43 Figtue 4.33 Comparison betweơn obsorver and posilion of x axis with Fa 30N 44 Figure 4.34 Comparison between observer and velocity of x axis with Fg=30N 44 Figure 4.35 Comparison bet
Trang 1TIANOI UNIVERSITY OF SCIENCE AND TECIINOLOGY
Control Engineering and Automation
Supervisor: Dr Nguyen Danh Huy
Superviser’s signature
School School of Flectrical and Electronie Bnginteering
Hanoi, 03/2023
Trang 2CONG HOA XÃ HOI CHU NGHIA VIRT NAM
Độc lập - Tự do— Hạnh phúc
BẢN XÁC NHẬN CHỈNH SỬA LUẬN VĂN THẠC SĨ
Tọ và tên tác giá luận văn: Tạ Thế Tải
Đề
Chuyên ngành: Kỹ thuật điều khiến và tự động hóa
Mã số SV: 20212587M
luận văn: Điều khiển hệ thống ô từ chủ động hình nón
‘Tac gia, Người hướng dẫn khoa học vả Liệt đồng chấm luận vẫn xác
nhận tác giả đã sửa chữa, bổ sung luận văn theo biên bản hợp Hội đồng ngày 28/04/2023 với các nội dung sau:
-_ Sữa số thứ tự các phương trình trong chương 2 và chương 3
Mô tâ thêm các kết quã mỗ phỏng trong các kịch bản mô phỏng
( Hìmh 4.2 đến 4 S5)
Neay tháng năm Giáo viên hướng dẫn 'Tác giá luận văn
CHỦ TỊCH HỘI ĐÓNG
Mẫu lc
Trang 3THESIS TOPIC Nonlinear control of conical magnetic bearing systems
Supervisor
Trang 433 Conclusion 28 CHAPTER 4 NUMERICAL SIMULATION STUDY
4.2 Resulis and Discussiot con non ¬-
CHAPTER § CONCLUSIONS AND FUTURE WORKS
Trang 5TABLE OF CONTENT CHAPTER 1 INIRODUCTION
11 State of the aFt ào
1.11 IaodueHonof Active Maenetic Hearing
Í
1.12 Principles of Magnetic Bearing Function
1.13 Advantages and disadvantages of AMBs
1.15 Conical Magnetic Bearings: An overview 4 1.16 Fundamental of Sliding Mode Control 7
118 — Extended state cbserver wd
Linearized bearing forces sec TỔ
Extcrnal đisturbaiiccs c cocociecccecree ¬ 4
Magnetic bearings actuation - - 22
CHAPTER 3 EXTENDED STATE OBSERVER BASED CONTROL
eu 24 Extended state observer, seven ¬ 3.2 Kracuonal Order Bliding Mode Contol
3.21 Principle of Sliding Mode Conuol and Chattering Problem
Trang 6
LIST OF FIGURES Figure 1.1 Active magnetic bearings in compressor [6j
Figure 1.2 Munction principle of an active electromagnetic bearing [3]
Figure 1.3 Applications of AMBs
Figure 1.4 System with cylindrical AMEs [14]
Figure 1.5 System conical AMBs [15] (1) impeller, (2) centering tip; (3) conical
geometry: (1) rotor; (5) electric motor, (6) magnetic actuators
Figure 2.1 AMBs structure with single-DOF
Figure 2.2 Simple electromagnet structure
Tigure 2.3 Sehematie of conical active rnagnetic bearing Íorcs
Figure 2.4 Ihustration of unbalanee rotor
Figure 4.2 Response to the position z, x, y
Figure 4.3 Response (o the position of the axis angle 6, ,Ay
Figure 4.4 Upper control currents response
Figure 4.5 Under control currents response .jsssssssiessstsoneeineen
Figure 4.6 Upper impact forces of electromagnsts
Figure 4.7 Under impact forces of electromagnets
Figure 4.8 Comparison betwoon observer and response position of z
Figure 4.9 Comparison between observer and response position af x
Figure 4.10 Comparison between observer and response position of y
Figure 4.11 Comparison between observer aud response position of x
Figure 4.12 Comparison between observer and respanse position of 0y
Figure 4.13 Comparison between observer and response velocity of z
Figure 4.14 Comparison between observer and response velocity of x
Figure 4.15 Comparison between observer and response velocity of y
Figure 4.16 Comparison between observer and response velocity of 8x
Figure 4.17 Comparison between observer and response velocity of Gy
Figure 4.18 Comparison between sign and sigmoid function
Figure 4.19 7, axis transionl response under the parameter uncerlaintics
Figure 4.20 X axis transient response under the parameter uncertairilics
Figure 4.21 Y axis transient response under the parameter uncertainties
Figure 4.22 Ox axis transient response under the parameter uncertainties
5
11
12
„Ö l$ 1d
20
31
Trang 7Figure 4.23 @y axis transient response under the parameter uncertainties
Figure 4.24 Upper current response under the parameter uncertainties
Figure 4.25 Under current response under the parameter uncertainties
Figure 4.26 Lixternal force Fa=30N oo ee cceccseteens cere ieeesiees
Figure 4.27 ADRC controller position response under Tu=30N
