A new control strategy for cutting force disturbance compensation for XY table ball screw driven system.
Faculty of Manufacturing Engineering
A NEW CONTROL STRATEGY FOR CUTTING FORCE
DISTURBANCE COMPENSATION FOR XY TABLE BALL SCREW
DRIVEN SYSTEM
Lokman Abdullah
Doctor of Philosophy in Manufacturing Engineering
2014
A NEW CONTROL STRATEGY FOR CUTTING FORCE DISTURBANCE
COMPENSATION FOR XY TABLE BALL SCREW DRIVEN SYSTEM
LOKMAN ABDULLAH
A thesis submitted
in fulfillment of the requirements for the degree of Doctor of Philosophy in
Manufacturing Engineering
Faculty of Manufacturing Engineering
UNIVERSITI TEKNIKAL MALAYSIA MELAKA
2014
DECLARATION
I declare that this thesis entitle “A New Control Strategy for Cutting Force Disturbance
Compensation for XY Table Ball Screw Driven System” is the result of my own research
except as cited in the references. The thesis has not been accepted for any degree and is not
concurrently submitted in candidature of any other degree.
Signature
:
...........................................
Name
:
LOKMAN ABDULLAH
Date
:
.......................................
APPROVAL
I hereby declare that I have read this thesis and in my opinion this thesis is sufficient in
terms of scope and quality for the award of Doctor of Philosophy in Manufacturing
Engineering.
Signature
:
.............................................................................
Name
:
ASSOC. PROF. DR. ZAMBERI JAMALUDIN
Date
:
..............................................................................
DEDIKASI
Ya Allah, hanya dengan keizinan-Mu kajian ini dapat disempurnakan.
Teristimewa buat mak dan abah,
Hjh. Mariyam binti Mohamad dan Hj. Abdullah bin Md. Said,
Terima kasih di atas doa kalian yang tidak pernah putus, dorongan yang tidak pernah lelah,
nasihat yang tidak pernah lekang. Moga Mak Abah sentiasa dalam redha Allah.
Terutama buat isteri yang di kasihi,
Nur Radziah binti Salim,
Terima kasih di atas doa, sokongan dan pengorbanan sayang yang tidak pernah jemu.
Buat penyejuk mata dan penghibur hati,
Irdina Ilmuna, Nur Husna Sakinah, Abd Rahman dan Nur Khadijah,
Baba doakan semoga kalian menjadi anak yang soleh dan solehah.
Seterusnya buat pendorong kejayaan ini,
Kakak, Adik, Ibu Bapa Mertua, teman seperjuangan dan semua yang terlibat.
Terima Kasih di atas tunjuk ajar dan sokongan kalian.
ABSTRACT
High tracking accuracy, precision and robustness are three vital components demanded in
controller design for machining processes in many manufacturing related activities. This
recent requirements or paradigm shift has led to a new and challenging era in the area of
machining tools and control. However, the presence of disturbances during machining
processes in the form of friction forces and cutting forces have greatly reduced
positioning and tracking accuracy of the system. The objective of this thesis is to propose,
design, develop and validate a new control strategy to further compensate effects of
cutting forces on the positioning accuracy of a XY table ball screw driven system by
Googoltech Inc. Issues pertaining to cutting force effects on machining process have
been explored comprehensively in the past where various techniques and thoughts were
introduced and validated. Conventional linear feedback control approach such as PI, PID
or cascade control alone are inadequate to totally compensate the cutting force
disturbance. This is due to the absence of adaptive element in the control scheme.
Adaptive element is essential to solve the issue of nonlinearity of cutting force
disturbance. This thesis proposes a new approach to compensate multiple frequency
components of cutting forces, named Nonlinear Cascade Feedforward (NCasFF)
controller. This new approach combined and embedded a modified nonlinear function, an
inverse plant model feedforward and a speed feedforward onto the Cascade P/PI
controller that serves as the primary position controller to further reduced the tracking
error. The performance of the proposed controller was validated numerically and
experimentally where actual machining process was performed on the test setup. The
results indicated that the Nonlinear Cascade Feedforward (NCasFF) controller is able to
compensate tracking errors introduced by the cutting forces. This thesis has successfully
demonstrated that the tracking performance of a machine tool was increased significantly
by the addition of dedicated compensation elements that supplement the classical
Cascade P/PI position controller. Results showed that the newly proposed NCasFF control
strategy manage to provide 33.80 % improved performance in terms of Root Mean Square
Error (RMSE) reduction than Cascade P/PI controller and 16.03 % better performance in
terms of Fast Fourier Transform (FFT) error than Cascade P/PI controller. Finally, in
terms of surface roughness, Ra value, NCasFF controller provide 20 % improved
performance than Cascade P/PI controller. However, further studies and improvement are
desired. The performance of the controller needs to be further enhanced so that it can
adapt to different conditions of cutting force disturbance. The improvement includes
addition of adaptive elements to the controller to compensate changing cutting force
characteristics and variable disturbance friction force resulting from different cutting
conditions. For example, changes in tools diameter, tracking speed and depth of cut.
i
ABSTRAK
Ketepatan, kepersisan dan keteguhan merupakan tiga komponen penting yang di perlukan
dalam proses rekebentuk sistem kawalan bagi proses pemesinan dalam sektor pembuatan.
Anjakan paradigma terhadap segala keperluan ini telah membuka dimensi baru dalam
sektor pembuatan. Namun, gangguan proses pemesinan seperti daya geseran dan daya
pemotongan boleh menyebabkan berlakunya banyak ketidaktepatan pada posisi dan
kebolehan mesin untuk bergerak mengikut trajektori yang di tetapkan. Objektif tesis ini
adalah untuk mencadang, merekabentuk, membangunkan dan membuat validasi terhadap
sistem kawalan yang akan direkabentuk bagi membolehkan ia mengatasi gangguan daya
pemotongan terhadap ketepatan posisi sistem mesin XY. Isu-isu berkaitan kesan daya
pemotongan terhadap proses pemesinan telah di kaji secara menyeluruh di mana pelbagai
kaedah telah pun di perkenalkan. Sistem kawalan konvensional seperti "PI","PID" dan
"Cascade" sahaja sebagai sistem kawalan tunggal adalah tidak mencukupi untuk
mengatasi kesan negatif gangguan daya pemotongan secara holistik. Ini adalah di
sebabkan oleh ketiadaan elemen "adaptive" pada struktur sistem kawalan tersebut. Elemen
"adaptive" ini adalah amat diperlukan bagi mengatasi masalah gangguan dan
ketidaktentuan pada daya pemotongan. Dalam tesis ini, pendekatan baru yang digunakan
untuk mengatasi gangguan daya pemotongan pelbagai dipanggil sistem kawalan
Nonlinear Cascade Feedforward (NCasFF). Sistem kawalan yang baru direkabentuk ini
adalah hasil gabungan fungsi tidak linear yang telah diubahsuai yang digabungkan
bersama sistem kawalan "Cascade P/PI" yang bertindak sebagai sistem kawalan utama.
Di samping itu, modul "inverse plant model feedforward" dan modul "speed feedforward"
juga digabungkan bersama "Cascade P/PI" bagi membantu mengurangkan lagi masalah
kesilapan trajektori oleh sistem. Proses pemotongan sebenar dijalankan ke atas mesin XY
bagi tujuan validasi. Berdasarkan keputusan yang dihasilkan, di dapati sistem kawalan
baru ini telah berjaya untuk mengatasi masalah kesan negatif daya pemotongan (yang
dipelbagaikan) terhadap posisi mesin XY. Hasil kerja dalam tesis ini telah berjaya
membuktikan bahawa dengan gabungan beberapa fungsi modul (yang ditambah baik)
yang digabungkan bersama sistem kawalan "Cascade P/PI" telah berjaya untuk
memperbaiki prestasi sistem perkakasan mesin. Hasil eksperimen menunjukkan bahawa
sistem kawalan "NCasFF" berjaya membuahkan hasil yang lebih baik sebanyak 33.80 %
dari aspek "Root Mean Square Error (RMSE) dan 16.03 % lebih baik dari aspek "Fast
Fourier Transform (FFT) Error" serta 20 % lebih baik dari aspek "Surface Roughness,
Ra" berbanding sistem kawalan "Cascade P/PI". Walaubagaimanapun, kajian lanjut dan
pembaharuan terhadap kajian ini adalah diperlukan. Tujuan penambaikan ini dilakukan
adalah untuk mempertingkatkan lagi kebolehan sistem kawalan tersebut agar ia mampu
bertahan pada pelbagai keadaan daya pemotongan. Antara penambahbaikan yang boleh
dilakukan ialah untuk memasukkan elemen "adaptive" terhadap sistem kawalan untuk
mengatasi masalah daya geseran dan juga untuk merekabentuk sistem kawalan yang boleh
mengatasi masalah kesilapan posisi mesin XY pada pelbagai situasi. Contohnya ialah
untuk merekabentuk sistem kawalan yang mampu berfungsi dengan baik semasa berlaku
perubahan pada diameter alat, kelajuan mesin dan kedalaman semasa proses pemotongan
sebenar.
ii
ACKNOWLEDGEMENTS
First and foremost, I would like to convey my deepest gratitude to my respected supervisor,
Assoc. Prof. Dr. Zamberi Jamaludin. It is a great honour and pleasure to be able to work
with him, a person of great control system background, experience, success, ideas and
stature. Your kind advice, time, attention and dedication towards realizing this works are
greatly appreciated and indebted. May 'Allah' the Almighty bless you. Thank you 'teacher'.
