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by SangJoo Kwon Committee:

Ph.D. Thesis Defence Mt. May 28, 2002. Robust Tracking Control and State Estimation of Mechanical Systems: A Perturbation Compensator Based Approach 기계 시스템의 강인 추종 제어 및 상태 추정 : 섭동 보상 기법에 의한 접근. by SangJoo Kwon Committee:

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  1. Ph.D. Thesis Defence Mt. May 28, 2002 Robust Tracking Control and State Estimation of Mechanical Systems: A Perturbation Compensator Based Approach 기계 시스템의 강인 추종 제어 및 상태 추정: 섭동 보상 기법에 의한 접근 by SangJoo Kwon Committee: Professor W. K. Chung (Chair), Professor Y. Youm, Professor J. S. Lee, Professor I. H. Suh, Professor M. Tomizuka Department of Mechanical Engineering Pohang University of Science & Technology, Pohang, Korea

  2. Progress After Proposal • Presentation at the Proposal meeting • Hierarchical Perturbation Compensation: concept, formulation, and its extension to Multiloop Perturbation Compensator. • Discrete-Time Analysis on the Q-filter effect. • Dual-stage Servo design for Coarse/fine dual-stage. • Progress After Proposal Meeting • All the chapters were technically refined with some new results. • Robust state estimation and Robust Kalman Filtering in terms of Perturbation observer. Ph.D. Thesis Defence Mt., May 28, 2002

  3. MOTIVATIONS Ph.D. Thesis Defence Mt., May 28, 2002

  4. Robust Motion Control • Nominal feedback loop:  Nominal performance and stability. • Perturbation compensation loop:  Robust performance to the uncertainties. A scheme to overcome the performance limit of the existing class of perturbation observers? What is the condition for robust stability in the presence of modeling error? What is the characteristics of the perturbation observer in discrete-time domain? Ph.D. Thesis Defence Mt., May 28, 2002

  5. Robust State Estimation • Standard state estimator (Luenberger observer or Kalman filter):  Nominal performance and stability. • Perturbation observer:  Robust performance to the unknown Error dynamics of the combined observer dynamically coupled? How much can the perturbation observer contribute to the accuracy of state estimation? How about the noise sensitivity? Ph.D. Thesis Defence Mt., May 28, 2002

  6. Objectives of Thesis 1. Development of the Hierarchical Perturbation Compensator.  Robust motion control in terms of perturbation observer. 2. Discrete-time design and analysis of perturbation observer.  In what way do the modeling error/Q-filter parameter/digital control frequency affect the performance and robustness of the perturbation compensation loop? 3. Combined synthesis of state estimator and perturbation observer.  Robust state estimation (or robust Kalman filtering) in terms of perturbation observer. 4. Applications to Mechanical Systems  XY positioner, Robot arm, Coarse/fine dual-stage, Micro-teloperation Ph.D. Thesis Defence Mt., May 28, 2002

  7. Flow of Presentation DD Arm Applications to Mechanical Systems Robust State Estimation with Perturbation Observer (Chap. 5) XY Positioner Coarse/Fine Dual-Stage PART II. The Q-filter Effect on the Performance and Robustness (Chap. 4) Hierarchical Perturbation Compensator (Chap. 2) PART I. Extension to N-Loop Case: Multi-Loop Perturbation Compensator (Chap. 3) PART III. Ph.D. Thesis Defence Mt., May 28, 2002

  8. PART I. Robust Tracking Control with Hierarchical Perturbation Compensation Ph.D. Thesis Defence Mt., May 28, 2002

  9. A Class of Perturbation Observers  Disturbance observer(DOB): Ohnishi’87, Umeno and Hori’91, Lee’94  Internal model controller(IMC): Morari’89  Time-delayed estimation or time delay controller(TDC): Morgan and Ogzuner’85, Tsia’89, Youcef-Toumi and Ito’90  Adaptive inverse controller: Widraw’96  Adaptive robust controller(ARC): Yao and Tomizuka’97  Model-based disturbance attenuator(MBDA): Choi et al.’99  Robust internal-loop compensator(RIC): Kim et al.’01 • Inverse-plant-model-based ones: • Reference model following internal feedback controllers: Ph.D. Thesis Defence Mt., May 28, 2002