Figure 4.28 SMC controller position response under Fa=30N
Figure 4.29 FOSMC controller position response under Fa-30N
Figure 4.30 Current response with ADRC controller under Fa=30N
Figure 4.31 Current response with SMC controller under Fy 30N-
Figure 4.32 Current response with FOSMC controller under Fg-30N 43
Figtue 4.33 Comparison betweơn obsorver and posilion of x axis with Fa 30N 44
Figure 4.34 Comparison between observer and velocity of x axis with Fg=30N 44 Figure 4.35 Comparison between observer and disturbance of x axis with Fa=30N
Figure 4.37 ADRC controller position response under #a-10UN 0
Figure 4.38 SMC controller position respouse under Fa 100N
Figure 4.39 FOSMC controller position response under Fa—100N
Figure 4.40 Current response with ADRC controller under Fa TOON
Figure 4.41 Current response with SMC controller under Fa=100N
Figure 4.12 Current response with FOSMC controller under Pa-L00N
Figure 4.43 Comparison between observer and position of x axis with Fa-100N
Figure 4.47 ADRC controller position response under hydrodynamic force
Figure 4.48 SMC controller position response under hydrodynamic force
Trang 8TABLE OF CONTENT CHAPTER 1 INIRODUCTION
11 State of the aFt ào
1.11 IaodueHonof Active Maenetic Hearing
Í
1.12 Principles of Magnetic Bearing Function
1.13 Advantages and disadvantages of AMBs
1.15 Conical Magnetic Bearings: An overview 4 1.16 Fundamental of Sliding Mode Control 7
118 — Extended state cbserver wd
Linearized bearing forces sec TỔ
Extcrnal đisturbaiiccs c cocociecccecree ¬ 4
Magnetic bearings actuation - - 22
CHAPTER 3 EXTENDED STATE OBSERVER BASED CONTROL
eu 24 Extended state observer, seven ¬ 3.2 Kracuonal Order Bliding Mode Contol
3.21 Principle of Sliding Mode Conuol and Chattering Problem
Trang 9
Table 4.2 The coniroi performanee benchmark in sccnari
Table 4.3 The control performance benohmiark _ - - 53
Trang 10Acknowledgment
I would like to thank Tanoi University of Science and Technology for building, maintaining, and developing a leading research and studying envirorment Also, thanks to the School of Electrical Enginccring and the Department of Industrial Automation teachers for teaching and imparting necessary knowledge from fundamental to in-depth In particular, many thanks to my supervisor, Dr Nguyen Danh Huy las oriented, guided, encouraged, and helped me throughout the process
of studying, researching, and completing the thesis ‘The knowledge, challenges, and experiences in studying and researching at the university will be a solid foundation and valuable experierwe for me to continue with iny research and
development orientation
Abstract
Aclive magnetic bearmgs (AMBs) are clectromagnetic mechanism systems in
which non-contact bearings support a rotating shaft using atwactive forces
generated by electromagnets through closed-loop control For complete support of
a five-degree of freedom (DOF) rotor system, most AMB structures imclude two
radial actuators and one for the axial direction Conical active magnetic bearing (CAMB) is one of the development directions of conventional magnetic bearings
in which the requirement of the axial bearing can be elimmated Due to the
nonlinearities and inherett coupling properlics of cornaal aetrve magnetic bearing system, it is essential to accomplish an appropriate mathematical model as well as
design a high accuracy control scheme In this thesis, extended state observer
(FSO) is applied to deal with the lumped disturbances of CAMB system which
come from extemal disturbances, uncertain electromagnetic forces and parametric
uncertainties The convergence properties of the tracking error are analytically
proven using Lyapunov’s theory Based on extended state observer, a fractional
order sliding mode control (FOSMC) is designed to achieve fast response and minimize tracking errors as well as better control quantity without chattering The
control performance of the proposed FOSMC-ESO is illustrated in Ierrns of very
good disturbance rejection capabilily that is demonstrated through
MATLAB/Simulink simulation results In addition, comparative simulations
combine wilh three performance indices are performed to quantitatively evaluate