I would also like to express my special gratitude to Prof. Jan Swevers; my Pro-motor
during my 6 months PhD attachment at K.U. Leuven, Belgium.
I would like to extend my gratitude to UTeM and FKP UTeM and to all academic and
supporting staffs for assisting me in terms of facility and moral support. This work is made
possible with the financial supports of the Ministry of Higher Education Malaysia (SLAB)
and UTeM. These financial supports are greatly appreciated and indebted.
A special thanks also to my colleagues from Control System in Machine Tools (CosMaT)
research group, Ms Nur Aidawaty Rafan, Mr. Chiew Tsung Heng, Mr. Jailani
Jamaludin ,Mr. Tang Teng Fong and Ms. Madihah Maarof. All I can say is "Engineering is
teamwork". Thanks a lot guys, our friendship and sweet memories together will always
remain in my heart. Finally and most importantly, I wish to express my deepest gratitude to
both of my parents, Hj. Abdullah Md. Said and Hjh Mariyam Mohamad, my sister
Khadijah Abdullah, my brother Dr. Abdul Rahim Abdullah, my father and mother-in-law
Hj Salim Jaafar and Hjh Hamidah Abdullah for their prayers, loves, cares and support. I
am greatly indebted to them and may 'Allah' repay all their good deeds and sacrifices. To
my beloved wife Nur Radziah Salim and my children (Irdina Ilmuna, Nur Husna Sakinah,
Abd. Rahman and Nur Khadijah), there are no words to portray how blessed and thankful I
am for your company during both the easy and the difficult times of this journey. I salute
your patience, pray, dedication, love, courage and care that have brought happiness and
serenity to our life.
iii
TABLE OF CONTENTS
PAGE
DECLARATION
DEDICATION
ABSTRACT
ABSTRAK
ACKNOWLEDGEMENTS
TABLE OF CONTENTS
LIST OF TABLES
LIST OF FIGURES
LIST OF SYMBOLS
LIST OF ABBREVIATIONS
LIST OF PUBLICATIONS
i
ii
iii
iv
vii
x
xvii
xviii
xix
CHAPTER
1
INTRODUCTION
1.1 Background
1.2 Problem Statements
1.3 Research Objectives
1.4 Scope of Work
1.5 Significance of Studies
1.6 Organization of Report
1
1
2
5
5
6
6
2
LITERATURE REVIEW
2.1 Introduction
2.2 State of the Art on Motion Control in Machine Tool
2.2.1
Mechanical Drive System
2.2.2
Disturbances in Drive System
2.2.2.1
Friction Forces
2.2.2.2
Cutting Forces
2.2.3
Cutting Forces Measurement Method
2.3 Cutting Force Compensation Method - A Controller Design Approach
2.3.1
Controller Design
2.3.2
Controller Design based on PID
2.3.3
Other Techniques of Controller Design
2.4 Summary
8
8
9
9
14
15
15
18
23
23
24
29
33
3
METHODOLOGY
3.1 Introduction
3.2 Experimental Setup
3.3 System Identification and System Modelling
3.4 Motor Constant Identification
3.5 Cutting Force Characterization
3.5.1
Experimental Setup of Cutting Force Measurement
3.5.2
Experimental Design for Cutting Force Characterization
35
35
38
40
45
46
46
49
iv
3.5.3
3.6
Characterization and Analysis of Cutting Forces
3.5.3.1
Conversion of Cutting Force Data (Newton to Volt)
3.5.4
Analysis of the Measured Cutting Forces
Summary
52
52
52
54
4
CONTROLLER DESIGN
55
4.1 Introduction
55
4.2 Cascade Controller
56
4.2.1
Cascade Control Structure and Configuration based on Ideal System 56
4.2.2
Analysis of the Closed Loop Behaviour with Proportional (P) Speed
Control
58
4.2.3
Analysis of the Closed Loop Behaviour with PI Speed Control
61
4.2.4
Design and Analysis of the PI Speed Controller based on Measured
FRF
64
4.2.5
Design and Analysis of the Position Loop based on measured FRF 71
4.2.6
Analysis of Tracking Performance
79
4.2.6.1
Numerical Validation of Tracking Performance
79
4.2.6.2
Experimental Validation of Tracking Performance
81
4.3 Nonlinear PID (NPID) Controller
83
4.3.1
Design and Analysis of PID Controller
83
4.3.2
General Structure and Configuration of NPID controller
87
4.3.3
Design and Analysis of NPID Controller
89
4.4 Nonlinear Cascade Feedforward (NCasFF)
94
4.4.1
Nonlinear Cascade Feedforward (NCasFF) control structure
94
4.4.2
Design Guidelines of NCasFF Controller
95
4.4.3
Design of Inverse Plant Model and Speed Feedforward
97
4.4.4
NCasFF Controller : Design of Nonlinear Function (Step 4)
99
4.4.5
NCasFF Controller : Design of Dead Zone Compensator (DZC) 108
4.4.6
Design Analysis of NCasFF Controller
113
4.4.7
NCasFF Controller : Numerical Analysis of Tracking Performance 116
4.5 Summary
118
5
RESULTS AND DISCUSSION
5.1 Introduction
5.2 Maximum Tracking Error
5.2.1
Cascade P/PI Controller
5.2.1.1
Simulation Results
5.2.1.2
Experimental Results
5.2.2
NPID Controller
5.2.2.1
Simulation Results
5.2.2.2
Experimental Results
5.2.3
Nonlinear Cascade Feedforward (NCasFF) Controller
5.2.3.1
Simulation Results
5.2.3.2
Experimental Results
5.3 Root Mean Square Error (RMSE)
5.4 Fast Fourier Transform (FFT) Error
5.5 Surface Finish Quality
5.6 Discussion
v
119
119
120
120
120
123
127
127
129
133
133
135
139
142
147
151
5.6.1
Discussion on Results of Maximum Tracking Error
5.6.1.1
Cascade P/PI Controller
5.6.1.2
NPID Controller
5.6.1.3
NCasFF Controller
Discussion on Results of RMSE Analysis
Discussion on Results of FFT Error Analysis
Discussion on Results of Surface Finish Quality
151
151
152
154
156
157
161
CONCLUSION AND SUGGESTION FOR FUTURE WORK
6.1 Conclusion
6.2 Suggestion for Future Work
162
162
165
5.6.2
5.6.3
5.6.4
6
REFERENCES
APPENDIX A
APPENDIX B
APPENDIX C
APPENDIX D
APPENDIX E
APPENDIX F
APPENDIX G
APPENDIX H
APPENDIX I
APPENDIX J
APPENDIX K
166
176
177
178
180
182
184
186
188
190
192
196
vi
LIST OF TABLES
TABLE
TITLE
PAGE
3.1
System model parameters for x and y axes
43
3.2
List of equipment with specifications
46
3.3
Recommended cutting parameters of milling operation
49
3.4
Cutting parameters of the experimental design
50
3.5
Amplitude cutting force at different spindle speed
53
4.1
Speed loop PI controller parameters of x and y axes
66
4.2
Gain margin and Phase margin of x and y axes open loop speed
67
4.3
Bandwidth of the speed loop based on sensitivity function
69
4.4
Gain margin and Phase margin of x and y axes open loop position
73
4.5
Bandwidth of the position loop
76
4.6
Gain values of Kp, Ki, and Kd for PID controller
84
4.7
Gain margin and Phase margin of x and y axes open loop position
85
4.8
Bandwidth of the position loop via PID controller
86
4.9
Value of tuned NPID parameters, KO and emax
92
4.10
Value of Nonlinear function parameters for NCasFF controller
100
4.11
Value of parameters in designing DZC
112
4.12
Bandwidth of the position loop
114
5.1
Research configurations
119
5.2
Simulated maximum tracking error with Cascade P/PI controller
122
5.3
Experimental maximum tracking error with Cascade P/PI controller
125
vii
5.4
Simulated maximum tracking error of system with NPID controller
128
5.5
Experimental maximum tracking error of system with NPID controller
131
5.6
Simulated maximum tracking error of system with NCasFF controller
134
5.7
Experimental maximum tracking error with NCasFF controller
137
5.8
X-axis: Comparison in RMSE values for different controllers at 0.3 Hz
139
5.9
X-axis: Comparison in RMSE values for different controllers at 0.7 Hz
141
5.10
X-axis : Comparison in magnitudes of FFT Error between NPID, 144
Cascade P/PI and NCasFF for cutting forces at spindle speed of 1000,
2000 and 3000 rpm at 0.7 Hz
5.11
X-axis : Average percentage of FFT error reduction between NPID, 144
Cascade P/PI and NCasFF for cutting forces at spindle speed of 1000,
2000 and 3000 rpm at 0.7 Hz
5.12
X-axis : Comparison in magnitudes of FFT Error between NPID, 145
Cascade P/PI and NCasFF for cutting forces at spindle speed of 1000,
2000 and 3000 rpm at 0.3 Hz
5.13
X-axis : Average percentage of FFT error reduction between NPID, 145
Cascade P/PI and NCasFF for cutting forces at spindle speed of 1000,
2000 and 3000 rpm at 0.3 Hz
5.14
Surface roughness comparison between controllers
149
6.1
Thesis conclusion
164
6.2
Simulated maximum tracking error of system with Cascade P/PI
179
6.3
Experimental maximum tracking error of system with Cascade P/PI
181
6.4
Simulated maximum tracking error of system with NPID controller
183
6.5
Experimental maximum tracking error of system with NPID controller
185
6.6
