Design Of PID And Nonlinear PID Controller For Tracking Performance Of XY Table Ball Screw Drive System.

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UNIVERSITI TEKNIKAL MALAYSIA MELAKA

DESIGN OF PID AND NONLINEAR PID CONTROLLER FOR

TRACKING PERFORMANCE OF XY TABLE BALL SCREW

DRIVE SYSTEM

This report submitted in accordance with requirement of the Universiti Teknikal Malaysia Melaka (UTeM) for the Bachelor Degree of Manufacturing Engineering

(Robotics and Automation) (Hons.)

NURUL HIDAYAH BINTI ZULKIFLI B051110080

920112-02-5440

FACULTY OF MANUFACTURING ENGINEERING 2015

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UNIVERSITI TEKNIKAL MALAYSIA MELAKA

BORANG PENGESAHAN STATUS LAPORAN PROJEK SARJANA MUDA

TAJUK: Design of PID and Nonlinear PID Controller for Tracking Performance of XY Table Ball Screw Drive System

SESI PENGAJIAN: 2014/15 Semester 2

Saya NURUL HIDAYAH BINTI ZULKIFLI

mengaku membenarkan Laporan PSM ini disimpan di Perpustakaan Universiti Teknikal Malaysia Melaka (UTeM) dengan syarat-syarat kegunaan seperti berikut: 1. Laporan PSM adalah hak milik Universiti Teknikal Malaysia Melaka dan penulis. 2. Perpustakaan Universiti Teknikal Malaysia Melaka dibenarkan membuat salinan

untuk tujuan pengajian sahaja dengan izin penulis.

3. Perpustakaan dibenarkan membuat salinan laporan PSM ini sebagai bahan pertukaran antara institusi pengajian tinggi.

4. **Sila tandakan ( ) SULIT

TERHAD

TIDAK TERHAD

(Mengandungi maklumat yang berdarjah keselamatan atau kepentingan Malaysia sebagaimana yang termaktub dalam AKTA RAHSIA RASMI 1972)

(Mengandungi maklumat TERHAD yang telah ditentukan oleh organisasi/badan di mana penyelidikan dijalankan)

Alamat Tetap:

NO. 2266, Kampung Pokok Pauh, Jalan Kubur Panjang,

06760 Alor Setar,Kedah.

Tarikh: ________________________

Disahkan oleh:

Cop Rasmi:

Tarikh: _______________________

** Jika Laporan PSM ini SULIT atau TERHAD, sila lampirkan surat daripada pihak berkuasa/organisasi berkenaan dengan menyatakan sekali sebab dan tempoh laporan PSM ini perlu dikelaskan sebagai SULIT atau TERHAD.

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DECLARATION

I hereby, declared this report entitled “Design of PID and Nonlinear PID Controller for Tracking Performance of XY Table Ball Screw Drive System” is the results of

my own research except as cited in references.

Signature : ……….

Author’s Name : NURUL HIDAYAH BINTI ZULKIFLI

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APPROVAL

This report is submitted to the Faculty of Manufacturing Engineering of UTeM as a partial fulfillment of the requirements for the degree of Bachelor of Manufacturing Engineering (Robotics & Automation) (Hons). The member of the supervisory is as follow:

……… (DR. IR. LOKMAN BIN ABDULLAH)

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ABSTRACT

This project report presents the work done on design of PID and Nonlinear PID (NPID) controller for XY table ball screw driven system in the CIM Laboratory, Faculty of Manufacturing Engineering, UTeM. 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 has led to a new and challenging era in the area of machining tools and control. The objective of this project is to design and validate a PID and NPID for tracking performance of the XY table ball screw driven system by Googoltech Inc and to validate the controller through simulation using MATLAB/Simulink software and experimental work using XY table ball screw driven system. This project proposes an approach to compensate multiple frequency components, named PID controller and NPID controller at the x-axis of the XY table ball screw driven system. 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 PID controller is able to compensate tracking errors better than PID controller. Results showed that the Nonlinear PID controller manages to have better performance in terms of maximum tracking error than PID controller. It is also 0.28% (f = 0.3 Hz) and 1.16% (f = 0.5 Hz ) better performance in terms of Root Mean Square Error (RMSE) than PID 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.