the tracking performance of proposed controllers against SMC and ADRC controllers
Author
Trang 11Figure 4.23 @y axis transient response under the parameter uncertainties
Figure 4.24 Upper current response under the parameter uncertainties
Figure 4.25 Under current response under the parameter uncertainties
Figure 4.26 Lixternal force Fa=30N oo ee cceccseteens cere ieeesiees
Figure 4.27 ADRC controller position response under Tu=30N
Figure 4.28 SMC controller position response under Fa=30N
Figure 4.29 FOSMC controller position response under Fa-30N
Figure 4.30 Current response with ADRC controller under Fa=30N
Figure 4.31 Current response with SMC controller under Fy 30N-
Figure 4.32 Current response with FOSMC controller under Fg-30N 43
Figtue 4.33 Comparison betweơn obsorver and posilion of x axis with Fa 30N 44
Figure 4.34 Comparison between observer and velocity of x axis with Fg=30N 44 Figure 4.35 Comparison between observer and disturbance of x axis with Fa=30N
Figure 4.37 ADRC controller position response under #a-10UN 0
Figure 4.38 SMC controller position respouse under Fa 100N
Figure 4.39 FOSMC controller position response under Fa—100N
Figure 4.40 Current response with ADRC controller under Fa TOON
Figure 4.41 Current response with SMC controller under Fa=100N
Figure 4.12 Current response with FOSMC controller under Pa-L00N
Figure 4.43 Comparison between observer and position of x axis with Fa-100N
Figure 4.47 ADRC controller position response under hydrodynamic force
Figure 4.48 SMC controller position response under hydrodynamic force
Trang 12Figure 4.23 @y axis transient response under the parameter uncertainties
Figure 4.24 Upper current response under the parameter uncertainties
Figure 4.25 Under current response under the parameter uncertainties
Figure 4.26 Lixternal force Fa=30N oo ee cceccseteens cere ieeesiees
Figure 4.27 ADRC controller position response under Tu=30N
Figure 4.28 SMC controller position response under Fa=30N
Figure 4.29 FOSMC controller position response under Fa-30N
Figure 4.30 Current response with ADRC controller under Fa=30N
Figure 4.31 Current response with SMC controller under Fy 30N-
Figure 4.32 Current response with FOSMC controller under Fg-30N 43
Figtue 4.33 Comparison betweơn obsorver and posilion of x axis with Fa 30N 44
Figure 4.34 Comparison between observer and velocity of x axis with Fg=30N 44 Figure 4.35 Comparison between observer and disturbance of x axis with Fa=30N
Figure 4.37 ADRC controller position response under #a-10UN 0
Figure 4.38 SMC controller position respouse under Fa 100N
Figure 4.39 FOSMC controller position response under Fa—100N
Figure 4.40 Current response with ADRC controller under Fa TOON
Figure 4.41 Current response with SMC controller under Fa=100N
Figure 4.12 Current response with FOSMC controller under Pa-L00N
Figure 4.43 Comparison between observer and position of x axis with Fa-100N
Figure 4.47 ADRC controller position response under hydrodynamic force
Figure 4.48 SMC controller position response under hydrodynamic force
Trang 13Figure 4.53 Comparison between observer and response position of x axis with
Figure 4.54 Comparison between observer and response velocity of x axis with
Figure 4.55 Comparison belween observer and real disturbance of x axis with
Trang 14TABLE OF CONTENT CHAPTER 1 INIRODUCTION
11 State of the aFt ào
1.11 IaodueHonof Active Maenetic Hearing
Í
1.12 Principles of Magnetic Bearing Function
1.13 Advantages and disadvantages of AMBs
1.15 Conical Magnetic Bearings: An overview 4 1.16 Fundamental of Sliding Mode Control 7
118 — Extended state cbserver wd
Linearized bearing forces sec TỔ
Extcrnal đisturbaiiccs c cocociecccecree ¬ 4
Magnetic bearings actuation - - 22
CHAPTER 3 EXTENDED STATE OBSERVER BASED CONTROL
eu 24 Extended state observer, seven ¬ 3.2 Kracuonal Order Bliding Mode Contol
3.21 Principle of Sliding Mode Conuol and Chattering Problem
Trang 15
TABLE OF CONTENT CHAPTER 1 INIRODUCTION
11 State of the aFt ào
1.11 IaodueHonof Active Maenetic Hearing
Í
1.12 Principles of Magnetic Bearing Function
1.13 Advantages and disadvantages of AMBs