Simulated maximum tracking error of system with NCasFF controller
187
6.7
Experimental maximum tracking error of system with NCasFF
189
6.8
Y-axis: Comparison of RMSE at frequency 0.7 Hz
190
6.9
Y-axis: Comparison of RMSE at frequency 0.3 Hz
191
viii
6.10
Y-axis: Comparison of FFT Error between controllers at f = 0.7 Hz
193
6.11
Y-axis: Average Percentage Error Reduction of FFT Error at f = 0.7 Hz
194
6.12
Y-axis: Comparison of FFT Error between controllers at f = 0.3 Hz
194
6.13
Y-axis: Average Percentage Error Reduction of FFT Error at f = 0.3 Hz
195
ix
LIST OF FIGURES
FIGURE
TITLE
PAGE
1.1
Quadrant glitches in circular test
03
2.1
Rack and pinion drive system
10
2.2
Ball screw driven system
11
2.3
Structure of iron-core linear drive system
12
2.4
Structure of piezoelectric drive system
13
2.5
Cutting parameter direction in the cutting zone
16
2.6
Kistler force measurement dynamometer
19
2.7
The setup of capacitive sensor on milling machine
20
2.8
Cylindrical capacitive displacement sensor
21
2.9
Plot of motor current versus cutting force
21
2.10
Structure of active electromagnetic bearings
22
2.11
Axial tracking error with (a) Cascade (b) Cascade with Speed & 26
Acceleration Feedforward
2.12
Diagram of cascade controller with cutting force estimator
31
2.13
Sample of Ferrari Sensors
32
2.14
Position errors at 1,2,3 and 15 harmonics using cutting force estimator
32
3.1
Flowchart of the research methodology
36
3.2
Googol Tech XYZ Milling Table
38
x
3.3
Schematic diagram of the experimental setup
39
3.4
Simulink diagram for FRF measurement
41
3.5
FRF's measurement of the x and y axes
42
3.6
X-axis : FRF measurement and proposed model
44
3.7
Y-axis : FRF measurement and proposed model
44
3.8
Block diagram of the open loop system to approximate the force 45
constant
3.9
Schematic diagram for cutting force characterization
47
3.10
Mounting points of the Kistler dynamometer
48
3.11
Aluminium block during milling operation
49
3.12
Cutting path planning for cutting force measurement
51
3.13
Example of measured cutting force at 1000 rpm
51
3.14
Method on how to inject the cutting forces into the system plant
52
3.15
FFT cutting forces at 1000, 2000 and 3000 rpm spindle speed rotation
53
4.1
General control structure of a cascade control
56
4.2
Ideal cascade control for a position control
58
4.3
Cascade P/PI control structure in frequency domain for control of a 64
motor
4.4
X-axis: Theoretical bode plot of speed open loop transfer function using 66
measured FRF of the system
4.5
Y-axis: Theoretical bode plot of speed open loop transfer function using 67
measured FRF of the system
4.6
X-axis: Nyquist diagram of the speed open loop transfer function based 68
on measured FRF of the system
4.7
Y-axis: Nyquist diagram of the speed open loop transfer function based 68
on measured FRF of the system
4.8
X-axis: Sensitivity function for the speed loop
69
4.9
Y-axis: Sensitivity function for the speed loop
69
xi
4.10
X-axis: Bode diagram of speed closed loop transfer function
70
4.11
Y-axis: Bode diagram of speed closed loop transfer function
70
4.12
X-axis: Theoretical bode plot of position open loop transfer function 72
based on measured FRF of the system
4.13
Y-axis: Theoretical bode plot of position open loop transfer function 72
based on measured FRF of the system
4.14
X-axis: Nyquist diagram of the position open loop transfer function 73
based on measured FRF of the system
4.15
Y-axis: Nyquist diagram of the position open loop transfer function 74
based on measured FRF of the system
4.16
X-axis: Sensitivity function for the position loop
75
4.17
Y-axis: Sensitivity function for the position loop
75
4.18
X-axis: Position closed loop transfer function
76
4.19
Y-axis: Position closed loop transfer function
77
4.20
X-axis: Comparison of dynamic stiffness between Cascade P/P and 78
Cascade P/PI
4.21
Y-axis: Comparison of dynamic stiffness between Cascade P/P and 78
Cascade P/PI
4.22
X-axis: Simulated position error for sinusoidal reference signal of an 79
amplitude 1mm and frequency of 0.7 Hz
4.23
Y-axis: Simulated position error for sinusoidal reference signal of an 80
amplitude 1mm and frequency of 0.7 Hz
4.24
X-axis: Position error transfer function
80
4.25
Y-axis: Position error transfer function
81
4.26
X-axis: Numerical and Experimental Position Closed Loop
82
4.27
Y-axis: Numerical and Experimental Position Closed Loop
82
4.28
PID control structure
83
4.29
Bode Diagram of Open Loop Transfer Function for x and y axes
85
xii
4.30
Nyquist plots of the x-axis (left) and the y-axis (right) position open 85
loop transfer function based on measured FRFs of the system via PID
controller
4.31
Bode magnitude diagram of sensitivity for x and y axes via PID 86
controller
4.32
Bode diagram of position closed loop for x and y axes via PID 87
controller
4.33
NPID control structure and configuration
88
4.34
Flowchart of the procedure to obtain parameters of NPID controller
89
4.35
X-axis : Popov plot of NPID controller
91
4.36
Y-axis : Popov plot of NPID controller
91
4.37
X-axis : Graph of nonlinear gain, Ke against error, e
93
4.38
Y-axis : Graph of nonlinear gain, Ke against error, e
93
4.39
Nonlinear cascade feedforward (NCasFF) control structure with speed 94
and inverse plant feedforward
4.40
Flowchart of design guidelines of NCasFF controller
96
4.41
Cascade P/PI with inverse plant model and speed feedforward
97
4.42
Simulated tracking error of the x-axis (left) and the y-axis (right) for 98
sinusoidal reference signal of an amplitude 1mm and freq. 0.7 Hz
4.43
General structure of independent feedforward controller
98
4.44
General structure of the nonlinear function
100
4.45
Switching function : (a) Signum function (b) Sigmoid function
102
4.46
Comparison of control input between signum and sigmoid function
103
4.47
Step by step procedures to tune parameters of nonlinear function, N
104
4.48
X-axis : Popov plot of NCasFF controller
105
4.49
Y-axis : Popov plot of NCasFF controller
105
4.50
Effect of Ke and e on variation of KO
106
4.51
Effect of Ke and e on variation of emax
107
xiii
4.52
Dead zone compensator in Nonlinear Cascade Feedforward controller
109
4.53
Dead zone characteristics of a system
109
4.54
System block diagram with Dead Zone Compensator
111
4.55
X-axis : Sensitivity function of NCasFF controller
114
4.56
Y-axis : Sensitivity function of NCasFF controller
114
4.57
X-axis : Dynamic stiffness of NCasFF controller (Ke = 1.0)
115
4.58
Y-axis : Dynamic stiffness of NCasFF controller (Ke = 1.0)
115
4.59
X-axis: Simulated error for sinusoidal reference signal of an amplitude 117
1mm, frequency of 0.7 Hz and Ke = 1.04 (left) and position error
transfer function (right)
4.60
Y-axis: Simulated error for sinusoidal reference signal of an amplitude 117
1mm, frequency of 0.7 Hz and Ke = 1.04 (left) and position error
transfer function (right)
5.1
X-axis: Simulated tracking error with Cascade P/PI controller at f = 0.3 121
Hz
5.2
X-axis: Simulated tracking error with Cascade P/PI controller at f = 0.7 121
Hz
5.3
Control scheme of Cascade P/PI controller for experimental validation
123
5.4
X-axis: Experimental tracking error with Cascade P/PI controller at 124
f = 0.3 Hz
5.5
X-axis: Experimental tracking error with Cascade P/PI controller at 124
f = 0.7 Hz
5.6
X-axis: Experimental positions against simulation positions for cutting 126
forces at spindle speed of 1000, 2000 and 3000 rpm for f = 0.3 Hz
5.7
X-axis: Experimental positions against simulation positions for cutting 126
forces at spindle speed of 1000, 2000 and 3000 rpm with f = 0.7 Hz
5.8
X-axis: Simulated tracking error for NPID controller at f = 0.3Hz
127
5.9
X-axis: Simulated tracking error for NPID controller at f = 0.7 Hz
128
5.10
Control scheme of NPID controller for experimental validation
129
xiv
5.11
X-axis: Experimental tracking error for NPID controller at f = 0.3 Hz
130
5.12
X-axis: Experimental tracking error for NPID controller at f = 0.7 Hz
130
5.13
X-axis: Experimental positions against simulated positions for cutting 132
forces at spindle speed of 1000, 2000 and 3000 rpm at f = 0.3 Hz.
