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
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
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
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.
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,
i 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
ii 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
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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.
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2.2 State of the Art on Motion Control in Machine Tool 9
2.2.1 Mechanical Drive System 9
2.2.2 Disturbances in Drive System 14
2.2.2.1 Friction Forces 15
2.2.2.2 Cutting Forces 15
2.2.3 Cutting Forces Measurement Method 18
2.3 Cutting Force Compensation Method - A Controller Design Approach 23
2.3.1 Controller Design 23
2.3.2 Controller Design based on PID 24
2.3.3 Other Techniques of Controller Design 29
2.4 Summary 33
3 METHODOLOGY 35
3.1 Introduction 35
3.2 Experimental Setup 38
3.3 System Identification and System Modelling 40
3.4 Motor Constant Identification 45
3.5 Cutting Force Characterization 46
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3.5.3 Characterization and Analysis of Cutting Forces 52 3.5.3.1 Conversion of Cutting Force Data (Newton to Volt) 52
3.5.4 Analysis of the Measured Cutting Forces 52
3.6 Summary 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 119
5.1 Introduction 119
5.2.3 Nonlinear Cascade Feedforward (NCasFF) Controller 133
5.2.3.1 Simulation Results 133
5.2.3.2 Experimental Results 135
5.3 Root Mean Square Error (RMSE) 139
5.4 Fast Fourier Transform (FFT) Error 142
5.5 Surface Finish Quality 147
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5.6.1 Discussion on Results of Maximum Tracking Error 151
5.6.1.1 Cascade P/PI Controller 151
5.6.1.2 NPID Controller 152
5.6.1.3 NCasFF Controller 154
5.6.2 Discussion on Results of RMSE Analysis 156
5.6.3 Discussion on Results of FFT Error Analysis 157 5.6.4 Discussion on Results of Surface Finish Quality 161
6 CONCLUSION AND SUGGESTION FOR FUTURE WORK 162
6.1 Conclusion 162
6.2 Suggestion for Future Work 165
REFERENCES 166
APPENDIX A 176
APPENDIX B 177
APPENDIX C 178
APPENDIX D 180
APPENDIX E 182
APPENDIX F 184
APPENDIX G 186
APPENDIX H 188
APPENDIX I 190
APPENDIX J 192
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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
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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,
Cascade P/PI and NCasFF for cutting forces at spindle speed of 1000, 2000 and 3000 rpm at 0.7 Hz
144
5.11 X-axis : Average percentage of FFT error reduction between NPID, Cascade P/PI and NCasFF for cutting forces at spindle speed of 1000, 2000 and 3000 rpm at 0.7 Hz
144
5.12 X-axis : Comparison in magnitudes of FFT Error between NPID, Cascade P/PI and NCasFF for cutting forces at spindle speed of 1000, 2000 and 3000 rpm at 0.3 Hz
145
5.13 X-axis : Average percentage of FFT error reduction between NPID, Cascade P/PI and NCasFF for cutting forces at spindle speed of 1000, 2000 and 3000 rpm at 0.3 Hz
145
5.14 Surface roughness comparison between controllers 149
6.1 Thesis conclusion 164
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x
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 & Acceleration Feedforward
26
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
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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 constant
45
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 motor
64
4.4 X-axis: Theoretical bode plot of speed open loop transfer function using measured FRF of the system
66
4.5 Y-axis: Theoretical bode plot of speed open loop transfer function using measured FRF of the system
67
4.6 X-axis: Nyquist diagram of the speed open loop transfer function based on measured FRF of the system
68
4.7 Y-axis: Nyquist diagram of the speed open loop transfer function based on measured FRF of the system
68
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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
based on measured FRF of the system
72
4.13 Y-axis: Theoretical bode plot of position open loop transfer function based on measured FRF of the system
72
4.14 X-axis: Nyquist diagram of the position open loop transfer function based on measured FRF of the system
73
4.15 Y-axis: Nyquist diagram of the position open loop transfer function based on measured FRF of the system
74
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 amplitude 1mm and frequency of 0.7 Hz
79
4.23 Y-axis: Simulated position error for sinusoidal reference signal of an amplitude 1mm and frequency of 0.7 Hz
80
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
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4.30 Nyquist plots of the x-axis (left) and the y-axis (right) position open loop transfer function based on measured FRFs of the system via PID 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, Keagainst 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 and inverse plant feedforward
94
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
sinusoidal reference signal of an amplitude 1mm and freq. 0.7 Hz
98
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 Keand e on variation of KO 106
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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 1mm, frequency of 0.7 Hz and Ke = 1.04 (left) and position error
transfer function (right)
117
4.60 Y-axis: Simulated error for sinusoidal reference signal of an amplitude 1mm, frequency of 0.7 Hz and Ke = 1.04 (left) and position error
transfer function (right)
117
5.1 X-axis: Simulated tracking error with Cascade P/PI controller at f = 0.3 Hz
121
5.2 X-axis: Simulated tracking error with Cascade P/PI controller at f = 0.7 Hz
121
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
5.6 X-axis: Experimental positions against simulation positions for cutting forces at spindle speed of 1000, 2000 and 3000 rpm for f = 0.3 Hz
126
5.7 X-axis: Experimental positions against simulation positions for cutting forces at spindle speed of 1000, 2000 and 3000 rpm with f = 0.7 Hz
126
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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
forces at spindle speed of 1000, 2000 and 3000 rpm at f = 0.3 Hz.
132
5.14 X-axis: Experimental positions against simulated positions for cutting forces at spindle speed of 1000, 2000 and 3000 rpm at f = 0.7 Hz
132
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
forces at spindle speed of 1000, 2000 and 3000 rpm at f = 0.3 Hz
138
5.21 X-axis: Experimental positions against simulated positions for cutting forces at spindle speed of 1000, 2000 and 3000 rpm at f = 0.7 Hz
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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 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
NCasFF controller at spindle speed of 1000 rpm at 0.7 and 0.3 Hz
192
6.16 Y-axis: Comparison of FFT Error between NPID, Cascade P/PI and NCasFF controller at spindle speed of 2000 rpm at 0.7 and 0.3 Hz
192
6.17 Y-axis: Comparison of FFT Error between NPID, Cascade P/PI and NCasFF controller at spindle speed of 3000 rpm at 0.7 and 0.3 Hz
193
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Zref - Reference position
Z - Output position
Sv - Sensitivity function of velocity loop
Sp - Sensitivity function of position loop
xviii
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
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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.