1.15 Conical Magnetic Bearings: An overview 4 1.16 Fundamental of Sliding Mode Control 7
118 — Extended state cbserver wd
Linearized bearing forces sec TỔ
Extcrnal đisturbaiiccs c cocociecccecree ¬ 4
Magnetic bearings actuation - - 22
CHAPTER 3 EXTENDED STATE OBSERVER BASED CONTROL
eu 24 Extended state observer, seven ¬ 3.2 Kracuonal Order Bliding Mode Contol
3.21 Principle of Sliding Mode Conuol and Chattering Problem
Trang 16
Figure 4.53 Comparison between observer and response position of x axis with
Figure 4.54 Comparison between observer and response velocity of x axis with
Figure 4.55 Comparison belween observer and real disturbance of x axis with
Trang 1733 Conclusion 28 CHAPTER 4 NUMERICAL SIMULATION STUDY
4.2 Resulis and Discussiot con non ¬-
CHAPTER § CONCLUSIONS AND FUTURE WORKS
Trang 18LIST OF FIGURES Figure 1.1 Active magnetic bearings in compressor [6j
Figure 1.2 Munction principle of an active electromagnetic bearing [3]
Figure 1.3 Applications of AMBs
Figure 1.4 System with cylindrical AMEs [14]
Figure 1.5 System conical AMBs [15] (1) impeller, (2) centering tip; (3) conical
geometry: (1) rotor; (5) electric motor, (6) magnetic actuators
Figure 2.1 AMBs structure with single-DOF
Figure 2.2 Simple electromagnet structure
Tigure 2.3 Sehematie of conical active rnagnetic bearing Íorcs
Figure 2.4 Ihustration of unbalanee rotor
Figure 4.2 Response to the position z, x, y
Figure 4.3 Response (o the position of the axis angle 6, ,Ay
Figure 4.4 Upper control currents response
Figure 4.5 Under control currents response .jsssssssiessstsoneeineen
Figure 4.6 Upper impact forces of electromagnsts
Figure 4.7 Under impact forces of electromagnets
Figure 4.8 Comparison betwoon observer and response position of z
Figure 4.9 Comparison between observer and response position af x
Figure 4.10 Comparison between observer and response position of y
Figure 4.11 Comparison between observer aud response position of x
Figure 4.12 Comparison between observer and respanse position of 0y
Figure 4.13 Comparison between observer and response velocity of z
Figure 4.14 Comparison between observer and response velocity of x
Figure 4.15 Comparison between observer and response velocity of y
Figure 4.16 Comparison between observer and response velocity of 8x
Figure 4.17 Comparison between observer and response velocity of Gy
Figure 4.18 Comparison between sign and sigmoid function
Figure 4.19 7, axis transionl response under the parameter uncerlaintics
Figure 4.20 X axis transient response under the parameter uncertairilics
Figure 4.21 Y axis transient response under the parameter uncertainties
Figure 4.22 Ox axis transient response under the parameter uncertainties
5
11
12
„Ö l$ 1d
20
31
Trang 19Acknowledgment
I would like to thank Tanoi University of Science and Technology for building, maintaining, and developing a leading research and studying envirorment Also, thanks to the School of Electrical Enginccring and the Department of Industrial Automation teachers for teaching and imparting necessary knowledge from fundamental to in-depth In particular, many thanks to my supervisor, Dr Nguyen Danh Huy las oriented, guided, encouraged, and helped me throughout the process
of studying, researching, and completing the thesis ‘The knowledge, challenges, and experiences in studying and researching at the university will be a solid foundation and valuable experierwe for me to continue with iny research and
development orientation
Abstract
Aclive magnetic bearmgs (AMBs) are clectromagnetic mechanism systems in
which non-contact bearings support a rotating shaft using atwactive forces
generated by electromagnets through closed-loop control For complete support of
a five-degree of freedom (DOF) rotor system, most AMB structures imclude two
radial actuators and one for the axial direction Conical active magnetic bearing (CAMB) is one of the development directions of conventional magnetic bearings
in which the requirement of the axial bearing can be elimmated Due to the
nonlinearities and inherett coupling properlics of cornaal aetrve magnetic bearing system, it is essential to accomplish an appropriate mathematical model as well as
design a high accuracy control scheme In this thesis, extended state observer