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ABSTRAK

Laporan projek ini membentangkan kerja yang dilakukan ke atas sistem kawalan “PID” dan “Nonlinear PID (NPID)” terhadap ketepatan posisi sistem mesin XY di Makmal CIM, Fakulti Kejuruteraan Pembuatan, UTeM. 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. Objektif laporan kajian ini adalah untuk mereka bentuk dan mengesahkan sistem kawalan “PID” dan “NPID” untuk ketepatan posisi sistem mesin XY didorong oleh sistem Googoltech Inc dan untuk mengesahkan pengawal melalui simulasi menggunakan perisian MATLAB /Simulink dan kerja uji kaji menggunakan mesin XY. Projek ini mencadangkan satu pendekatan untuk mengatasi frekuensi yang pelbagai, dipanggil sistem kawalan “PID” dan “NPID” di paksi x bagi mesin XY. Proses pemotongan sebenar dijalankan ke atas mesin XY bagi tujuan validasi. Berdasarkan keputusan yang dihasilkan, di dapati sistem kawalan ‘NPID” telah berjaya untuk mengatasi masalah pengesanan lebih baik daripada sistem kawalan“PID’. Hasil eksperimen menunjukkan bahawa sistem kawalan "NPID" berjaya membuahkan hasil yang lebih baik dari aspek kesilapan maksimum pengesanan daripada sistem kawalan PID. Ianya juga, 0.28% (f =0.3 Hz) dan 1.16% (f=0.5 Hz) lebih baik dalam aspek "Root Mean Square Error (RMSE) daipada sistem kawalan “PID”. 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.

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iii

DEDICATION

To my beloved parents

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ACKNOWLEDGEMENT

First and foremost, I would like to convey my deepest gratitude to my respected supervisor, Dr. Ir. Lokman bin Abdullah. It is a great honors and pleasure to be able to work with him. 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'.

A special thanks also to my colleagues from Bachelor of Manufacturing (Robotics & Automation). 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, Zulkifli bin Hussain and Suriani binti Mat Rashid, my sisters Nurul Shafinaz Zukifli and Nurul Sakinah Zulkifli, my brothers Mohd Shahrul Anuar Zulkifli and Muhammad Aiman Zulkfili, my grandfather and grandmother Hussain bin Darus and Meriam binti Idris for their prayers, loves, cares and support. I am greatly indebted to them and may 'Allah' repay all their good deeds and sacrifices. I salute their patience, pray, dedication, love, courage and care that have brought happiness and serenity to our life.

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TABLE OF CONTENT

Declaration Approval

Abstract i

Abstrak ii

Dedication iii

Acknowledgement iv

Table of Content v

List of Tables viii

List of Figures ix

List of Abbreviations, Symbol and Nomenclature xi

CHAPTER 1: INTRODUCTION 1

1.1 Background 1

1.2 Problem Statement 2

1.3 Objectives 3

1.4 Scope of Project 3

1.5 Organization of the Report 4

CHAPTER 2: LITERATURE REVIEW 5

2.1 Introduction 5

2.2 State of the Art on Motion Control in Machine Tool 6

2.2.1 Mechanical Drive System 6

2.2.2 Disturbance in Drive System 12 2.3 Tracking Performance of Machine Tools–A Controller Design Approved 17

2.3.1 Controller Design 17

2.3.2 Controller Design based on PID 18

2.3.3 Controller Design based on NPID 20

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CHAPTER 3: METHODOLOGY 23

3.1 Introduction 23

3.2 Flowchart 23

3.3 Experimental Setup 27

3.4 System Identification and Modelling 29

3.5 Summary 32

CHAPTER 4: RESULT AND DISCUSSION 33

4.1 Controller Design 33

4.1.1 PID Controller 33

4.1.1.1General Structure and Configuration of PID Controller 33 4.1.1.2Design and Analysis of PID Controller 35 4.1.1.3Transient Response Analysis for PID Controller 39

