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Title Page

Abstract

Contents

1. Introduction 12

2. Preliminaries 15

2.1. Time Delay Estimation (TDE) 15

2.2. Nussbaum function and modified Nussbaum function 16

3. Physically meaningful, practical, and adaptive PID control robust against significant inertia change based on Nussbaum function with TDE 18

3.1. The auto-tuning algorithm of a time-delay controller using a modified Nussbaum function. 18

3.2. Physically meaningful, practical, and adaptive PID control. 19

3.2.1. Modified auto-tuning algorithm with the forgetting factor 19

3.2.2. Adaptive PID gain selection using a systematic discrete PID gain selection method. 20

3.3. Tuning procedure 21

3.4. Discussion 22

4. Simulation 23

4.1. Simulation setup 23

4.2. Simulation results 26

4.2.1. Simulation results 26

4.3. Simulation with various combination of update gain 27

4.3.1. Simulation with various combinations of γ. 27

4.3.2. Simulation with various combinations of η. 28

4.4. Conclusion 30

5. Experiment 31

5.1. Experiment setup 31

5.1.1. Experiment under payload condition 32

5.1.2. Experiment results under payload condition 33

5.1.3. Experiment with other Nussbaum function 38

5.2. Experiment under spring condition 40

5.2.1. Experiment setup 40

5.2.2. Experiment results 41

6. Discussion 44

6.1. Advantages 44

6.2. The gains of the proposed PID control 45

7. Conclusion 46

8. Appendix: Stability proof 47

9. Reference 51

Curriculum Vitae 55

Education 55

Award 55

List of Tables

Table 1. Specification of 2 DOF Direct-drive planar robot manipulator 23

Table 2. Specification of 2-DOF Direct-Drive planar robot manipulator. 31

Table 3. Root Mean Square of Peak error at last cycle of proposed PID, constant gain PID tuned... 34

Table 4. Root Mean Square of peak errors at the last cycle. The modified Nussbaum function... 39

Table 5. Root Mean Square of Peak error at the last cycle of proposed PID, and constant gain PID... 41

List of Figures

Figure 1. Modified Nussbaum function ζ²sin(π/2ζ).[이미지참조] 16

Figure 2. 2 DOF planar Direct-Drive planar robot manipulator 23

Figure 3. Desired joint angle trajectory of simulation and experiment 25

Figure 4. The scenario of simulation 25

Figure 5. Angular position error of proposed PID control and the KP gain of the proposed control.[이미지참조] 26

Figure 6. The error dynamics, v, and sliding variable,s, of the proposed control. 26

Figure 7. The KP gain of proposed control with various combinations of γ.[이미지참조] 27

Figure 9. The angular position errors of proposed control with various combinations of γ when... 28

Figure 10. The angular position errors of proposed control with various combinations of γ when... 28

Figure 11. The KP gain of proposed control with various combinations of η.[이미지참조] 29

Figure 12. The angular position errors of proposed control with various combinations of η. 29

Figure 13. The angular position errors of proposed control with various combinations of η when... 29

Figure 14. The angular position errors of proposed control with various combinations of η when... 29

Figure 15. Experiment setup. 2-DOF Direct-Drive planar robot 31

Figure 16. Angular position error of proposed PID control (red solid), constant gain PID control... 33

Figure 17. Root mean square of Peak Error Ratio (RPER) of proposed control to constant gain... 33

Figure 18. Control gain of proposed PID control (red solid), constant gain PID control (blue dot),... 35

Figure 19. Error dynamics and sliding variable of the proposed control (red solid), and constant... 36

Figure 20. Control input and derivative of control input of proposed control (red solid), and... 37

Figure 21. Angular position error and gain KP of modified Nussbaum function...[이미지참조] 38

Figure 22. Angular position error and gain KP of modified Nussbaum function...[이미지참조] 38

Figure 23. Experiment setup with the spring 40

Figure 24. The desired trajectory of the spring experiment 40

Figure 25. Angular position error of proposed PID control (red solid), and constant gain PID... 41

Figure 26. Control gain of proposed PID control (red solid), and constant gain PID control (blue dot) 42

초록보기

This thesis proposes a physically meaningful, practical, and adaptive Proportional-Integral-Derivative (PID) control robust against significant changes in external and robot dynamics. The proposed PID control achieved robustness against significant inertia change and external disturbance force with Nussbaum based adaptive control law. Considering the practical implementation problem in a digital platform caused by measurement, quantization, and numerical calculation noise, the forgetting factor is applied in the proposed PID control. The forgetting factor of the proposed control law prevents incorrect gain calculation and gain drift by measurement, quantization, and numerical calculation noise that cannot represent the current system state. Furthermore, thanks to Time-Delay Estimation (TDE), the proposed PID control practically can be implemented in a digital system as it does not require an accurate robot model and complicated dynamics calculation. Besides, there are only two meaningful tuning parameters that are tuned by trial-and-error. The robustness against a significant robot and external dynamics variation verified with the simulation and experimental studies with 2 Degree-Of-Freedom (DOF) Direct-Drive planner robot. The simulation results showed that the proposed PID control robust against a significant robot and external dynamics changes. The experiment results showed that the proposed PID control achieves high robustness against significant robot dynamics changes, compared to the constant PID control.

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