5.14
X-axis: Experimental positions against simulated positions for cutting 132
forces at spindle speed of 1000, 2000 and 3000 rpm at f = 0.7 Hz
5.15
X-axis: Simulated tracking error of NCasFF controller at f = 0.3 Hz
133
5.16
X-axis: Simulated tracking error of NCasFF controller at f = 0.7 Hz
134
5.17
Control scheme of NCasFF controller for experimental validation
135
5.18
X-axis: Experimental tracking error for NCasFF controller at f = 0.3 Hz
136
5.19
X-axis: Experimental tracking error for NCasFF controller at f = 0.7 Hz
136
5.20
X-axis: Experimental positions against simulated positions for cutting 138
forces at spindle speed of 1000, 2000 and 3000 rpm at f = 0.3 Hz
5.21
X-axis: Experimental positions against simulated positions for cutting 138
forces at spindle speed of 1000, 2000 and 3000 rpm at f = 0.7 Hz
5.22
X-axis: RMSE values for different controllers and cutting forces at 140
f = 0.3 Hz
5.23
X-axis: RMSE values for different controllers and cutting forces at 141
f = 0.7 Hz
5.24
X-axis: Comparison of FFT Error between NPID, Cascade P/PI and 143
NCasFF controller at frequency 0.3 Hz and spindle speed of (a) 1000
rpm (b) 2000 rpm (c) 3000 rpm
5.25
X-axis: Comparison of FFT Error between NPID, Cascade P/PI and 143
NCasFF controller at frequency 0.7 Hz and spindle speed of (a) 1000
rpm (b) 2000 rpm (c) 3000 rpm
5.26
Surface roughness profile (reproduced from Colak et al., 2007)
147
5.27
Workpiece with straight cutting performed at spindle speed of 1000, 148
2000 and 3000 rpm
5.28
Comparison of dynamic stiffness between NPID, Cascade P/PI and 155
NCasFF
xv
5.29
Dynamic stiffness of NCasFF controller
156
5.30
X-axis: FFT Error for NPID, Cascade P/PI and NCasFF at f = 0.7 Hz
159
5.31
X-axis: FFT Error for NPID, Cascade P/PI and NCasFF at f = 0.3 Hz
160
6.1
Y-axis: Simulated tracking error with Cascade P/PI controller at 178
f = 0.7 Hz.
6.2
Y-axis: Simulated tracking error with Cascade P/PI controller at 178
f = 0.3 Hz.
6.3
Y-axis: Experimental tracking error with Cascade P/PI controller at 180
f = 0.7 Hz.
6.4
Y-axis: Experimental tracking error with Cascade P/PI controller at 180
f = 0.3 Hz.
6.5
Y-axis: Simulated tracking error of system with NPID at f = 0.7 Hz.
182
6.6
Y-axis: Simulated tracking error of system with NPID at f = 0.3 Hz.
182
6.7
Y-axis: Experimental tracking error with NPID controller at f = 0.7 Hz.
184
6.8
Y-axis: Experimental tracking error with NPID controller at f = 0.3 Hz.
184
6.9
Y-axis: Simulated tracking error with NCasFF controller at f = 0.7 Hz.
186
6.10
Y-axis: Simulated tracking error with NCasFF controller at f = 0.3 Hz.
186
6.11
Y-axis: Experimental tracking error via NCasFF controller at f=0.7 Hz.
188
6.12
Y-axis: Experimental tracking error via NCasFF controller at f =0.3 Hz.
188
6.13
Y-axis: Comparison of RMSE at frequency 0.7 Hz
190
6.14
Y-axis: Comparison of RMSE at frequency 0.3 Hz
191
6.15
Y-axis: Comparison of FFT Error between NPID, Cascade P/PI and 192
NCasFF controller at spindle speed of 1000 rpm at 0.7 and 0.3 Hz
6.16
Y-axis: Comparison of FFT Error between NPID, Cascade P/PI and 192
NCasFF controller at spindle speed of 2000 rpm at 0.7 and 0.3 Hz
6.17
Y-axis: Comparison of FFT Error between NPID, Cascade P/PI and 193
NCasFF controller at spindle speed of 3000 rpm at 0.7 and 0.3 Hz
6.18
Mitutoyo portable surface roughness tester (Surftest SJ-301)
xvi
196
LIST OF SYMBOLS
R
-
Resultant force
Fc
-
Cutting force
Ft
-
Thrust force
Fs
-
Cutting speed
Ft
-
Thrust force
Kf
-
Motor constant
M
-
Mass
Zref
-
Reference position
Z
-
Output position
G(s)
-
System
Gm (s)
-
System model transfer function
Ĝ (s)
-
FRF of the considered system
Gm-1(s)
-
Inverse system model transfer function
Gs(s)
-
Speed feedforward
d(t)
-
Disturbances
N(t)
-
Noises
Td
-
Time delay
ep(t)
-
Position tracking error
ev(t)
-
Velocity tracking error
Sv
-
Sensitivity function of velocity loop
Sp
-
Sensitivity function of position loop
Kp
-
Proportional gain
Ki
-
Integral gain
Kd
-
Derivative gain
Ke
-
Nonlinear gain
fe
-
Scaled error
KO
-
Rate of variation of nonlinear gain
emax
-
Range value of error variation
xvii
LIST OF ABBREVIATIONS
AC
-
Alternating current
CNC
-
Computer numerical control
DAC
-
Digital to analog
DFO
-
Disturbance force observer
DSP
-
Digital signal processor
EDM
-
Electro discharge machine
FFT
-
Fast fourier transform
FLC
-
Fuzzy logic control
FRF
-
Frequency response function
HSS
-
High speed steel
I/O
-
Input/output
ISMC
-
Integral sliding mode control
LTI
-
Linear time invariant
LQG
-
Linear quadratic regulator
MBC
-
Model based compensator
MMI
-
Man machine interface
NCasFF
-
Nonlinear cascade feedforward
NLLS
-
Nonlinear least square
NPID
-
Nonlinear proportional-integral-derivative
P
-
Proportional
PDF
-
Pseudo derivative feedback
PI
-
Proportional-integral
PID
-
Proportional-integral-derivative
RMSE
-
Root mean square error
RPM
-
Revolution per minute
SISO
-
Single input single output
SMC
-
Sliding mode control
Vest
-
Estimate velocity
xviii
LIST OF PUBLICATIONS
Journals:
1.
Abdullah, L., Jamaludin, Z., Salleh, M. R., Abu Bakar, B., Jamaludin, J., Chiew, T.
H., and Rafan, N.A. 2014. Theoretical Analysis of Velocity and Position Loop
Behaviour of Nonlinear Cascade Feedforward Controller for Positioning of XY
Table Ballscrew Drive System. Advanced Materials Research, 845, pp. 831 – 836.
2.
Abdullah, L., Jamaludin, Z., Chiew, T. H., Rafan, N. A., and Shaaban, A., 2014.
Spectral Analysis of Cutting Forces Data for XY Table Ballscrew Drive System.
Applied Mechanics and Materials, 471, pp. 241 – 246.
3.
Abdullah, L., Jamaludin, Z., Ahsan, Q., Jamaludin, J., Rafan, N. A., Chiew, T. H.,
Jusoff, K., and Yusoff, M. 2013. Evaluation on Tracking Performance of PID, Gain
Scheduling and Classical Cascade P/PI controller on XY Table Ballscrew Drive
System. World Applied Sciences Journal, 21(1), 01-10.
4.
Abdullah, L. Jamaludin, Z., Chiew, T. H., Rafan, N. A., and Maidin, S., 2013.
Theoretical Analysis of Close loop Behaviour of Ideal Cascade Controller Structure
for Positioning of XY Table Ballscrew Drive System. Applied Mechanics and
Materials, 315, pp. 493 – 497.
5.
Abdullah, L., Jamaludin, Z., Chiew, T. H., Rafan, N. A., and Syed Mohamed, M. S.,
2012. System Identification of XY Table Ballscrew Drive using Parametric and
Non Parametric Frequency Domain Estimation via Deterministic Approach.
Procedia Engineering, 41, pp. 567 – 574.
6.
Abdullah, L., Jamaludin, Z., Chiew, T. H., and Rafan, N. A., 2012. Systematic
Method for Cutting Forces Characterization for XY Milling Table Ballscrew Drive
System. International Journal of Mechanical & Mechatronics Engineering, 12(6),
pp. 28 – 33.
7.
Abdullah, L., Jamaludin, Z., Chiew, T. H., Rafan, N. A., and Yuhazri, M. Y., 2012.