(FSO) is applied to deal with the lumped disturbances of CAMB system which
come from extemal disturbances, uncertain electromagnetic forces and parametric
uncertainties The convergence properties of the tracking error are analytically
proven using Lyapunov’s theory Based on extended state observer, a fractional
order sliding mode control (FOSMC) is designed to achieve fast response and minimize tracking errors as well as better control quantity without chattering The
control performance of the proposed FOSMC-ESO is illustrated in Ierrns of very
good disturbance rejection capabilily that is demonstrated through
MATLAB/Simulink simulation results In addition, comparative simulations
combine wilh three performance indices are performed to quantitatively evaluate
the tracking performance of proposed controllers against SMC and ADRC controllers
Author
Trang 20TABLE OF CONTENT CHAPTER 1 INIRODUCTION
11 State of the aFt ào
1.11 IaodueHonof Active Maenetic Hearing
Í
1.12 Principles of Magnetic Bearing Function
1.13 Advantages and disadvantages of AMBs
1.15 Conical Magnetic Bearings: An overview 4 1.16 Fundamental of Sliding Mode Control 7
118 — Extended state cbserver wd
Linearized bearing forces sec TỔ
Extcrnal đisturbaiiccs c cocociecccecree ¬ 4
Magnetic bearings actuation - - 22
CHAPTER 3 EXTENDED STATE OBSERVER BASED CONTROL
eu 24 Extended state observer, seven ¬ 3.2 Kracuonal Order Bliding Mode Contol
3.21 Principle of Sliding Mode Conuol and Chattering Problem
Trang 21
TABLE OF CONTENT CHAPTER 1 INIRODUCTION
11 State of the aFt ào
1.11 IaodueHonof Active Maenetic Hearing
Í
1.12 Principles of Magnetic Bearing Function
1.13 Advantages and disadvantages of AMBs
1.15 Conical Magnetic Bearings: An overview 4 1.16 Fundamental of Sliding Mode Control 7
118 — Extended state cbserver wd
Linearized bearing forces sec TỔ
Extcrnal đisturbaiiccs c cocociecccecree ¬ 4
Magnetic bearings actuation - - 22
CHAPTER 3 EXTENDED STATE OBSERVER BASED CONTROL
eu 24 Extended state observer, seven ¬ 3.2 Kracuonal Order Bliding Mode Contol
3.21 Principle of Sliding Mode Conuol and Chattering Problem
Trang 22
Figure 4.53 Comparison between observer and response position of x axis with
Figure 4.54 Comparison between observer and response velocity of x axis with
Figure 4.55 Comparison belween observer and real disturbance of x axis with
Trang 23LIST OF FIGURES Figure 1.1 Active magnetic bearings in compressor [6j
Figure 1.2 Munction principle of an active electromagnetic bearing [3]
Figure 1.3 Applications of AMBs
Figure 1.4 System with cylindrical AMEs [14]
Figure 1.5 System conical AMBs [15] (1) impeller, (2) centering tip; (3) conical
geometry: (1) rotor; (5) electric motor, (6) magnetic actuators
Figure 2.1 AMBs structure with single-DOF
Figure 2.2 Simple electromagnet structure
Tigure 2.3 Sehematie of conical active rnagnetic bearing Íorcs
Figure 2.4 Ihustration of unbalanee rotor
Figure 4.2 Response to the position z, x, y
Figure 4.3 Response (o the position of the axis angle 6, ,Ay
Figure 4.4 Upper control currents response
Figure 4.5 Under control currents response .jsssssssiessstsoneeineen
Figure 4.6 Upper impact forces of electromagnsts
Figure 4.7 Under impact forces of electromagnets
Figure 4.8 Comparison betwoon observer and response position of z
Figure 4.9 Comparison between observer and response position af x
Figure 4.10 Comparison between observer and response position of y
Figure 4.11 Comparison between observer aud response position of x
Figure 4.12 Comparison between observer and respanse position of 0y
Figure 4.13 Comparison between observer and response velocity of z
Figure 4.14 Comparison between observer and response velocity of x
Figure 4.15 Comparison between observer and response velocity of y
Figure 4.16 Comparison between observer and response velocity of 8x
Figure 4.17 Comparison between observer and response velocity of Gy
Figure 4.18 Comparison between sign and sigmoid function
Figure 4.19 7, axis transionl response under the parameter uncerlaintics
Figure 4.20 X axis transient response under the parameter uncertairilics
Figure 4.21 Y axis transient response under the parameter uncertainties