4.1.2 NPID Controller 41

4.1.2.1General Structure and Configuration of NPID Controller 41 4.1.2.2Design and Analysis of NPID Controller 42

4.2 Maximum Tracking Error 46

4.2.1 PID Controller 46

4.2.1.1Simulation Result 46

4.2.1.2Experimental Result 48

4.2.2 NPID Controller 50

4.2.2.1Simulation Result 50

4.2.2.2Experimental Result 52

4.3 Root Mean Square Error (RMSE) 54

4.4 Discussion 56

4.4.1 Discussion on Results of Maximum Tracking Error 56

4.4.2 Discussion on Result of RMSE 57

4.5 Summary 58

CHAPTER 5: CONCLUSION AND RECOMMENDATION FOR

FUTURE WORK 59

5.1 Conclusion 59

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vii

REFERENCES 61

APPENDICES

A POPOV PLOT CODING

B TO PLOT GRAPH Ke VS e

C TO PLOT GRAPH FROM SIMULATION

D VALUE OF TUNING Ke PARAMETER

E GANTT CHART FOR SEMESTER I

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viii

LIST OF TABLES

2.1 Relationship between gain parameter of PID controller in a

close loop system 19

3. 1 Main component of the experimental setup 28

3. 2 Summarises the model parameters, A, B, C and Td for x-axis. 31

4. 1 Gain values of the Kp, Ki and Kd of x-axis for PID controller 36

4. 2 Gain and Phase margin of x-axis open loop position 37 4. 3 Transient response criteria for PID controller 40

4. 4 Value of tuned NPID parameters 44

4. 5 Simulated maximum tracking error of the system with PID controller 47 4. 6 Experimental maximum tracking error of system with PID controller 50 4. 7 Simulated maximum tracking error of system with NPID controller 52 4. 8 Experimental maximum tracking error of system with NPID controller 54 4. 9 Comparison in RMSE values for different controller 55 4. 10 Comparison in maximum tracking error for different between 61

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LIST OF FIGURE

2.1 Rack and pinion drive system 7

2.2 Structure of iron-core linear drive system 8

2.3 Direct linear drive system 9

2.4 Ball screw drive system 9

2.5 Ball screw and nut mechanism 10

2.6 Mechanical efficiency of ball screw 10

2.7 Structure of piezoelectric drive system 11

2.8 Piezoelectric stack 12

2.9 Friction force motion 13

2.10 Quadrant glitches in circular test 14

2.11 Cutting parameter direction in the cutting zone 15

2.12 Basic structure of PID controller 19

2.13 Nonlinear PID controller 21

3.1 Flowchart of the research methodology 25

3.2 Googol Tech XY Milling Table 27

3.3 Schematic diagram of the experimental setup 28

3.4 Simulink diagram for FRF measurement 29

3.5 FRF's measurement of the x-axis and y-axis 30

3.6 FRF measurement and proposed for x-axis 31

4.1 PID control structure 34

4.2 Flowchart of the procedure to obtain parameter of PID controller 35

4.3 Bode Diagram of Open Loop Function of x-axis 36

4.4 Nyquist plot of the x-axis position open loop transfer function

based on measured FRFs of the system via PID controller 37 4.5 Bode magnitude diagram of sensitivity for x-axis via PID controller 38 4.6 Bode diagram of position closed loop via PID controller 39

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4.7 Step Response of PID Controller 40