Extensive Tracking Performance Analysis of Classical Feedback Control for XY
Stage Ballscrew System. Applied Mechanics and Materials, 229 – 231, pp. 750 – 7
55.
xix
A NEW CONTROL STRATEGY FOR CUTTING FORCE
DISTURBANCE COMPENSATION FOR XY TABLE BALL SCREW
DRIVEN SYSTEM
Lokman Abdullah
Doctor of Philosophy in Manufacturing Engineering
2014
A NEW CONTROL STRATEGY FOR CUTTING FORCE DISTURBANCE
COMPENSATION FOR XY TABLE BALL SCREW DRIVEN SYSTEM
LOKMAN ABDULLAH
A thesis submitted
in fulfillment of the requirements for the degree of Doctor of Philosophy in
Manufacturing Engineering
Faculty of Manufacturing Engineering
UNIVERSITI TEKNIKAL MALAYSIA MELAKA
2014
DECLARATION
I declare that this thesis entitle “A New Control Strategy for Cutting Force Disturbance
Compensation for XY Table Ball Screw Driven System” is the result of my own research
except as cited in the references. The thesis has not been accepted for any degree and is not
concurrently submitted in candidature of any other degree.
Signature
:
...........................................
Name
:
LOKMAN ABDULLAH
Date
:
.......................................
APPROVAL
I hereby declare that I have read this thesis and in my opinion this thesis is sufficient in
terms of scope and quality for the award of Doctor of Philosophy in Manufacturing
Engineering.
Signature
:
.............................................................................
Name
:
ASSOC. PROF. DR. ZAMBERI JAMALUDIN
Date
:
..............................................................................
DEDIKASI
Ya Allah, hanya dengan keizinan-Mu kajian ini dapat disempurnakan.
Teristimewa buat mak dan abah,
Hjh. Mariyam binti Mohamad dan Hj. Abdullah bin Md. Said,
Terima kasih di atas doa kalian yang tidak pernah putus, dorongan yang tidak pernah lelah,
nasihat yang tidak pernah lekang. Moga Mak Abah sentiasa dalam redha Allah.
Terutama buat isteri yang di kasihi,
Nur Radziah binti Salim,
Terima kasih di atas doa, sokongan dan pengorbanan sayang yang tidak pernah jemu.
Buat penyejuk mata dan penghibur hati,
Irdina Ilmuna, Nur Husna Sakinah, Abd Rahman dan Nur Khadijah,
Baba doakan semoga kalian menjadi anak yang soleh dan solehah.
Seterusnya buat pendorong kejayaan ini,
Kakak, Adik, Ibu Bapa Mertua, teman seperjuangan dan semua yang terlibat.
Terima Kasih di atas tunjuk ajar dan sokongan kalian.
ABSTRACT
High tracking accuracy, precision and robustness are three vital components demanded in
controller design for machining processes in many manufacturing related activities. This
recent requirements or paradigm shift has led to a new and challenging era in the area of
machining tools and control. However, the presence of disturbances during machining
processes in the form of friction forces and cutting forces have greatly reduced
positioning and tracking accuracy of the system. The objective of this thesis is to propose,
design, develop and validate a new control strategy to further compensate effects of
cutting forces on the positioning accuracy of a XY table ball screw driven system by
Googoltech Inc. Issues pertaining to cutting force effects on machining process have
been explored comprehensively in the past where various techniques and thoughts were
introduced and validated. Conventional linear feedback control approach such as PI, PID
or cascade control alone are inadequate to totally compensate the cutting force
disturbance. This is due to the absence of adaptive element in the control scheme.
Adaptive element is essential to solve the issue of nonlinearity of cutting force
disturbance. This thesis proposes a new approach to compensate multiple frequency
components of cutting forces, named Nonlinear Cascade Feedforward (NCasFF)
controller. This new approach combined and embedded a modified nonlinear function, an
inverse plant model feedforward and a speed feedforward onto the Cascade P/PI
controller that serves as the primary position controller to further reduced the tracking
error. The performance of the proposed controller was validated numerically and
experimentally where actual machining process was performed on the test setup. The
results indicated that the Nonlinear Cascade Feedforward (NCasFF) controller is able to
compensate tracking errors introduced by the cutting forces. This thesis has successfully
demonstrated that the tracking performance of a machine tool was increased significantly
by the addition of dedicated compensation elements that supplement the classical
Cascade P/PI position controller. Results showed that the newly proposed NCasFF control
strategy manage to provide 33.80 % improved performance in terms of Root Mean Square
Error (RMSE) reduction than Cascade P/PI controller and 16.03 % better performance in
terms of Fast Fourier Transform (FFT) error than Cascade P/PI controller. Finally, in
terms of surface roughness, Ra value, NCasFF controller provide 20 % improved
performance than Cascade P/PI controller. However, further studies and improvement are
desired. The performance of the controller needs to be further enhanced so that it can
adapt to different conditions of cutting force disturbance. The improvement includes
addition of adaptive elements to the controller to compensate changing cutting force
characteristics and variable disturbance friction force resulting from different cutting
conditions. For example, changes in tools diameter, tracking speed and depth of cut.
i
ABSTRAK
Ketepatan, kepersisan dan keteguhan merupakan tiga komponen penting yang di perlukan
dalam proses rekebentuk sistem kawalan bagi proses pemesinan dalam sektor pembuatan.
Anjakan paradigma terhadap segala keperluan ini telah membuka dimensi baru dalam
sektor pembuatan. Namun, gangguan proses pemesinan seperti daya geseran dan daya
pemotongan boleh menyebabkan berlakunya banyak ketidaktepatan pada posisi dan
kebolehan mesin untuk bergerak mengikut trajektori yang di tetapkan. Objektif tesis ini
adalah untuk mencadang, merekabentuk, membangunkan dan membuat validasi terhadap
sistem kawalan yang akan direkabentuk bagi membolehkan ia mengatasi gangguan daya
pemotongan terhadap ketepatan posisi sistem mesin XY. Isu-isu berkaitan kesan daya
pemotongan terhadap proses pemesinan telah di kaji secara menyeluruh di mana pelbagai
kaedah telah pun di perkenalkan. Sistem kawalan konvensional seperti "PI","PID" dan
"Cascade" sahaja sebagai sistem kawalan tunggal adalah tidak mencukupi untuk
mengatasi kesan negatif gangguan daya pemotongan secara holistik. Ini adalah di
sebabkan oleh ketiadaan elemen "adaptive" pada struktur sistem kawalan tersebut. Elemen
"adaptive" ini adalah amat diperlukan bagi mengatasi masalah gangguan dan
ketidaktentuan pada daya pemotongan. Dalam tesis ini, pendekatan baru yang digunakan
untuk mengatasi gangguan daya pemotongan pelbagai dipanggil sistem kawalan
Nonlinear Cascade Feedforward (NCasFF). Sistem kawalan yang baru direkabentuk ini
adalah hasil gabungan fungsi tidak linear yang telah diubahsuai yang digabungkan
bersama sistem kawalan "Cascade P/PI" yang bertindak sebagai sistem kawalan utama.
Di samping itu, modul "inverse plant model feedforward" dan modul "speed feedforward"
juga digabungkan bersama "Cascade P/PI" bagi membantu mengurangkan lagi masalah
kesilapan trajektori oleh sistem. Proses pemotongan sebenar dijalankan ke atas mesin XY
bagi tujuan validasi. Berdasarkan keputusan yang dihasilkan, di dapati sistem kawalan
baru ini telah berjaya untuk mengatasi masalah kesan negatif daya pemotongan (yang
dipelbagaikan) terhadap posisi mesin XY. Hasil kerja dalam tesis ini telah berjaya
membuktikan bahawa dengan gabungan beberapa fungsi modul (yang ditambah baik)
yang digabungkan bersama sistem kawalan "Cascade P/PI" telah berjaya untuk
memperbaiki prestasi sistem perkakasan mesin. Hasil eksperimen menunjukkan bahawa
sistem kawalan "NCasFF" berjaya membuahkan hasil yang lebih baik sebanyak 33.80 %
dari aspek "Root Mean Square Error (RMSE) dan 16.03 % lebih baik dari aspek "Fast
Fourier Transform (FFT) Error" serta 20 % lebih baik dari aspek "Surface Roughness,
Ra" berbanding sistem kawalan "Cascade P/PI". Walaubagaimanapun, kajian lanjut dan
pembaharuan terhadap kajian ini adalah diperlukan. Tujuan penambaikan ini dilakukan
adalah untuk mempertingkatkan lagi kebolehan sistem kawalan tersebut agar ia mampu
bertahan pada pelbagai keadaan daya pemotongan. Antara penambahbaikan yang boleh
dilakukan ialah untuk memasukkan elemen "adaptive" terhadap sistem kawalan untuk
mengatasi masalah daya geseran dan juga untuk merekabentuk sistem kawalan yang boleh
mengatasi masalah kesilapan posisi mesin XY pada pelbagai situasi. Contohnya ialah
untuk merekabentuk sistem kawalan yang mampu berfungsi dengan baik semasa berlaku
perubahan pada diameter alat, kelajuan mesin dan kedalaman semasa proses pemotongan
sebenar.
ii
ACKNOWLEDGEMENTS
First and foremost, I would like to convey my deepest gratitude to my respected supervisor,
Assoc. Prof. Dr. Zamberi Jamaludin. It is a great honour and pleasure to be able to work
with him, a person of great control system background, experience, success, ideas and
stature. Your kind advice, time, attention and dedication towards realizing this works are
greatly appreciated and indebted. May 'Allah' the Almighty bless you. Thank you 'teacher'.
