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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Integer Order PID Controller Design 16

Integer Order PID Controller Design 17

Integer Order PID Controller Design 18

Integer Order PID Controller Design 19

Integer Order PID Controller Design 20

Integer Order PID Controller Design 21

Integer Order PID Controller Design 22

Integer Order PID Controller Design 23

Integer Order PID Controller Design 24

Integer Order PID Controller Design 25

Integer Order PID Controller Design 26

Integer Order PID Controller Design 27

Integer Order PID Controller Design 28

Integer Order PID Controller Design 29

Integer Order PID Controller Design 30

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

Fractional Order PD Controller Design 32

Fractional Order PD Controller Design 33

Fractional Order PD Controller Design 34

Fractional Order PD Controller Design 35

Fractional Order PD Controller Design 36

Fractional Order PD Controller Design 37

Fractional Order PD Controller Design 38

Fractional Order PD Controller Design 39

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

Fractional Order (PD) Controller Design 41

Fractional Order (PD) Controller Design 42

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Fractional Order (PD) Controller Design 44

Fractional Order (PD) Controller Design 45

Fractional Order (PD) Controller Design 46

Fractional Order (PD) Controller Design 47

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Fractional Order (PD) Controller Design 49

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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

Implementation of Two Fractional Operators 53

Implementation of Two Fractional Operators 54

Implementation of Two Fractional Operators 55

Implementation of Two Fractional Operators 56

Implementation of Two Fractional Operators 57

Implementation of Two Fractional Operators 58

Implementation of Two Fractional Operators 59

Implementation of Two Fractional Operators 60

Implementation of Two Fractional Operators 61

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

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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

Experiment 86

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Experiment 91

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

Conclusion 93

Thanks for your attention ! 94