Intelligent Control for Magnetic Levitation System

NguyenHoSiHung TV pdf Master’s Thesis Graduate Institute of Digital Mechatronic Technology College of Engineering Chinese Culture University Intelligent Control for Magnetic Levitation System Advisor[.]

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Master’s Thesis Graduate Institute of Digital Mechatronic Technology

College of Engineering Chinese Culture University

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Intelligent Control for Magnetic Levitation System

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Advisor: Professor Jeng-Tze Huang

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Graduate Student: Nguyen Ho Si Hung

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June 2014

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ACKNOWLEDGMENTS

First of all, I would like to express my deepest gratitude to my research, Professor Zeng-Tze Huang, for giving me valuable advice, guidance, and encouragement on this research and influencing my way of thinking He helped me focus on this topic, gave

me the corrections by all his patience He taught me many things not only on my research but also on how an engineer and a researcher should be I have benefited from his vast wealth of knowledge and his constructive comments during this research

I would also like to thank to Shiu,Wei-Jen, assistant of the Graduate Institute of Digital Mechatronic Technology for her kindness and enthusiasm of providing me the useful and quick information, helping me to carry out all procedures of the graduation process

My thanks are extended research friends who helped me complete this thesis I’m very happy to get in Huang’s laboratory and meet the members Especially, Tran Van Hung and Nguyen Xuan Bao are the members who get in this laboratory at the same time I am very grateful their great support and kindness

Finally, I am thankful my parents, my brother, my sisters, girlfriend, all of my good friends and other relatives for their encouragement and support

Nguyen Ho Si Hung

June 27th 2014

ABSTRACT

This thesis presents an approach to control the magnetic levitation system (Maglev) with uncertainty To achieve precise control system, a neural network based intelligent control system was proposed to compensate the uncertainties First, the dynamic model of a magnetic levitation system was built Second, a sliding mode control (SMC) was applied to compensate the uncertainties that occurred in the magnetic levitation system The applied controller guarantees the stability of the system Moreover, to increase the robustness and to release the requirement of the uncertainty bound, a sliding mode control using a radial basic function network (SMCRBFN) is proposed The effectiveness was verified through the simulation and experimental results

Keywords: Magnetic levitation system (Maglev), sliding mode control (SMC), sliding

mode control using radial basic function network (SMCRBFN)