I would also like to express my special gratitude to Prof. Jan Swevers; my Pro-motor
during my 6 months PhD attachment at K.U. Leuven, Belgium.
I would like to extend my gratitude to UTeM and FKP UTeM and to all academic and
supporting staffs for assisting me in terms of facility and moral support. This work is made
possible with the financial supports of the Ministry of Higher Education Malaysia (SLAB)
and UTeM. These financial supports are greatly appreciated and indebted.
A special thanks also to my colleagues from Control System in Machine Tools (CosMaT)
research group, Ms Nur Aidawaty Rafan, Mr. Chiew Tsung Heng, Mr. Jailani
Jamaludin ,Mr. Tang Teng Fong and Ms. Madihah Maarof. All I can say is "Engineering is
teamwork". Thanks a lot guys, our friendship and sweet memories together will always
remain in my heart. Finally and most importantly, I wish to express my deepest gratitude to
both of my parents, Hj. Abdullah Md. Said and Hjh Mariyam Mohamad, my sister
Khadijah Abdullah, my brother Dr. Abdul Rahim Abdullah, my father and mother-in-law
Hj Salim Jaafar and Hjh Hamidah Abdullah for their prayers, loves, cares and support. I
am greatly indebted to them and may 'Allah' repay all their good deeds and sacrifices. To
my beloved wife Nur Radziah Salim and my children (Irdina Ilmuna, Nur Husna Sakinah,
Abd. Rahman and Nur Khadijah), there are no words to portray how blessed and thankful I
am for your company during both the easy and the difficult times of this journey. I salute
your patience, pray, dedication, love, courage and care that have brought happiness and
serenity to our life.
iii
TABLE OF CONTENTS
PAGE
DECLARATION
DEDICATION
ABSTRACT
ABSTRAK
ACKNOWLEDGEMENTS
TABLE OF CONTENTS
LIST OF TABLES
LIST OF FIGURES
LIST OF SYMBOLS
LIST OF ABBREVIATIONS
LIST OF PUBLICATIONS
i
ii
iii
iv
vii
x
xvii
xviii
xix
CHAPTER
1
INTRODUCTION
1.1 Background
1.2 Problem Statements
1.3 Research Objectives
1.4 Scope of Work
1.5 Significance of Studies
1.6 Organization of Report
1
1
2
5
5
6
6
2
LITERATURE REVIEW
2.1 Introduction
2.2 State of the Art on Motion Control in Machine Tool
2.2.1
Mechanical Drive System
2.2.2
Disturbances in Drive System
2.2.2.1
Friction Forces
2.2.2.2
Cutting Forces
2.2.3
Cutting Forces Measurement Method
2.3 Cutting Force Compensation Method - A Controller Design Approach
2.3.1
Controller Design
2.3.2
Controller Design based on PID
2.3.3
Other Techniques of Controller Design
2.4 Summary
8
8
9
9
14
15
15
18
23
23
24
29
33
3
METHODOLOGY
3.1 Introduction
3.2 Experimental Setup
3.3 System Identification and System Modelling
3.4 Motor Constant Identification
3.5 Cutting Force Characterization
3.5.1
Experimental Setup of Cutting Force Measurement
3.5.2
Experimental Design for Cutting Force Characterization
35
35
38
40
45
46
46
49
iv
3.5.3
3.6
Characterization and Analysis of Cutting Forces
3.5.3.1
Conversion of Cutting Force Data (Newton to Volt)
3.5.4
Analysis of the Measured Cutting Forces
Summary
52
52
52
54
4
CONTROLLER DESIGN
55
4.1 Introduction
55
4.2 Cascade Controller
56
4.2.1
Cascade Control Structure and Configuration based on Ideal System 56
4.2.2
Analysis of the Closed Loop Behaviour with Proportional (P) Speed
Control
58
4.2.3
Analysis of the Closed Loop Behaviour with PI Speed Control
61
4.2.4
Design and Analysis of the PI Speed Controller based on Measured
FRF
64
4.2.5
Design and Analysis of the Position Loop based on measured FRF 71
4.2.6
Analysis of Tracking Performance
79
4.2.6.1
Numerical Validation of Tracking Performance
79
4.2.6.2
Experimental Validation of Tracking Performance
81
4.3 Nonlinear PID (NPID) Controller
83
4.3.1
Design and Analysis of PID Controller
83
4.3.2
General Structure and Configuration of NPID controller
87
4.3.3
Design and Analysis of NPID Controller
89
4.4 Nonlinear Cascade Feedforward (NCasFF)
94
4.4.1
Nonlinear Cascade Feedforward (NCasFF) control structure
94
4.4.2
Design Guidelines of NCasFF Controller
95
4.4.3
Design of Inverse Plant Model and Speed Feedforward
97
4.4.4
NCasFF Controller : Design of Nonlinear Function (Step 4)
99
4.4.5
NCasFF Controller : Design of Dead Zone Compensator (DZC) 108
4.4.6
Design Analysis of NCasFF Controller
113
4.4.7
NCasFF Controller : Numerical Analysis of Tracking Performance 116
4.5 Summary
118
5
RESULTS AND DISCUSSION
5.1 Introduction
5.2 Maximum Tracking Error
5.2.1
Cascade P/PI Controller
5.2.1.1
Simulation Results
5.2.1.2
Experimental Results
5.2.2
NPID Controller
5.2.2.1
Simulation Results
5.2.2.2
Experimental Results
5.2.3
Nonlinear Cascade Feedforward (NCasFF) Controller
5.2.3.1
Simulation Results
5.2.3.2
Experimental Results
5.3 Root Mean Square Error (RMSE)
5.4 Fast Fourier Transform (FFT) Error
5.5 Surface Finish Quality
5.6 Discussion
v
119
119
120
120
120
123
127
127
129
133
133
135
139
142
147
151
5.6.1
Discussion on Results of Maximum Tracking Error
5.6.1.1
Cascade P/PI Controller
5.6.1.2
NPID Controller
5.6.1.3
NCasFF Controller
Discussion on Results of RMSE Analysis
Discussion on Results of FFT Error Analysis
Discussion on Results of Surface Finish Quality
151
151
152
154
156
157
161
CONCLUSION AND SUGGESTION FOR FUTURE WORK
6.1 Conclusion
6.2 Suggestion for Future Work
162
162
165
5.6.2
5.6.3
5.6.4
6
REFERENCES
APPENDIX A
APPENDIX B
APPENDIX C
APPENDIX D
APPENDIX E
APPENDIX F
APPENDIX G
APPENDIX H
APPENDIX I
APPENDIX J
APPENDIX K
166
176
177
178
180
182
184
186
188
190
192
196
vi
LIST OF TABLES
TABLE
TITLE
PAGE
3.1
System model parameters for x and y axes
43
3.2
List of equipment with specifications
46
3.3
Recommended cutting parameters of milling operation
49
3.4
Cutting parameters of the experimental design
50
3.5
Amplitude cutting force at different spindle speed
53
4.1
Speed loop PI controller parameters of x and y axes
66
4.2
Gain margin and Phase margin of x and y axes open loop speed
67
4.3
Bandwidth of the speed loop based on sensitivity function
69
4.4
Gain margin and Phase margin of x and y axes open loop position
73
4.5
Bandwidth of the position loop
76
4.6
Gain values of Kp, Ki, and Kd for PID controller
84
4.7
Gain margin and Phase margin of x and y axes open loop position
85
4.8
Bandwidth of the position loop via PID controller
86
4.9
Value of tuned NPID parameters, KO and emax
92
4.10
Value of Nonlinear function parameters for NCasFF controller
100
4.11
Value of parameters in designing DZC
112
4.12
Bandwidth of the position loop
114
5.1
Research configurations
119
5.2
Simulated maximum tracking error with Cascade P/PI controller
122
5.3
Experimental maximum tracking error with Cascade P/PI controller
125
vii
5.4
Simulated maximum tracking error of system with NPID controller
128
5.5
Experimental maximum tracking error of system with NPID controller
131
5.6
Simulated maximum tracking error of system with NCasFF controller
134
5.7
Experimental maximum tracking error with NCasFF controller
137
5.8
X-axis: Comparison in RMSE values for different controllers at 0.3 Hz
139
5.9
X-axis: Comparison in RMSE values for different controllers at 0.7 Hz
141
5.10
X-axis : Comparison in magnitudes of FFT Error between NPID, 144
Cascade P/PI and NCasFF for cutting forces at spindle speed of 1000,
2000 and 3000 rpm at 0.7 Hz
5.11
X-axis : Average percentage of FFT error reduction between NPID, 144
Cascade P/PI and NCasFF for cutting forces at spindle speed of 1000,
2000 and 3000 rpm at 0.7 Hz
5.12
X-axis : Comparison in magnitudes of FFT Error between NPID, 145
Cascade P/PI and NCasFF for cutting forces at spindle speed of 1000,
2000 and 3000 rpm at 0.3 Hz
5.13
X-axis : Average percentage of FFT error reduction between NPID, 145
Cascade P/PI and NCasFF for cutting forces at spindle speed of 1000,
2000 and 3000 rpm at 0.3 Hz
5.14
Surface roughness comparison between controllers
149
6.1
Thesis conclusion
164
6.2
Simulated maximum tracking error of system with Cascade P/PI
179
6.3
Experimental maximum tracking error of system with Cascade P/PI
181
6.4
Simulated maximum tracking error of system with NPID controller
183
6.5
Experimental maximum tracking error of system with NPID controller
185
6.6