4.8 NPID control structure and configuration 41

4. 9 Flowchart of the procedure to obtain parameter of NPID controller 43

4. 10 Popov plot function 44

4. 11 Graph of nonlinear gain, Ke against error, e 45 4. 12 Simulated tracking error for PID controller at f=0.3 Hz 46 4. 13 Simulated tracking error of PID controller at f=0.5 Hz 47 4. 14 Control scheme of PID controller for experimental validation 48 4. 15 Experimental maximum tracking error for PID controller at f=0.3 Hz 49 4. 16 Experimental maximum tracking error for PID controller at f=0.5 Hz 49 4. 17 Simulated tracking error for NPID controller at f = 0.3 Hz 51 4. 18 Simulated tracking error for NPID controller at f = 0.5 Hz 51 4. 19 Control scheme of NPID controller for experimental validation 52 4. 20 Experimental tracking error for NPID controller at f = 0.3 Hz 53 4. 21 Experimental tracking error for NPID controller at f = 0.5 Hz 53 4. 22 Comparison of experimental RMSE of the controller 55

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LIST OF ABBREVIATIONS, SYMBOLS AND

NOMENCLATURE

CCC - Cross-Coupling Controller

CNC - Control Numerical Computer ENPID - Enhanced Nonlinear PID FLC - Fuzzy Logic Control

FRF - Frequency Response Function

I/O - Input/Output

LTI - Linear Time Invariant MMI - Man-Machine Interphase MRR - Material Removal Rate NPID - Nonlinear PID

PID - Proportional, Integral and Derivative RMSE - Root Mean Square Error

SISO - Single Input Single Output SMC - Sliding Mode Controller

Fc - Cutting Force

Ft - Thrust Force

Fs - Cutting Speed

N - Normal Direction

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1 This chapter presents a brief introduction about the project. Firstly is the background of the project entitle Design of PID and Nonlinear PID Controller for Tracking Performance of XY Table Ball Screw Drive System. Then, the detail of the problem statement of the project and followed by the objectives of the project. Based on the problem statement and the objectives of the project, the scope of this project is identified. Finally the organization of the project is elaborated in Section 1.5.

1.1 Background

XY table ball screw drive system is a basic structure of CNC machine. In machine tools environment, the area of interest of CNC machine is to obtain high accuracy, precise positioning and robustness of a system. In order to obtain high accuracy and precise positioning of machine tools, it is important to consider the presence of disturbance forces in the system. The disturbance forces will negatively limit the performance of the controlled system. The disturbance forces are friction force and cutting force.

Cutting force disturbance exist in nature during milling process. It is not possible to avoid the cutting force disturbance as it is automatically generate from the interaction between the cutting tool and the work piece

.

The cutting force characteristics are influenced by the cutting parameters such as depth of cut, spindle speed, and feed rate. Variations in these cutting conditions will affect behaviour of the cutting forces

INTRODUCTION

CHAPTER 1

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2 in terms of its magnitudes and its harmonics content. Failure to realize this phenomenon could reduce the quality of the finished product as the cutting forces may cause vibration of the structure thus leading to a poor surface finish. Hence, an efficient and reliable compensation technique is desired in order to improve the tracking performance in machine tools applications ( Abdullah et al., 2013)

Previously, PID controller has been designed to compensate the cutting force disturbance. However, the conventional PID position controller shows its limitation especially at varying cutting force disturbance (Zhao et al., 2009). In this project, PID controller and nonlinear PID (NPID) controller is designed to obtain tracking performance in XY table ball screw drive system. However, in this research project the disturbance is not consider because we focusing on the performance of the tracking error with different frequencies.

1.2 Problem Statement

XY table ball-screw driven system is a mechanism that is actuated by AC servo drives. It has been widely used in many applications due to its low cost (Tao et al., 2006). Nowadays, machine tools industries are looking for high accuracy and precise positioning and to obtain better surface finish product. There are various types of controller that can be used to obtain these criteria. However to design a good controller for the machine tools, the understanding about the control system is needed.

According to (Rao, 2006), there are three requirement of the control systems analysis and design. First is to produce a good transient response. Second is to minimize the steady-state error. Last but not least is to achieve the stability. The main problem of this research is to design a controller that have a good stability with the lowest error.

