Robust track-following control for dual-stage servo systems in HDDs

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

2. Outline • Track following control in HDDs • Worst-case H2 performance minimization • Design techniques • Multirate control • Robust control (Mixed H2/H1, Mixed H2/m, Robust H2) • Examples • Conclusions

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

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

5. Outline • Track following control in HDDs • Worst-case H2 performance minimization • Design techniques • Multirate control • Robust control (Mixed H2/H1, Mixed H2/m, Robust H2) • Examples • Conclusions

6. Worst-case H2 minimization Uncertainty Parametric uncertainties in Dynamic uncertainty Dual-stage multi-sens. system : Disturbances (runout, windage, noise) : PES etc. Measurements Control inputs Design K s.t. Controller K Optimality Robustness MultirateMultivariable : map from w to z : robustly stabilizing controller set S :Multirate sampler, H :Multirate hold

7. Outline • Track following control in HDDs • Worst-case H2 performance minimization • Design techniques • Multirate control • Robust control (Mixed H2/H1, Mixed H2/m, Robust H2) • Examples • Conclusions Control for LTI systems

8. Outline • Track following control in HDDs • Worst-case H2 performance minimization • Design techniques • Multirate control • Robust control (Mixed H2/H1, Mixed H2/m, Robust H2) • Examples • Conclusions

9. Mixed H2/H1 synthesis(Scherer, Oliveira, etc) Original formulation Dynamic uncertainty Performance : Nominal Stability : Dynamic uncertainty Nominal We solve a convex optimization problem. Advantage : Computationally inexpensive K Disadvantage :Insufficient robustness conditions

10. Mixed H2/m synthesis(Packard, Doyle, Young, etc) Original formulation Dynamic & parametric uncertainties Performance : Nominal Stability : Dynamic & parametric Nominal We combine a mixed H2/H1 technique with D-K iterations. Advantage : Guaranteed robust stability K Disadvantage : No robust performance

11. RobustH2synthesis(Kanev, Scherer, Paganini, etc) Original formulation Parametric uncertainties Performance : Robust Stability : Parametric uncertainties Nominal We solve a series of convex optimization problems. Advantage : Robust performance K Disadvantage :Computationally expensive No dynamic uncertainty

12. Outline • Track following control in HDDs • Worst-case H2 performance minimization • Design techniques • Multirate control • Robust control (Mixed H2/H1, Mixed H2/m, Robust H2) • Examples • Conclusions

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

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

15. Example 1 : Simulation result 200 enumerations of parametric variations

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

17. Example2 : Modeling d1 d2I d3I uV to yLDV uV E-block Suspension modes uPZT to yLDV uPZT yLDV PZT-driver Experiment Experiment Sampled models Sampled models uV to yLDV uPZT to yLDV

18. Example 2 : Controller design runout • Robust H2 synthesis • Single-rate controller • deg K = 13 + - K uV plant - uPZT yLDV PES Amplitude plots of sensitivity functions (from runout to PES) Simulation Experiment

19. Outline • Track following control in HDDs • Worst-case H2 performance minimization • Design techniques • Multirate control • Robust control (Mixed H2/H1, Mixed H2/m, Robust H2) • Examples • Conclusions

20. Conclusions • A multirate multivariable robust optimal track-following control in HDDs • Worst-case H2 minimization problem • Design methods via convex optimization • Mixed H2/H1 • Mixed H2/m • Robust H2 • General dual-stage multi-sensing systems

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