Simulated maximum tracking error of system with NCasFF controller
187
6.7
Experimental maximum tracking error of system with NCasFF
189
6.8
Y-axis: Comparison of RMSE at frequency 0.7 Hz
190
6.9
Y-axis: Comparison of RMSE at frequency 0.3 Hz
191
viii
6.10
Y-axis: Comparison of FFT Error between controllers at f = 0.7 Hz
193
6.11
Y-axis: Average Percentage Error Reduction of FFT Error at f = 0.7 Hz
194
6.12
Y-axis: Comparison of FFT Error between controllers at f = 0.3 Hz
194
6.13
Y-axis: Average Percentage Error Reduction of FFT Error at f = 0.3 Hz
195
ix
LIST OF FIGURES
FIGURE
TITLE
PAGE
1.1
Quadrant glitches in circular test
03
2.1
Rack and pinion drive system
10
2.2
Ball screw driven system
11
2.3
Structure of iron-core linear drive system
12
2.4
Structure of piezoelectric drive system
13
2.5
Cutting parameter direction in the cutting zone
16
2.6
Kistler force measurement dynamometer
19
2.7
The setup of capacitive sensor on milling machine
20
2.8
Cylindrical capacitive displacement sensor
21
2.9
Plot of motor current versus cutting force
21
2.10
Structure of active electromagnetic bearings
22
2.11
Axial tracking error with (a) Cascade (b) Cascade with Speed & 26
Acceleration Feedforward
2.12
Diagram of cascade controller with cutting force estimator
31
2.13
Sample of Ferrari Sensors
32
2.14
Position errors at 1,2,3 and 15 harmonics using cutting force estimator
32
3.1
Flowchart of the research methodology
36
3.2
Googol Tech XYZ Milling Table
38
x
3.3
Schematic diagram of the experimental setup
39
3.4
Simulink diagram for FRF measurement
41
3.5
FRF's measurement of the x and y axes
42
3.6
X-axis : FRF measurement and proposed model
44
3.7
Y-axis : FRF measurement and proposed model
44
3.8
Block diagram of the open loop system to approximate the force 45
constant
3.9
Schematic diagram for cutting force characterization
47
3.10
Mounting points of the Kistler dynamometer
48
3.11
Aluminium block during milling operation
49
3.12
Cutting path planning for cutting force measurement
51
3.13
Example of measured cutting force at 1000 rpm
51
3.14
Method on how to inject the cutting forces into the system plant
52
3.15
FFT cutting forces at 1000, 2000 and 3000 rpm spindle speed rotation
53
4.1
General control structure of a cascade control
56
4.2
Ideal cascade control for a position control
58
4.3
Cascade P/PI control structure in frequency domain for control of a 64
motor
4.4
X-axis: Theoretical bode plot of speed open loop transfer function using 66
measured FRF of the system
4.5
Y-axis: Theoretical bode plot of speed open loop transfer function using 67
measured FRF of the system
4.6
X-axis: Nyquist diagram of the speed open loop transfer function based 68
on measured FRF of the system
4.7
Y-axis: Nyquist diagram of the speed open loop transfer function based 68
on measured FRF of the system
4.8
X-axis: Sensitivity function for the speed loop
69
4.9
Y-axis: Sensitivity function for the speed loop
69
xi
4.10
X-axis: Bode diagram of speed closed loop transfer function
70
4.11
Y-axis: Bode diagram of speed closed loop transfer function
70
4.12
X-axis: Theoretical bode plot of position open loop transfer function 72
based on measured FRF of the system
4.13
Y-axis: Theoretical bode plot of position open loop transfer function 72
based on measured FRF of the system
4.14
X-axis: Nyquist diagram of the position open loop transfer function 73
based on measured FRF of the system
4.15
Y-axis: Nyquist diagram of the position open loop transfer function 74
based on measured FRF of the system
4.16
X-axis: Sensitivity function for the position loop
75
4.17
Y-axis: Sensitivity function for the position loop
75
4.18
X-axis: Position closed loop transfer function
76
4.19
Y-axis: Position closed loop transfer function
77
4.20
X-axis: Comparison of dynamic stiffness between Cascade P/P and 78
Cascade P/PI
4.21
Y-axis: Comparison of dynamic stiffness between Cascade P/P and 78
Cascade P/PI
4.22
X-axis: Simulated position error for sinusoidal reference signal of an 79
amplitude 1mm and frequency of 0.7 Hz
4.23
Y-axis: Simulated position error for sinusoidal reference signal of an 80
amplitude 1mm and frequency of 0.7 Hz
4.24
X-axis: Position error transfer function
80
4.25
Y-axis: Position error transfer function
81
4.26
X-axis: Numerical and Experimental Position Closed Loop
82
4.27
Y-axis: Numerical and Experimental Position Closed Loop
82
4.28
PID control structure
83
4.29
Bode Diagram of Open Loop Transfer Function for x and y axes
85
xii
4.30
Nyquist plots of the x-axis (left) and the y-axis (right) position open 85
loop transfer function based on measured FRFs of the system via PID
controller
4.31
Bode magnitude diagram of sensitivity for x and y axes via PID 86
controller
4.32
Bode diagram of position closed loop for x and y axes via PID 87
controller
4.33
NPID control structure and configuration
88
4.34
Flowchart of the procedure to obtain parameters of NPID controller
89
4.35
X-axis : Popov plot of NPID controller
91
4.36
Y-axis : Popov plot of NPID controller
91
4.37
X-axis : Graph of nonlinear gain, Ke against error, e
93
4.38
Y-axis : Graph of nonlinear gain, Ke against error, e
93
4.39
Nonlinear cascade feedforward (NCasFF) control structure with speed 94
and inverse plant feedforward
4.40
Flowchart of design guidelines of NCasFF controller
96
4.41
Cascade P/PI with inverse plant model and speed feedforward
97
4.42
Simulated tracking error of the x-axis (left) and the y-axis (right) for 98
sinusoidal reference signal of an amplitude 1mm and freq. 0.7 Hz
4.43
General structure of independent feedforward controller
98
4.44
General structure of the nonlinear function
100
4.45
Switching function : (a) Signum function (b) Sigmoid function
102
4.46
Comparison of control input between signum and sigmoid function
103
4.47
Step by step procedures to tune parameters of nonlinear function, N
104
4.48
X-axis : Popov plot of NCasFF controller
105
4.49
Y-axis : Popov plot of NCasFF controller
105
4.50
Effect of Ke and e on variation of KO
106
4.51
Effect of Ke and e on variation of emax
107
xiii
4.52
Dead zone compensator in Nonlinear Cascade Feedforward controller
109
4.53
Dead zone characteristics of a system
109
4.54
System block diagram with Dead Zone Compensator
111
4.55
X-axis : Sensitivity function of NCasFF controller
114
4.56
Y-axis : Sensitivity function of NCasFF controller
114
4.57
X-axis : Dynamic stiffness of NCasFF controller (Ke = 1.0)
115
4.58
Y-axis : Dynamic stiffness of NCasFF controller (Ke = 1.0)
115
4.59
X-axis: Simulated error for sinusoidal reference signal of an amplitude 117
1mm, frequency of 0.7 Hz and Ke = 1.04 (left) and position error
transfer function (right)
4.60
Y-axis: Simulated error for sinusoidal reference signal of an amplitude 117
1mm, frequency of 0.7 Hz and Ke = 1.04 (left) and position error
transfer function (right)
5.1
X-axis: Simulated tracking error with Cascade P/PI controller at f = 0.3 121
Hz
5.2
X-axis: Simulated tracking error with Cascade P/PI controller at f = 0.7 121
Hz
5.3
Control scheme of Cascade P/PI controller for experimental validation
123
5.4
X-axis: Experimental tracking error with Cascade P/PI controller at 124
f = 0.3 Hz
5.5
X-axis: Experimental tracking error with Cascade P/PI controller at 124
f = 0.7 Hz
5.6
X-axis: Experimental positions against simulation positions for cutting 126
forces at spindle speed of 1000, 2000 and 3000 rpm for f = 0.3 Hz
5.7
X-axis: Experimental positions against simulation positions for cutting 126
forces at spindle speed of 1000, 2000 and 3000 rpm with f = 0.7 Hz
5.8
X-axis: Simulated tracking error for NPID controller at f = 0.3Hz
127
5.9
X-axis: Simulated tracking error for NPID controller at f = 0.7 Hz
128
5.10
Control scheme of NPID controller for experimental validation
129
xiv
5.11
X-axis: Experimental tracking error for NPID controller at f = 0.3 Hz
130
5.12
X-axis: Experimental tracking error for NPID controller at f = 0.7 Hz
130
5.13
X-axis: Experimental positions against simulated positions for cutting 132
forces at spindle speed of 1000, 2000 and 3000 rpm at f = 0.3 Hz.