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1.3 Objective

The objectives of this project are:

i. To design PID and Nonlinear PID controller for improvement in tracking performance of the XY table ball screw drive system.

ii. To validate the controller through simulation using MATLAB/Simulink software and experimental work using XY table ball screw drive system.

1.4 Scope of Project

The scopes of this project are:

i. Analysis of the performance of the XY table ball screw drive system is using PID and nonlinear PID controller.

ii. The axis used in this research is focused on the x-axis of the XY table ball screw drive system. This is due to the transfer function that been used is just for x-axis.

iii. In order to obtain tracking performance of XY table ball screw drive system, the input signal used must be sinusoidal or sine input.

iv. The frequencies used in this research are 0.3 Hz and 0.5 Hz. This is because of the machine limitation.

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1.5 Organization of the Report

The report is organized as follows:

i. Chapter 2 consists of literature review on mechanical drive system in machine tools, disturbance forces in drive system and a controller design of tracking performance of machine tools.

ii. Chapter 3 describes the methodology of this research work. In general, it includes the overall flowchart on how the research is carried out. In addition, it discusses about experimental setup and system identification and system modelling of the system and finally it touches Gantt chart during this final year project.

iii. Chapter 4 elaborates and discusses on design and analysis of the controller. Basically, it involves the procedural steps on how to design the selected control techniques. This chapter also discussed on general structure and configuration of the controller. Next, the result and discussion on the numerical and experimental results of each design controller in term of maximum tracking error and root mean square error (RMSE). The discussion also focusses on performance measures analysis of the controllers.

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5 This chapter provide the information that relevant to the project. The introduction of the project is elaborated in section 2.1. In section 2.2, the state of the art on motion control in machine tools is elaborate in details. It covers the mechanical drive system and disturbance force in drive system in section 2.2.1 and section 2.2.2 respectively. Finally in section 2.3, a controller design approach is elaborated in great detail. It consist of section 2.3.1 controller design, section 2.3.2 a controller design based on PID and section 2.3.3 a controller design base on NPID. Last but not least is a summary of the literature review in section 2.4.

2.1 Introduction

In machine tools environment, the demand of CNC machine is high accuracy, precision and robustness attributes (Moriwaki, 2008). Besides, a low cost and great control system towards various disturbance force also an advantage to control engineer if they able to fulfil these need. According to Moriwaki (2008), in order to increase flexibility in the design of machine tool controllers, the open controller architecture is also an important issue. In order to obtain high accuracy, precise positioning and robustness in machine tools, presence of disturbance force must be considered. This is because these disturbance forces will affect the tracking performance of machine tools. In general, with the intention of improving tracking performance of the XY table, this research is concentrate on compensating cutting force disturbance.

LITERATURE REVIEW

CHAPTER 2

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2.2 State of the Art on Motion Control in Machine Tool

Nowadays, mechanical drive system move toward new technology in order to meet the demand for precision positioning and high speed of the system. This technology gives more challenging task to the control society in order to compensating disturbance force and achieving better tracking performance. This section is a discussion on the change in the mechanical drive system and a literature review on the disturbance force and a controller design approach in order to obtain tracking performance of the machine tools.

2.2.1 Mechanical Drive System

Mechanical drives system technology has seen a change from rack and pinion drive system to a more sophisticated linear direct drive and piezoelectric drive system. The changes of direct drive systems over conservative electromechanical drive systems have provided the industry with high tracking performance and speed. In addition it will eliminate the conservative electromechanical drive system as discussed in the following paragraph. There are four types of mechanical drive systems in machine tools namely;

i. Rack and pinion drives system. ii. Linear direct drive system iii. Ball screw drive system iv. Piezoelectric drive system.

Rack and pinion drive system is a first mechanical drive system that consists of a pair of gears which are a circular gear known as pinion and a linear gear recognize as rack. As illustrates in Figure 2.1, it show that rack and pinion drive system change rotational motion to a linear motion. According to (Altintas et al., 2011) the rack and pinion drives are suitable for long travel distances machine tools. This is because the rack and pinion drive system with low revolution in power transfer produced high torque. The rack and pinion drive system is possible to be improvised in term of

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7 performance by designing it with clearance freedom and high torsional stiffness (Altintas et al., 2011).

