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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)

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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

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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

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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

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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

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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

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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

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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

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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)

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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)

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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)

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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

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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

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

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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

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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

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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

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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

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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

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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

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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

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