1. A Fractional Order (Proportional and Derivative) Motion Controller Design for A Class of Second-order Systems Center for Self-Organizing Intelligent Systems (CSOIS), Dep. Electrical and Computer Engineering, Utah State University, Logan, UT, USA. Ying Luo

2. Outline
Introduction
Typical second-order system concerned and the specifications for the three controllers design
Integer Order PID Controller Design
Fractional Order PD Controller Design
Fractional Order (PD) Controller Design
Implementation of Two Fractional Order Operators for Two Fractional Order Controllers
Simulation
Experiment
Conclusion 2

3. Outline
Introduction
Typical second-order system concerned and the specifications for the three controllers design
Integer Order PID Controller Design
Fractional Order PD Controller Design
Fractional Order (PD) Controller Design
Implementation of Two Fractional Order Operators for Two Fractional Order Controllers
Simulation
Experiment
Conclusion 3

4. Introduction In this work, practical and systemic design methods of
integer order PID (IO-PID) controller, fractional order proportional and derivative (FO-PD) controller and fractional
order (proportional and derivative) controller for a typical
second-order plant are proposed. The control performances with the proposed two fractional order controllers
and the traditional IO-PID controller which are all properly
designed are compared fairly through the simulation and
experiment.
The two fractional order controllers can achieve much better dynamic performance and robustness over the traditional IO-PID controller. Furthermore, the proposed fractional order (proportional and derivative) (FO-(PD)) controller performances even better then the FO-PD controller. 4

5. Introduction The major contributions of this work include:
1) Practical and systemic design procedures of IO-PID, FOPD and FO-(PD) controllers for a class of typical second order plants;
2) Simulation fair comparison of performances with the proposed two fractional order controllers and the traditional IO-PID controller;
3) Experiment verification of the proposed FO-(PD) controller on the real-time dynamometer position control system;
4) Demonstration of the advantage of the FO-(PD) controller performing the simulation and experimental comparisons with the traditional IO-PID controller and the FO-PD controller. 5

6. Outline
Introduction
Typical second-order system concerned and the specifications for the three controllers design
Integer Order PID Controller Design
Fractional Order PD Controller Design
Fractional Order (PD) Controller Design
Implementation of Two Fractional Operators for Two Fractional Order Controllers
Simulation
Experiment 6

7. Typical second-order system concerned and the specifications for the three controllers design7

8. Typical second-order system concerned and the specifications for the three controllers design8

9. Typical second-order system concerned and the specifications for the three controllers design9

10. Typical second-order system concerned and the specifications for the three controllers design10

11. Typical second-order system concerned and the specifications for the three controllers design11

12. Typical second-order system concerned and the specifications for the three controllers design12

13. Typical second-order system concerned and the specifications for the three controllers design13

14. Typical second-order system concerned and the specifications for the three controllers design14

15. Outline
Introduction
Typical second-order system concerned and the specifications for the three controllers design
Integer Order PID Controller Design
Fractional Order PD Controller Design
Fractional Order (PD) Controller Design
Implementation of Two Fractional Operators for Two Fractional Order Controllers
Simulation
Experiment
Conclusion 15

16. Integer Order PID Controller Design16

17. Integer Order PID Controller Design17

18. Integer Order PID Controller Design18

19. Integer Order PID Controller Design19

20. Integer Order PID Controller Design20

21. Integer Order PID Controller Design21

22. Integer Order PID Controller Design22

23. Integer Order PID Controller Design23

24. Integer Order PID Controller Design24

25. Integer Order PID Controller Design25

26. Integer Order PID Controller Design26

27. Integer Order PID Controller Design27

28. Integer Order PID Controller Design28

29. Integer Order PID Controller Design29

30. Integer Order PID Controller Design30

31. Outline
Introduction
Typical second-order system concerned and the specifications for the three controllers design
Integer Order PID Controller Design
Fractional Order PD Controller Design
Fractional Order (PD) Controller Design
Implementation of Two Fractional Operators for Two Fractional Order Controllers
Simulation
Experiment
Conclusion 31

32. Fractional Order PD Controller Design32

33. Fractional Order PD Controller Design33

34. Fractional Order PD Controller Design34

35. Fractional Order PD Controller Design35

36. Fractional Order PD Controller Design36

37. Fractional Order PD Controller Design37

38. Fractional Order PD Controller Design38

39. Fractional Order PD Controller Design39

40. Outline
Introduction
Typical second-order system concerned and the specifications for the three controllers design
Integer Order PID Controller Design
Fractional Order PD Controller Design
Fractional Order (PD) Controller Design
Implementation of Two Fractional Operators for Two Fractional Order Controllers
Simulation
Experiment
Conclusion 40

41. Fractional Order (PD) Controller Design41

42. Fractional Order (PD) Controller Design42

43. Fractional Order (PD) Controller Design43

44. Fractional Order (PD) Controller Design44

45. Fractional Order (PD) Controller Design45

46. Fractional Order (PD) Controller Design46

47. Fractional Order (PD) Controller Design47

48. Fractional Order (PD) Controller Design48

49. Fractional Order (PD) Controller Design49

50. Fractional Order (PD) Controller Design50

51. Fractional Order (PD) Controller Design51

52. Outline
Introduction
Typical second-order system concerned and the specifications for the three controllers design
Integer Order PID Controller Design
Fractional Order PD Controller Design
Fractional Order (PD) Controller Design
Implementation of Two Fractional Operators for Two Fractional Order Controllers
Simulation
Experiment
Conclusion 52

53. Implementation of Two Fractional Operators53

54. Implementation of Two Fractional Operators54

55. Implementation of Two Fractional Operators55

56. Implementation of Two Fractional Operators56

57. Implementation of Two Fractional Operators57

58. Implementation of Two Fractional Operators58

59. Implementation of Two Fractional Operators59

60. Implementation of Two Fractional Operators60

61. Implementation of Two Fractional Operators61

62. Outline
Introduction
Typical second-order system concerned and the specifications for the three controllers design
Integer Order PID Controller Design
Fractional Order PD Controller Design
Fractional Order (PD) Controller Design
Implementation of Two Fractional Operators for Two Fractional Order Controllers
Simulation
Experiment
Conclusion 62

63. Simulation 63

64. Simulation 64

65. Simulation 65

66. Simulation 66

67. Simulation 67

68. Simulation 68

69. Simulation 69

70. Simulation 70

71. Simulation 71

72. Simulation 72

73. Simulation 73

74. Simulation 74

75. Simulation 75

76. Simulation 76

77. Simulation 77

78. Simulation 78

79. Simulation 79

80. Simulation 80

81. Simulation 81

82. Simulation 82

83. Simulation 83

84. Simulation 84

85. Outline
Introduction
Typical second-order system concerned and the specifications for the three controllers design
Integer Order PID Controller Design
Fractional Order PD Controller Design
Fractional Order (PD) Controller Design
Implementation of Two Fractional Operators for Two Fractional Order Controllers
Simulation
Experiment
Conclusion 85

86. Experiment 86

87. Experiment 87

88. Experiment 88

89. Experiment 89

90. Experiment 90

91. Experiment 91

92. Outline
Introduction
Typical second-order system concerned and the specifications for the three controllers design
Integer Order PID Controller Design
Fractional Order PD Controller Design
Fractional Order (PD) Controller Design
Implementation of Two Fractional Operators for Two Fractional Order Controllers
Simulation
Experiment
Conclusion 92

93. Conclusion 93

94. Thanks for your attention !94