Figure 2.1: Rack and pinion drive system

Secondly is the direct drive linear motors drive system. Direct drive linear motors drive system started to capture attention within the machine tools society. Linear motor stages are directly driven axes with linear motors, which are designed as a plug and play solution. Standardized cable chains and customized cable guides are possible as an option. They are complete axes with distance measurement system, linear guide way, limit switch and optionally covers as protection against ambient influences (Anonymous, n.d.). Besides, an arresting brake also can be added as an option. Due to the direct drive, the linear stages are backlash-free, very dynamic, low maintenance and can be equipped with several blocks.

In general, direct drive system comprises of lamination stacks, coils and magnets while the type of motor associated with the direct drive is the special class of synchronous brushless servo motor as shown in Figure 2.2. The key attribute of a direct drive system is the mechanism that transform the electrical energy to linear mechanical movement as a result of the electromagnetic interaction between a coil assembly which is the fundamental part and the permanent magnet assemble (secondary part).

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8 Figure 2.2: Structure of iron-core linear drive system

Direct drive system has no physical transmission between motor and load (Chiew,2013). These conditions as a result lead to eliminating the negative effect of friction and backlash that are naturally exist in the transmission mechanism in ball screw drive system. Hence, better tracking performance is now possible to be achieved in the absence of the transmission errors. There are some disadvantages in linear direct drive system. First, due to the absence of transmission mechanism, load variations, external disturbances and cogging forces will greatly affect the tracking performance of the system. Thus, it makes the design of controller becomes more overwhelming job. Secondly, direct drive is more expensive than ball screw drive. Pritschow (1998) claims that for same level of power values, the size of ball screw drive is smaller than the total size of linear drive. There are a lot of criteria for the direct drive linear to be a good drive system. There are:

i. Drive is free of friction and wear ii. Several blocks per axis

iii. Can be combined with other linear stage iv. Smooth running

v. Long operating life and reliability vi. High moving speed

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9 Figure 2.3: Direct linear drive system

The third drive system is ball screw drive system. Ball screw drive system is more efficiency and because of that it has widely used in manufacturing industrial all over the world because of the efficiency factor that is offered by the ball screw drive system. Ball screws also known as ball bearing screws or recirculating ball screws consist of a nut integrated with balls and a screw spindle and the balls’ return mechanism, return caps or return tubes. Ball screws are the most common type of drive system that used in precision machines and industrial machinery. The primary function of a ball screw is to transform rotary motion to linear motion or torque to thrust, and vice versa, with the features of reversibility, high accuracy and efficiency. Ball screw drive system consists of a nut with recirculating balls, and a lead screw supported by bearings at two ends as shown in Figure 2.4.

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1.5 Organization of the Report

The report is organized as follows:

i. Chapter 2 consists of literature review on mechanical drive system in machine tools, disturbance forces in drive system and a controller design of tracking performance of machine tools.

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2.1 Introduction

LITERATURE REVIEW

CHAPTER 2

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2.2 State of the Art on Motion Control in Machine Tool

2.2.1 Mechanical Drive System

i. Rack and pinion drives system. ii. Linear direct drive system iii. Ball screw drive system iv. Piezoelectric drive system.

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7 performance by designing it with clearance freedom and high torsional stiffness (Altintas et al., 2011).

Figure 2.1: Rack and pinion drive system

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8 Figure 2.2: Structure of iron-core linear drive system

i. Drive is free of friction and wear ii. Several blocks per axis

iii. Can be combined with other linear stage iv. Smooth running

v. Long operating life and reliability vi. High moving speed

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9 Figure 2.3: Direct linear drive system

Design Of PID And Nonlinear PID Controller For Tracking Performance Of XY Table Ball Screw Drive System.

UNIVERSITI TEKNIKAL MALAYSIA MELAKA