1. Robust track-following control for dual-stage servo systems in HDDs Ryozo Nagamune Division of Optimization & Systems Theory Royal Institute of Technology, Sweden Seminar at Department of Mechanical Engineering, University of British Columbia February 3 rd, 2006 (Joint work with R. Horowitz and his students at UC Berkeley)

2. Outline Track following control in HDDs Worst-case H 2 performance minimization Design techniques –Multirate control –Robust control (Mixed H 2 /H 1, Mixed H 2 / , Robust H 2 ) Examples Conclusions

3. Track following control www.westerndigital.com Data track Read/Write head Goal: Control the R/W head to follow the data track in a highly accurate manner Inputs : Voice Coil Motor (VCM) + mini/micro-actuator Measurements : Position Error Signal (PES) + other sensor signals VCM Servo sector Dual-stage & multi-sensing system

4. Robust control theory Dual-stage multi-sensing control Dual-stage multi- sensing system PESVCM Micro- actuator Sensor signals (PZT-sensor etc) Fixed sampling rate : Disturbances (track runout, windage, measurement noise, etc.) Variations 1. Multivariable control 2. Possibly multirate control 4. Optimal control 3. Robust control Control features Conventional methods PQ method Sensitivity decoupling

5. Outline Track following control in HDDs Worst-case H 2 performance minimization Design techniques –Multirate control –Robust control (Mixed H 2 /H 1, Mixed H 2 / , Robust H 2 ) Examples Conclusions

6. Dual-stage multi-sens. system S : Multirate sampler, H : Multirate hold K : PES etc. : Disturbances (runout, windage, noise) Multirate Multivariable Design K s.t. MeasurementsControl inputs RobustnessOptimality : map from w to z Controller Uncertainty : robustly stabilizing controller set Parametric uncertainties in Dynamic uncertainty Worst-case H 2 minimization

7. Outline Track following control in HDDs Worst-case H 2 performance minimization Design techniques –Multirate control –Robust control (Mixed H 2 /H 1, Mixed H 2 / , Robust H 2 ) Examples Conclusions Control for LTI systems

8. Outline Track following control in HDDs Worst-case H 2 performance minimization Design techniques –Multirate control –Robust control (Mixed H 2 /H 1, Mixed H 2 / , Robust H 2 ) Examples Conclusions

9. Nominal K Dynamic uncertainty Original formulation Performance : Nominal Stability : Dynamic uncertainty Advantage : Computationally inexpensive Disadvantage : Insufficient robustness conditions We solve a convex optimization problem. Mixed H 2 /H 1 synthesis (Scherer, Oliveira, etc)

10. Nominal K Dynamic & parametric uncertainties Original formulation Performance : Nominal Stability : Dynamic & parametric Advantage : Guaranteed robust stability Disadvantage : No robust performance We combine a mixed H 2 /H 1 technique with D-K iterations. Mixed H 2 /  synthesis (Packard, Doyle, Young, etc)

11. Nominal K Parametric uncertainties Original formulation Performance : Robust Stability : Parametric uncertainties Advantage : Robust performance Disadvantage : Computationally expensive No dynamic uncertainty We solve a series of convex optimization problems. Robust H 2 synthesis (Kanev, Scherer, Paganini, etc)

12. Outline Track following control in HDDs Worst-case H 2 performance minimization Design techniques –Multirate control –Robust control (Mixed H 2 /H 1, Mixed H 2 / , Robust H 2 ) Examples Conclusions

13. VCM Relative position error signal Position Error Signal (PES) Vibration signal Slider Read/write head Micro- actuator (MA) Two inputs Sampling/hold rates twice faster than that of PES Noise Airflow Track runout Three outputs Example 1: Setting

14. Example 1 : Block diagram Gvcm Gma Gc Input Output Disturbance Parametric uncertainty Dynamic uncertainty VCM dynamics Microactuator dynamics Runout model

15. Example 1 : Simulation result Design method RMS value of PES (nm) degK ( before reduction ) NominalWorst PQ method 7.7510.00 6 Sensitivity decoupling 7.11 8.35 6 Mixed H 2 /H 1 6.57 7.82 8 (13) Mixed H 2 /  5.31 5.88 8 (13) Robust H 2 5.93 6.47 9 (11) 200 enumerations of parametric variations

16. Example 2 : Setting (with R. de Callafon at UC San Diego) Inputs : u V (VCM) u PZT (PZT-actuator) Measurement : y LDV (Head position) Frequency responses for 36 dual-stage systems u V to y LDV u PZT to y LDV PZT-actuated suspension

17. Example2 : Modeling Suspension modes E-block PZT-driver uVuV y LDV u PZT    u V to y LDV u PZT to y LDV Experiment Sampled models u V to y LDV u PZT to y LDV

18. Example 2 : Controller design SimulationExperiment Amplitude plots of sensitivity functions (from runout to PES)  Robust H 2 synthesis  Single-rate controller  deg K = 13 runout + - PES plantK - uVuV u PZT y LDV

19. Outline Track following control in HDDs Worst-case H 2 performance minimization Design techniques –Multirate control –Robust control (Mixed H 2 /H 1, Mixed H 2 / , Robust H 2 ) Examples Conclusions

20.  A multirate multivariable robust optimal track-following control in HDDs  Worst-case H 2 minimization problem  Design methods via convex optimization  Mixed H 2 /H 1  Mixed H 2 /   Robust H 2  General dual-stage multi-sensing systems Conclusions

21. Future research topics  Sampled-data control Inter-sampling behavior  Performance analysis tool Degradation of track-following property  Multiple controller / Adaptive controller Improvement of tracking precision  Probabilistic approach More accurate uncertainty description  User-friendly software