Figure 4.22 Ox axis transient response under the parameter uncertainties
5
11
12
„Ö l$ 1d
20
31
Trang 24Table 4.2 The coniroi performanee benchmark in sccnari
Table 4.3 The control performance benohmiark _ - - 53
Trang 25Figure 4.53 Comparison between observer and response position of x axis with
Figure 4.54 Comparison between observer and response velocity of x axis with
Figure 4.55 Comparison belween observer and real disturbance of x axis with
Trang 26Acknowledgment
I would like to thank Tanoi University of Science and Technology for building, maintaining, and developing a leading research and studying envirorment Also, thanks to the School of Electrical Enginccring and the Department of Industrial Automation teachers for teaching and imparting necessary knowledge from fundamental to in-depth In particular, many thanks to my supervisor, Dr Nguyen Danh Huy las oriented, guided, encouraged, and helped me throughout the process
of studying, researching, and completing the thesis ‘The knowledge, challenges, and experiences in studying and researching at the university will be a solid foundation and valuable experierwe for me to continue with iny research and
development orientation
Abstract
Aclive magnetic bearmgs (AMBs) are clectromagnetic mechanism systems in
which non-contact bearings support a rotating shaft using atwactive forces
generated by electromagnets through closed-loop control For complete support of
a five-degree of freedom (DOF) rotor system, most AMB structures imclude two
radial actuators and one for the axial direction Conical active magnetic bearing (CAMB) is one of the development directions of conventional magnetic bearings
in which the requirement of the axial bearing can be elimmated Due to the
nonlinearities and inherett coupling properlics of cornaal aetrve magnetic bearing system, it is essential to accomplish an appropriate mathematical model as well as
design a high accuracy control scheme In this thesis, extended state observer
(FSO) is applied to deal with the lumped disturbances of CAMB system which
come from extemal disturbances, uncertain electromagnetic forces and parametric
uncertainties The convergence properties of the tracking error are analytically
proven using Lyapunov’s theory Based on extended state observer, a fractional
order sliding mode control (FOSMC) is designed to achieve fast response and minimize tracking errors as well as better control quantity without chattering The
control performance of the proposed FOSMC-ESO is illustrated in Ierrns of very
good disturbance rejection capabilily that is demonstrated through
MATLAB/Simulink simulation results In addition, comparative simulations
combine wilh three performance indices are performed to quantitatively evaluate
the tracking performance of proposed controllers against SMC and ADRC controllers
Author
Trang 27LIST OF FIGURES Figure 1.1 Active magnetic bearings in compressor [6j
Figure 1.2 Munction principle of an active electromagnetic bearing [3]
Figure 1.3 Applications of AMBs
Figure 1.4 System with cylindrical AMEs [14]
Figure 1.5 System conical AMBs [15] (1) impeller, (2) centering tip; (3) conical
geometry: (1) rotor; (5) electric motor, (6) magnetic actuators
Figure 2.1 AMBs structure with single-DOF
Figure 2.2 Simple electromagnet structure
Tigure 2.3 Sehematie of conical active rnagnetic bearing Íorcs
Figure 2.4 Ihustration of unbalanee rotor
Figure 4.2 Response to the position z, x, y
Figure 4.3 Response (o the position of the axis angle 6, ,Ay
Figure 4.4 Upper control currents response
Figure 4.5 Under control currents response .jsssssssiessstsoneeineen
Figure 4.6 Upper impact forces of electromagnsts
Figure 4.7 Under impact forces of electromagnets
Figure 4.8 Comparison betwoon observer and response position of z
Figure 4.9 Comparison between observer and response position af x
Figure 4.10 Comparison between observer and response position of y
Figure 4.11 Comparison between observer aud response position of x
Figure 4.12 Comparison between observer and respanse position of 0y
Figure 4.13 Comparison between observer and response velocity of z