  10. Notion of Perturbation Observer Ph.D. Thesis Defence Mt., May 28, 2002

  11. Problem Statement “Hierarchical Perturbation Compensator (HPC)” Ph.D. Thesis Defence Mt., May 28, 2002

  12. Flow of Presentation Applications to Mechanical Systems Robust State Estimation with Perturbation Observer (Chap. 5) The Q-filter Effect on the Performance and Robustness (Chap. 4) Hierarchical Perturbation Compensator (Chap. 2) PART II. PART I. Extension to N-Loop Case: Multi-Loop Perturbation Compensator (Chap. 3) PART III. Ph.D. Thesis Defence Mt., May 28, 2002

  13. Three Points of View (FBPO) • FBPO input drives the inner loop to the nominal plant dynamics: • The existing class of perturbation observers fundamentally belongs to the FBPO. Ph.D. Thesis Defence Mt., May 28, 2002

  14. Three Points of View (FFPO) • FFPO input drives the inner loop to the desired plant dynamics: Ph.D. Thesis Defence Mt., May 28, 2002

  15. Three Points of View (SMPO) Ph.D. Thesis Defence Mt., May 28, 2002

  16. Hierarchical Perturbation Compensator (HPC) • Hierarchical loops to compensate residual perturbations. • Use of both preview and feedback signals. Ph.D. Thesis Defence Mt., May 28, 2002

  17. Hierarchical Perturbation Compensator (HPC) Ph.D. Thesis Defence Mt., May 28, 2002

  18. A Smooth Sliding Mode Control As the perturbation observer is hierarchically added, the control performance is gradually enhanced. Perturbation Compensated Sliding Mode Control (PCSMC) = Tracking control using the sliding surface + Perturbation Compensator instead of Discrete Switching Control. Ph.D. Thesis Defence Mt., May 28, 2002

  19. Stability Ph.D. Thesis Defence Mt., May 28, 2002

  20. Compensation Error Dynamics Robust stability condition (Limit of modeling error) Ph.D. Thesis Defence Mt., May 28, 2002

  21. Comparison (Result 1) Perturbation Observer relaxes the external disturbance condition. (Result 2) HPC reduces the robust stability margin on the inertia uncertainty. Ph.D. Thesis Defence Mt., May 28, 2002

  22. Frequency Response 1st order filter case 3rd order filter case Q-filter cut-off • (Result 3) HPC enhances the perturbation attenuation performance. • (Result 4) Performance significantly depends on the filter order. Ph.D. Thesis Defence Mt., May 28, 2002

  23. Comparative Experiment XY Positioner Circle tracking (encoder signal) + “Sinusoidal Disturbance” Reference traj. (R=500um, 30mm) Ph.D. Thesis Defence Mt., May 28, 2002

  24. Comparative Experiment Ph.D. Thesis Defence Mt., May 28, 2002

  25. Flow of Presentation Applications to Mechanical Systems Robust State Estimation with Perturbation Observer (Chap. 5) The Q-filter Effect on the Performance and Robustness (Chap. 4) Hierarchical Perturbation Compensator (Chap. 2) PART II. PART I. Extension to N-Loop Case: Multi-Loop Perturbation Compensator (Chap. 3) PART III. Ph.D. Thesis Defence Mt., May 28, 2002

  26. Extension to N-Loop Case:Multiloop Perturbation Compensator (MPEC) Performance Tuning: 1. Get the best performance of the 1st loop. 2. Do fine tuning through the next loops. Ph.D. Thesis Defence Mt., May 28, 2002

  27. Compensation Error Dynamics Ph.D. Thesis Defence Mt., May 28, 2002

  28. Sensitivity Change As n increases, perturbation attenuation performance is gradually enhanced Ph.D. Thesis Defence Mt., May 28, 2002

  29. Stability Margin As the number of loops increases (n=1,2,3, …),  Control performance could be enhanced.  But, the robust stability margin is accordingly reduced. Ph.D. Thesis Defence Mt., May 28, 2002