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CONTENTS

CHAPTER 1 : INTRODUCTION 5

1.1 Research background 5

1.2 ECP model 730 maglev machine 7

1.3 Motivation, methodologies and resources 8

1.3.1 Motivation 8

1.3.2 Task execution methodology 9

1.3.2.1 Research methodology 9

1.3.2.2 Approach analysis 9

1.3.2.3 Execution 9

1.3.2.4 Review 9

1.3.3 Resource analysis 10

1.3.3.1 Maglev apparatus 10

1.3.3.2 ECP control system software 11

1.3.3.3 MATLAB program and computer system 12

1.3.3.4 Data storage and protection 12

CHAPTER 2 : LITERATURE REVIEW 14

2.1 Sliding model control 14

2.2 Neural network 16

CHAPTER 3 : ECP MODEL 730 MAGLEV 21

3.1 ECP model 730 Maglev 21

3.1.1 Introduction 21

3.1.2 System overview 22

3.1.3 Electromechanical plant 22

3.1.4 ECP executive software 23

3.2 Dynamic system of the Maglev 24

3.2.1 ECP model 730 Maglev machine 24

3.2.2 Nonlinear actuator (coil) characteristic 26

3.2.3 Linearization using Taylor’ Series expansion 29

3.2.4 Nonlinear model of Maglev 31

3.2.5 Test Maglev model with simple algorithm 31

3.2.5.1 Test model at equilibrium positions 31

3.2.5.2 Test model by PID 33

CHAPTER 4 : CONTROL DESIGN 35

4.1 Design sliding mode controller 35

4.1.1 Theory 35

4.1.2 Design sliding mode controller for Maglev 37

4.1.2.1 Design control law of SMC 37

4.1.2.2 Stability of the robust sliding mode controller 39

4.2 Sliding mode control using RBF neural network 41

4.2.1 Theory 41

4.2.1.1 Problem statement 41

4.2.1.2 Controller design based on a radial basic function neural network 42

4.2.2 Design sliding mode control based on RBF neural network for Maglev 44

4.2.2.1 Design control law of SMCRBFN 44

4.2.2.2 Stability of SMCRBFN 47

CHAPTER 5 : SIMULATION AND EXPERIMENTAL RESULTS 49

5.1 Simulation and plant comparison 49

5.2 Simulation results 52

5.2.1 Simulation of sliding mode controller 52

5.2.2 Simulation of SMCRBFN 54

5.2 Experimental results 56

5.2.1 PID control 56

5.2.2 SMC control 60

5.2.3 SMCRBFN controller 64

5.3 Analysis and evaluation of results 68

CHAPTER 6 : CONCLUSION AND FUTURE WORKS 70

6.1 Conclusion 70

6.2 Further works 72

REFERENCE 73

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LIST OF FIGURES

Figure 1.1 : Transrapid Maglev 6

Figure 1.2 : Magnetic Levitation System 7

Figure 1.3: ECP Model 730 Magnetic Levitation Plant 10

Figure 1.4: ECP Control System Software 11

Figure 2.1: An approaching phase (a) and sliding phase (b) 15

Figure 2.2: Structure of a neuron 17

Figure 2.3: Structure of a multilayer feed-forward neural network 18

Figure 3.1: The model 730 Experimental Control System 21

Figure 3.2: MagLev Apparatus, side view (a) and front view (b) (Source: Educational Control Products 1999) 23

Figure 3.3: Free-body diagram 24

Figure 3.4 : Free-body diagram with a magnet 25

Figure 3.5: Physical measurements obtained from the Maglev plant 27

Figure 3.6: Representation of the estimated curve against the experimental data 28

Figure 3.7: Taylor’s linearization theorem representation, about point A (2 cm) 30

Figure 3.8: Nonlinear model of Maglev 31

Figure 3.9: Actuator Characteristics, measured data 32

Figure 3.10: Nonlinear Actuator Characteristic 33

Figure 3.11: Characteristic of simulation model and real system 33

Figure 3.12: Performance of PID through simulation program 34

Figure 3.13: Performance of PID through experimental program 34

Figure 4.1 : Free Body Diagram and Dynamic Configuration 37

Figure 4.2: Sliding mode controller 41

Figure 4.3 : Network structure of an RBFN 45

Figure 4.4 : Control block diagram of an SMCRBFN 46

Figure 5.1: Performance of simulation model with sampling time tdesign=0.0071s (a) and tdesign=0.001768s (b) 50

Figure 5.2: Error of simulation model with sampling time tdesign=0.0071s (a) and tdesign=0.001768s (b) 51

Figure 5.3 : Simulation results of an SMC system due to periodic step command 52

Figure 5.4 : Simulation results of an SMC system due to periodic sinusoidal command 53

Figure 5.5 : Simulation results of an SMC system due to periodic trapezoidal

command 53 Figure 5.6 : Simulation results of an SMCRBFN system due to periodic step command 54 Figure 5.7 : Simulation results of an SMCRBFN system due to periodic sinusoidal command 55 Figure 5.8 : Simulation results of an SMCRBFN system due to periodic trapezoidal command 55 Figure 5.9 : Performance (a) and error (b) of PID due to step command in case 1 56 Figure 5.10: Performance (a) and error (b) of PID due to sinusoidal command in case

1 57 Figure 5.11 : Performance (a) and error (b) of PID due to trapezoidal command in case

1 57 Figure 5.12 : Performance (a) and error (b) of PID due to step command in case 2 58 Figure 5.13 : Performance (a) and error (b) of PID due to sinusoidal command in case

2 59 Figure 5.14 : Performance (a) and error (b) of PID due to trapezoidal command in case

2 59 Figure 5.15: Performance (a) and error (b) of SMC due to step command in case 1 60 Figure 5.16: Performance (a) and error (b) of SMC due to sinusoidal command in case

1 61 Figure 5.17 : Performance (a) and error (b) of SMC due to trapezoidal command in case 1 61 Figure 5.18 : Performance (a) and error (b) of SMC due to step command in case 2 62 Figure 5.19: Performance (a) and error (b) of SMC due to sinusoidal command in case

2 63 Figure 5.20: Performance (a) and error (b) of SMC due to trapezoidal command in case 2 63 Figure 5.21 : Performance (a) and error (b) of SMCRBFN due to step command in case 1 64 Figure 5.22 : Performance (a) and error (b) of SMCRBFN due to sinusoidal command

in case 1 65 Figure 5.23: Performance (a) and error (b) of SMCRBFN due to trapezoidal command

in case 1 65

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Figure 5.24 : Performance (a) and error (b) of SMCRBFN due to step command in case 2 66 Figure 5.25 : Performance (a) and error (b) of SMCRBFN due to sinusoidal command

in case 2 67 Figure 5.26: Performance (a) and error (b) of SMCRBFN due to trapezoidal command

in case 2 67

LIST OF TABLES

Table 3.1: Definition of Maglev plant-specific variables 25

Table 3.2: Relation between position and control effort 28

Table 5.1: Performance measures of PID in case 1 58

Table 5.2: Performance measures of PID in case 2 60

Table 5.3: Performance measures of SMC in case 1 62

Table 5.4: Performance measures of SMC in case 2 64

Table 5.5: Performance measures of SMCRBFN in case 1 66

Table 5.6: Performance measures of SMCRBFN in case 2 68