5.14
X-axis: Experimental positions against simulated positions for cutting 132
forces at spindle speed of 1000, 2000 and 3000 rpm at f = 0.7 Hz
5.15
X-axis: Simulated tracking error of NCasFF controller at f = 0.3 Hz
133
5.16
X-axis: Simulated tracking error of NCasFF controller at f = 0.7 Hz
134
5.17
Control scheme of NCasFF controller for experimental validation
135
5.18
X-axis: Experimental tracking error for NCasFF controller at f = 0.3 Hz
136
5.19
X-axis: Experimental tracking error for NCasFF controller at f = 0.7 Hz
136
5.20
X-axis: Experimental positions against simulated positions for cutting 138
forces at spindle speed of 1000, 2000 and 3000 rpm at f = 0.3 Hz
5.21
X-axis: Experimental positions against simulated positions for cutting 138
forces at spindle speed of 1000, 2000 and 3000 rpm at f = 0.7 Hz
5.22
X-axis: RMSE values for different controllers and cutting forces at 140
f = 0.3 Hz
5.23
X-axis: RMSE values for different controllers and cutting forces at 141
f = 0.7 Hz
5.24
X-axis: Comparison of FFT Error between NPID, Cascade P/PI and 143
NCasFF controller at frequency 0.3 Hz and spindle speed of (a) 1000
rpm (b) 2000 rpm (c) 3000 rpm
5.25
X-axis: Comparison of FFT Error between NPID, Cascade P/PI and 143
NCasFF controller at frequency 0.7 Hz and spindle speed of (a) 1000
rpm (b) 2000 rpm (c) 3000 rpm
5.26
Surface roughness profile (reproduced from Colak et al., 2007)
147
5.27
Workpiece with straight cutting performed at spindle speed of 1000, 148
2000 and 3000 rpm
5.28
Comparison of dynamic stiffness between NPID, Cascade P/PI and 155
NCasFF
xv
5.29
Dynamic stiffness of NCasFF controller
156
5.30
X-axis: FFT Error for NPID, Cascade P/PI and NCasFF at f = 0.7 Hz
159
5.31
X-axis: FFT Error for NPID, Cascade P/PI and NCasFF at f = 0.3 Hz
160
6.1
Y-axis: Simulated tracking error with Cascade P/PI controller at 178
f = 0.7 Hz.
6.2
Y-axis: Simulated tracking error with Cascade P/PI controller at 178
f = 0.3 Hz.
6.3
Y-axis: Experimental tracking error with Cascade P/PI controller at 180
f = 0.7 Hz.
6.4
Y-axis: Experimental tracking error with Cascade P/PI controller at 180
f = 0.3 Hz.
6.5
Y-axis: Simulated tracking error of system with NPID at f = 0.7 Hz.
182
6.6
Y-axis: Simulated tracking error of system with NPID at f = 0.3 Hz.
182
6.7
Y-axis: Experimental tracking error with NPID controller at f = 0.7 Hz.
184
6.8
Y-axis: Experimental tracking error with NPID controller at f = 0.3 Hz.
184
6.9
Y-axis: Simulated tracking error with NCasFF controller at f = 0.7 Hz.
186
6.10
Y-axis: Simulated tracking error with NCasFF controller at f = 0.3 Hz.
186
6.11
Y-axis: Experimental tracking error via NCasFF controller at f=0.7 Hz.
188
6.12
Y-axis: Experimental tracking error via NCasFF controller at f =0.3 Hz.
188
6.13
Y-axis: Comparison of RMSE at frequency 0.7 Hz
190
6.14
Y-axis: Comparison of RMSE at frequency 0.3 Hz
191
6.15
Y-axis: Comparison of FFT Error between NPID, Cascade P/PI and 192
NCasFF controller at spindle speed of 1000 rpm at 0.7 and 0.3 Hz
6.16
Y-axis: Comparison of FFT Error between NPID, Cascade P/PI and 192
NCasFF controller at spindle speed of 2000 rpm at 0.7 and 0.3 Hz
6.17
Y-axis: Comparison of FFT Error between NPID, Cascade P/PI and 193
NCasFF controller at spindle speed of 3000 rpm at 0.7 and 0.3 Hz
6.18
Mitutoyo portable surface roughness tester (Surftest SJ-301)
xvi
196
LIST OF SYMBOLS
R
-
Resultant force
Fc
-
Cutting force
Ft
-
Thrust force
Fs
-
Cutting speed
Ft
-
Thrust force
Kf
-
Motor constant
M
-
Mass
Zref
-
Reference position
Z
-
Output position
G(s)
-
System
Gm (s)
-
System model transfer function
Ĝ (s)
-
FRF of the considered system
Gm-1(s)
-
Inverse system model transfer function
Gs(s)
-
Speed feedforward
d(t)
-
Disturbances
N(t)
-
Noises
Td
-
Time delay
ep(t)
-
Position tracking error
ev(t)
-
Velocity tracking error
Sv
-
Sensitivity function of velocity loop
Sp
-
Sensitivity function of position loop
Kp
-
Proportional gain
Ki
-
Integral gain
Kd
-
Derivative gain
Ke
-
Nonlinear gain
fe
-
Scaled error
KO
-
Rate of variation of nonlinear gain
emax
-
Range value of error variation
xvii
LIST OF ABBREVIATIONS
AC
-
Alternating current
CNC
-
Computer numerical control
DAC
-
Digital to analog
DFO
-
Disturbance force observer
DSP
-
Digital signal processor
EDM
-
Electro discharge machine
FFT
-
Fast fourier transform
FLC
-
Fuzzy logic control
FRF
-
Frequency response function
HSS
-
High speed steel
I/O
-
Input/output
ISMC
-
Integral sliding mode control
LTI
-
Linear time invariant
LQG
-
Linear quadratic regulator
MBC
-
Model based compensator
MMI
-
Man machine interface
NCasFF
-
Nonlinear cascade feedforward
NLLS
-
Nonlinear least square
NPID
-
Nonlinear proportional-integral-derivative
P
-
Proportional
-
Pseudo derivative feedback
PI
-
Proportional-integral
PID
-
Proportional-integral-derivative
RMSE
-
Root mean square error
RPM
-
Revolution per minute
SISO
-
Single input single output
SMC
-
Sliding mode control
Vest
-
Estimate velocity
xviii
LIST OF PUBLICATIONS
Journals:
1.
Abdullah, L., Jamaludin, Z., Salleh, M. R., Abu Bakar, B., Jamaludin, J., Chiew, T.
H., and Rafan, N.A. 2014. Theoretical Analysis of Velocity and Position Loop
Behaviour of Nonlinear Cascade Feedforward Controller for Positioning of XY
Table Ballscrew Drive System. Advanced Materials Research, 845, pp. 831 – 836.
2.
Abdullah, L., Jamaludin, Z., Chiew, T. H., Rafan, N. A., and Shaaban, A., 2014.
Spectral Analysis of Cutting Forces Data for XY Table Ballscrew Drive System.
Applied Mechanics and Materials, 471, pp. 241 – 246.
3.
Abdullah, L., Jamaludin, Z., Ahsan, Q., Jamaludin, J., Rafan, N. A., Chiew, T. H.,
Jusoff, K., and Yusoff, M. 2013. Evaluation on Tracking Performance of PID, Gain
Scheduling and Classical Cascade P/PI controller on XY Table Ballscrew Drive
System. World Applied Sciences Journal, 21(1), 01-10.
4.
Abdullah, L. Jamaludin, Z., Chiew, T. H., Rafan, N. A., and Maidin, S., 2013.
Theoretical Analysis of Close loop Behaviour of Ideal Cascade Controller Structure
for Positioning of XY Table Ballscrew Drive System. Applied Mechanics and
Materials, 315, pp. 493 – 497.
5.
Abdullah, L., Jamaludin, Z., Chiew, T. H., Rafan, N. A., and Syed Mohamed, M. S.,
2012. System Identification of XY Table Ballscrew Drive using Parametric and
Non Parametric Frequency Domain Estimation via Deterministic Approach.
Procedia Engineering, 41, pp. 567 – 574.
6.
Abdullah, L., Jamaludin, Z., Chiew, T. H., and Rafan, N. A., 2012. Systematic
Method for Cutting Forces Characterization for XY Milling Table Ballscrew Drive
System. International Journal of Mechanical & Mechatronics Engineering, 12(6),
pp. 28 – 33.
7.
Abdullah, L., Jamaludin, Z., Chiew, T. H., Rafan, N. A., and Yuhazri, M. Y., 2012.
Extensive Tracking Performance Analysis of Classical Feedback Control for XY
Stage Ballscrew System. Applied Mechanics and Materials, 229 – 231, pp. 750 – 7
55.
xix