  30. Experiment (XY Positioner) Reference trajectory Ph.D. Thesis Defence Mt., May 28, 2002

  31. Experiment (2 DOF DD Arm) Ph.D. Thesis Defence Mt., May 28, 2002

  32. Summary of PART I • Three kinds of viewpoint on the perturbation compensation.  Suggestion of FBPO, FFPO, SMPO • Suggestion of the notion of residual perturbation compensation and the hierarchical perturbation compensator (HPC).  It enables advanced motion control. • Extension to the general n-loop case: MPEC • Analytical and experimental results show the feasibility of the proposed schemes. Ph.D. Thesis Defence Mt., May 28, 2002

  33. Flow of Presentation The Q-filter Effect on the Performance and Robustness (Chap. 4) Applications to Mechanical Systems Robust State Estimation with Perturbation Observer (Chap. 5) Hierarchical Perturbation Compensator (Chap. 2) PART II. PART I. Extension to N-Loop Case: Multi-Loop Perturbation Compensator (Chap. 3) PART III. Ph.D. Thesis Defence Mt., May 28, 2002

  34. PART II. The Effect of Q-filter on the Performance and Robustness of Perturbation Observer Ph.D. Thesis Defence Mt., May 28, 2002

  35. Perturbation Observer Based Robust Control Q-filter (Critical tuning parameter) • It determines the performance and robustness of the perturbation compensation loop. • Still, we have no reliable guidelines for the discrete Q-filter. • The discrete-time effect of the perturbation observer such as disturbance observer or time-delayed estimation is still not so clear. Ph.D. Thesis Defence Mt., May 28, 2002

  36. A Discrete Perturbation Observer Ph.D. Thesis Defence Mt., May 28, 2002

  37. Perturbation Compensation Error Dynamics Ph.D. Thesis Defence Mt., May 28, 2002

  38. Perturbation Compensation Error Dynamics Ph.D. Thesis Defence Mt., May 28, 2002

  39. Stability • Error dynamics in matrix form: Ph.D. Thesis Defence Mt., May 28, 2002

  40. Binomial Filters Ph.D. Thesis Defence Mt., May 28, 2002

  41. Robustness Analysis Ph.D. Thesis Defence Mt., May 28, 2002

  42. Sensitivity Analysis The sensitivity is decreased (I.e., performance is enhanced) as the Q-filter has high numerator order. Q-filter cut-off freq. Ph.D. Thesis Defence Mt., May 28, 2002

  43. Effect of Sampling Frequency Change Q-filter cut-off freq. Continuous VS. Discrete System: Performance of continuous system is recovered in limited bandwidths. • Fast sampling extends the frequency band to the low frequency region. Case of 3rd order filters • The sampling freq. should be sufficiently high for the Q-filter with high numerator order to be effective. Ph.D. Thesis Defence Mt., May 28, 2002

  44. Transition of Sensitivity (Performance) Ph.D. Thesis Defence Mt., May 28, 2002

  45. Closed-loop Sensitivity Effect of inertia perturbation Ph.D. Thesis Defence Mt., May 28, 2002

  46. An Experiment XY Positioner + • Variation of tracking performance according to the filter order Ph.D. Thesis Defence Mt., May 28, 2002

  47. Summary of PART II • A transparent relationship between the performance and robustness.  Effect of Q-filter parameters.  Effect of digital control frequency.  Effect of plant parameter (inertia) perturbation. • A criteria to determine a proper discrete Q-filter which compromises the performance and robust stability. The discrete-time design and analysis of perturbation observer provides, Ph.D. Thesis Defence Mt., May 28, 2002

  48. Application to Micro-Teleoperation Acknowledgement: Many colleagues in POSTECH, Hanyang University, and KIST were involved in building up the experimental setup. We appreciate their devotion. Ph.D. Thesis Defence Mt., May 28, 2002

  49. Flow of Presentation Robust State Estimation with Perturbation Observer (Chap. 5) Discrete-time Analysis of the Q-filter (Chap. 4) Hierarchical Perturbation Compensator (Chap. 2) PART II. PART I. Extension to N-Loop Case: Multi-Loop Perturbation Compensator (Chap. 3) Applications to Mechanical Systems PART III. Ph.D. Thesis Defence Mt., May 28, 2002

  50. PART III. Robust State Estimation and Robust Kalman Filtering with Perturbation Observer Ph.D. Thesis Defence Mt., May 28, 2002

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