and Control, Hong Kong, China, pp. 577-582, July 1999. 152 [...]... performance In this thesis, the presented work is mainly focused on the optimal control design for the track-following servo in the hard disk drives Our concern is to increase the servo bandwidth of the hard disk drive systems via the optimal control methods Since the dual stage actuator structure is another main concern recently, all the control designs that we considered have been applied to both the single-stage... But the complexity and cost of manufacturing the dual-stage actuators, together with the impressive performance of the single-stage actuator, prevented the use of the dual-stage actuators in hard disk drives Now with the development of hard disk drives, the research interest of dual-stage actuator hard disk drives becomes stronger and stronger We first check the mechanism of dual-stage actuators in hard. .. allowed to offset the heads from the target The solution to this problem is to construct a type-one position loop All the above factors need to be taken into account when doing the servo design work [87] 1.3 Contributions And Organizations of Thesis In this thesis our research emphasis is the optimal control applications in the hard disk drive servo systems, mainly the robust and perfect tracking control. .. of these control design methods, such as high order of the controller, the difficulty of parameter tuning and etc., there is still the need to study and apply the newly developed control methods in the hard disk servo to meet the higher performance requirement The dual-stage actuator is considered as another solution to the problem of increasing the servo bandwidth The dual-actuator method to increase... used The design method is applied to both the single-stage actuator system and the dual-stage actuator system At last, the newly developed PQ method has been considered to be used with H2 optimal control to have a more implementable control design 15 Chapter 2 Modeling And Identification of Hard Disk Drive Actuators Before carrying out the control design for the hard disk drive servo, we should obtain the. .. DISK DRIVE ACTUATORS 2.2 Dual-actuator Structure in Hard Disk Drives As we know, the linear voice coil motor actuators have been working in most of the disk drives from the 1950’s to the 1980’s It is thus understandable that to overcome the limitations of VCM in the hard disk drives, adding a micro-actuator to the system would be a reasonable attempt in next step This type of dual-stage servo system has... proposed One is to make use of the RPT control design work for VCM loop and design a PI controller for the micro-actuator loop The design philosophy is to push the micro-actuator servo bandwidth as high as we desire The simulation and implementation results are given The other design is to apply the discrete-time RPT control to the micro-actuator loop, while the traditional control applies to the VCM loop... refers to the case that there is a small actuator mounted on a large conventional voice coil motor (VCM) actuator This small actuator is referred as the fine or secondary actuator and the large actuator is referred to as the coarse or primary actuator The dual-stage actuator structure has been used in optical disk drives for a long time Now it is drawing more and more interests among the hard disk drive servo. .. Mainly, there are two obstacles to increase the bandwidth One is the sampling frequency, and the other is the mechanical resonance The sampling frequency of the 3.5-inch hard disk drives has been increasing to meet the development of the track density, and most recent rate is about 20 kHz On the other hand, it is not easy to increase the mechanical resonance frequency of the VCM arm assembly in the disk drives,... computers to desktop and laptop computers With the rapid development of the data storage capacity and low cost, the hard disk drive is even considered as one of the key components in the future consumer electronics, such as, to store the digital video and audio data in so-called hard disk recorder (HDR) [96] The rapid evolution of magnetic hard disk drives in form factor, performance and cost during the . OPTIMAL CONTROL ISSUES RELATED TO THE HARD DISK DRIVE SERVO SYSTEMS ZHONGMING LI DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2000 OPTIMAL CONTROL ISSUES RELATED. accuracy. Later the RPT design is applied to the dual-stage actuator hard disk drives. We considered two different control strategies in the dual-stage actuator hard disk drives. One is to apply robust. to VCM actuator and the conventional PID design to the micro-actuator. Another design is to apply the robust and perfect tracking to the micro-actuator, and conventional design to VCM loop. These