Figure 4.14 Comparison between observer and response velocity of x
Figure 4.15 Comparison between observer and response velocity of y
Figure 4.16 Comparison between observer and response velocity of 8x
Figure 4.17 Comparison between observer and response velocity of Gy
Figure 4.18 Comparison between sign and sigmoid function
Figure 4.19 7, axis transionl response under the parameter uncerlaintics
Figure 4.20 X axis transient response under the parameter uncertairilics
Figure 4.21 Y axis transient response under the parameter uncertainties
Figure 4.22 Ox axis transient response under the parameter uncertainties
5
11
12
„Ö l$ 1d
20
31
Trang 28Acknowledgment
I would like to thank Tanoi University of Science and Technology for building, maintaining, and developing a leading research and studying envirorment Also, thanks to the School of Electrical Enginccring and the Department of Industrial Automation teachers for teaching and imparting necessary knowledge from fundamental to in-depth In particular, many thanks to my supervisor, Dr Nguyen Danh Huy las oriented, guided, encouraged, and helped me throughout the process
of studying, researching, and completing the thesis ‘The knowledge, challenges, and experiences in studying and researching at the university will be a solid foundation and valuable experierwe for me to continue with iny research and
development orientation
Abstract
Aclive magnetic bearmgs (AMBs) are clectromagnetic mechanism systems in
which non-contact bearings support a rotating shaft using atwactive forces
generated by electromagnets through closed-loop control For complete support of
a five-degree of freedom (DOF) rotor system, most AMB structures imclude two
radial actuators and one for the axial direction Conical active magnetic bearing (CAMB) is one of the development directions of conventional magnetic bearings
in which the requirement of the axial bearing can be elimmated Due to the
nonlinearities and inherett coupling properlics of cornaal aetrve magnetic bearing system, it is essential to accomplish an appropriate mathematical model as well as
design a high accuracy control scheme In this thesis, extended state observer
(FSO) is applied to deal with the lumped disturbances of CAMB system which
come from extemal disturbances, uncertain electromagnetic forces and parametric
uncertainties The convergence properties of the tracking error are analytically
proven using Lyapunov’s theory Based on extended state observer, a fractional
order sliding mode control (FOSMC) is designed to achieve fast response and minimize tracking errors as well as better control quantity without chattering The
control performance of the proposed FOSMC-ESO is illustrated in Ierrns of very
good disturbance rejection capabilily that is demonstrated through
MATLAB/Simulink simulation results In addition, comparative simulations
combine wilh three performance indices are performed to quantitatively evaluate
the tracking performance of proposed controllers against SMC and ADRC controllers
Author
Trang 29Figure 4.53 Comparison between observer and response position of x axis with
Figure 4.54 Comparison between observer and response velocity of x axis with
Figure 4.55 Comparison belween observer and real disturbance of x axis with
Trang 30Figure 4.53 Comparison between observer and response position of x axis with
Figure 4.54 Comparison between observer and response velocity of x axis with
Figure 4.55 Comparison belween observer and real disturbance of x axis with
Trang 31Figure 4.23 @y axis transient response under the parameter uncertainties
Figure 4.24 Upper current response under the parameter uncertainties
Figure 4.25 Under current response under the parameter uncertainties
Figure 4.26 Lixternal force Fa=30N oo ee cceccseteens cere ieeesiees
Figure 4.27 ADRC controller position response under Tu=30N
Figure 4.28 SMC controller position response under Fa=30N
Figure 4.29 FOSMC controller position response under Fa-30N
Figure 4.30 Current response with ADRC controller under Fa=30N
Figure 4.31 Current response with SMC controller under Fy 30N-
Figure 4.32 Current response with FOSMC controller under Fg-30N 43
Figtue 4.33 Comparison betweơn obsorver and posilion of x axis with Fa 30N 44
Figure 4.34 Comparison between observer and velocity of x axis with Fg=30N 44 Figure 4.35 Comparison between observer and disturbance of x axis with Fa=30N
Figure 4.37 ADRC controller position response under #a-10UN 0
Figure 4.38 SMC controller position respouse under Fa 100N
Figure 4.39 FOSMC controller position response under Fa—100N
Figure 4.40 Current response with ADRC controller under Fa TOON
Figure 4.41 Current response with SMC controller under Fa=100N
Figure 4.12 Current response with FOSMC controller under Pa-L00N
Figure 4.43 Comparison between observer and position of x axis with Fa-100N
Figure 4.47 ADRC controller position response under hydrodynamic force
Figure 4.48 SMC controller position response under hydrodynamic force
Trang 32Figure 4.53 Comparison between observer and response position of x axis with
Figure 4.54 Comparison between observer and response velocity of x axis with
Figure 4.55 Comparison belween observer and real disturbance of x axis with
Trang 33Figure 4.53 Comparison between observer and response position of x axis with
Figure 4.54 Comparison between observer and response velocity of x axis with
Figure 4.55 Comparison belween observer and real disturbance of x axis with
Trang 3433 Conclusion 28 CHAPTER 4 NUMERICAL SIMULATION STUDY
4.2 Resulis and Discussiot con non ¬-
CHAPTER § CONCLUSIONS AND FUTURE WORKS
Trang 35Figure 4.53 Comparison between observer and response position of x axis with
Figure 4.54 Comparison between observer and response velocity of x axis with
Figure 4.55 Comparison belween observer and real disturbance of x axis with
Trang 36Table 4.2 The coniroi performanee benchmark in sccnari
Table 4.3 The control performance benohmiark _ - - 53
Trang 37Acknowledgment
I would like to thank Tanoi University of Science and Technology for building, maintaining, and developing a leading research and studying envirorment Also, thanks to the School of Electrical Enginccring and the Department of Industrial Automation teachers for teaching and imparting necessary knowledge from fundamental to in-depth In particular, many thanks to my supervisor, Dr Nguyen Danh Huy las oriented, guided, encouraged, and helped me throughout the process
of studying, researching, and completing the thesis ‘The knowledge, challenges, and experiences in studying and researching at the university will be a solid foundation and valuable experierwe for me to continue with iny research and
development orientation
Abstract
Aclive magnetic bearmgs (AMBs) are clectromagnetic mechanism systems in
which non-contact bearings support a rotating shaft using atwactive forces
generated by electromagnets through closed-loop control For complete support of
a five-degree of freedom (DOF) rotor system, most AMB structures imclude two
radial actuators and one for the axial direction Conical active magnetic bearing (CAMB) is one of the development directions of conventional magnetic bearings
in which the requirement of the axial bearing can be elimmated Due to the
nonlinearities and inherett coupling properlics of cornaal aetrve magnetic bearing system, it is essential to accomplish an appropriate mathematical model as well as
design a high accuracy control scheme In this thesis, extended state observer
(FSO) is applied to deal with the lumped disturbances of CAMB system which
come from extemal disturbances, uncertain electromagnetic forces and parametric
uncertainties The convergence properties of the tracking error are analytically
proven using Lyapunov’s theory Based on extended state observer, a fractional
order sliding mode control (FOSMC) is designed to achieve fast response and minimize tracking errors as well as better control quantity without chattering The
control performance of the proposed FOSMC-ESO is illustrated in Ierrns of very
good disturbance rejection capabilily that is demonstrated through
MATLAB/Simulink simulation results In addition, comparative simulations
combine wilh three performance indices are performed to quantitatively evaluate
the tracking performance of proposed controllers against SMC and ADRC controllers
Author