design of controllers for improving contour accuracy in a high-speed milling machine

141 Pages·2005·2.1 MB·English

DESIGN OF CONTROLLERS FOR IMPROVING CONTOUR ACCURACY IN A
HIGH-SPEED MILLING MACHINE

By

JINHO LEE

A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2005
Copyright 2005

by

Jinho Lee
ACKNOWLEDGMENTS
I express my sincerest appreciation to Dr. John Ziegert for his patience, support and
guidance. I also express my gratitude to Dr. Warren Dixon for his valuable advice on
nonlinear control. Furthermore, I thank Dr. John Schueller, Dr. Tony Schmitz and Dr.
Jacob Hammer for serving on my supervisory committee. I also thank all of the members
of the Machine Tool Research Center for their assistance and friendship.
I thank Curt Wilson (Delta Tau Data Systems Inc.) who kindly replied to my
continuous questions and gave valuable advice.
I extend most heartfelt thanks to my parents for their endless support, sacrifice, and
unconditional love. I also thank my sister, brother, brother-in-law, and sister-in-law for
their constant understanding and encouragement. My thanks also go to my cute and
lovable nephew and nieces for making me smile whenever I think of them. The warm
love of my family motivates me to go on.
Last but foremost, I thank my wife, Seung-Yoon Ryu. Without her, I could
complete nothing that is worth accomplishing. She gave me endless love and support,
which are deeply appreciated.
iii
TABLE OF CONTENTS

page
ACKNOWLEDGMENTS.................................................................................................iii
LIST OF TABLES............................................................................................................vii
LIST OF FIGURES.........................................................................................................viii
ABSTRACT......................................................................................................................xii
CHAPTER
1 INTRODUCTION...................................................................................................1
1.1 Controllers....................................................................................................2
1.1.1 Feedback Controllers.......................................................................2
1.1.2 Feedforward Controllers..................................................................3
1.1.3 Robust Controllers...........................................................................3
1.1.4 Cross Coupling Controllers..............................................................4
1.2 Literature Review of Cross Coupling Controllers.......................................5
1.3 Task Specification........................................................................................7
2 DESCRIPTION OF TEST BED..............................................................................9
2.1 Mechanical Subsystem...............................................................................10
2.1.1 X-axis ............................................................................................10
2.1.2 Y-axis ............................................................................................11
2.1.3 Z-axis ............................................................................................11
2.2 Electrical Subsystem..................................................................................11
2.2.1 Controller.......................................................................................12
2.2.2 Interface Modules..........................................................................13
2.2.3 Amplifiers......................................................................................13
3 SYSTEM IDENTIFICATION...............................................................................15
3.1 System Modeling.......................................................................................15
3.1.1 Position Feedback..........................................................................16
3.1.2 Current Feedback...........................................................................16
3.1.3 Electromechanical Feed Drive System..........................................17

iv
3.2 X-axis System Modeling and Verification................................................18
3.2.1 Modeling the Viscous Friction Coefficient (B )............................18
x
3.2.2 Modeling the Equivalent Moment of Inertia (J ).........................21
eq
3.2.3 Modeling Verification....................................................................21
3.3 Y-axis System Modeling and Verification................................................23
3.3.1 Modeling the Viscous Friction Coefficient (B )............................23
y
3.3.2 Modeling the Total Moving Mass (M)...........................................25
3.3.3 Modeling Verification....................................................................28
3.4 Sensitivity of Model Parameters................................................................28
3.5 Reversal Error of X-axis............................................................................30
4 DESIGN OF THE PROPORTIONAL-INTEGRAL-DERIVATIVE
CONTROLLER.....................................................................................................34
4.1 Tuning Procedures.....................................................................................34
4.1.1 Proportional-Integral-Derivative Tuning for the X-axis................36
4.1.2 Proportional-Integral-Derivative Tuning for the Y-axis................37
4.2 Balancing Servo Parameters between the X- and Y-axes..........................39
5 DESIGN OF THE FEEDFORWARD CONTROLLER.......................................43
5.1 Tuning Procedures.....................................................................................44
5.1.1 Feedforward Tuning for the X-axis...............................................44
5.1.2 Feedforward Tuning for the Y-axis...............................................45
5.2 Balancing Servo Parameters between the X- and Y-axes..........................49
6 DESIGN OF THE TRADITIONAL CROSS COUPLING CONTROLLER........51
6.1 Variable Gain for Cross Coupling Controller............................................52
6.1 1 Linear Contour...............................................................................52
6.1.2 Circular Contour............................................................................53
6.2 Implementation Method.............................................................................54
7 DESIGN OF THE ADAPTIVE NONLINEAR CROSS COUPLING
CONTROLLER.....................................................................................................56
7.1 Three-Axis Computer Numerical Control (CNC) Machine Tool
Dynamics...................................................................................................56
7.2 Control Development.................................................................................61
7.2.1 Control Objective...........................................................................61
7.2.2 Closed-Loop Error System............................................................61
7.2.3 Stability Analysis...........................................................................62
7.3 Unknown Disturbance Extension..............................................................64
7.3.1 Control Formulation.......................................................................64
7.3.2 Stability Analysis...........................................................................67
7.4 Implementation Method.............................................................................67

v
8 EXPERIMENTAL RESULTS...............................................................................70
8.1 Square Path................................................................................................72
8.2 Diamond Path.............................................................................................73
8.3 Circular Path..............................................................................................74
9 CONCLUSIONS AND FUTURE WORKS..........................................................93
APPENDIX
A SPECIFICATIONS OF TEST BED......................................................................95
B MEASUREMENT OF X- AND Y-AXIS INERTIAL PARAMETERS...............97
B.1 Equivalent Moment of Inertia of X-axis....................................................97
B.2 Total Moving Mass of Y-axis....................................................................98
C USER-WRITTEN SERVO ALGORITHMS FOR TRADITIONAL CROSS
COUPLING CONTROLLER................................................................................99
C.1 User-Written Servo Algorithm for Traditional Cross Coupling
Controller (Linear Contour).....................................................................100
C.2 User-Written Servo Algorithm for Traditional Cross Coupling
Controller (Circular Contour)..................................................................101
D IMPORTANT VARIABLES SETUP FOR TRADITIONAL CROSS
COUPLING CONTROLLER..............................................................................103
E DERIVATION OF LINEAR REGRESSION MATRIX.....................................104
F USER-WRITTEN SERVO ALGORITHM FOR ADAPTIVE NONLINEAR
CROSS COUPLING CONTROLLER................................................................106
F.1 User-Written Servo Algorithm for Adaptive Nonlinear Cross Coupling
Controller (Linear Contour).....................................................................106
F.2 User-Written Servo Algorithm for Adaptive Nonlinear Cross Coupling
Controller (Circular Contour)..................................................................109
G EXPERIMENTAL RESULTS FROM GRID PLATE........................................114
LIST OF REFERENCES.................................................................................................125
BIOGRAPHICAL SKETCH...........................................................................................128

vi
LIST OF TABLES
Table page

3-1 Summary of the obtained J ...................................................................................22
eq.
3-2 Summary of the obtained M.....................................................................................27
4-1 Proportional and derivative gain tuning for the x-axis.............................................37
4-2 Proportional and derivative gain tuning for the y-axis.............................................39
5-1 Proportional, derivative and feedforward gain tuning for the x-axis.......................45
5-2 Proportional, derivative and feedforward gain tuning for the y-axis.......................47
8-1 Feedrates and accelerations for each path................................................................72
8-2 Comparison of contouring performance for circular path........................................91
8-3 Comparison of control effort for circular path.........................................................92
A-1 Specifications for the x- and z-axis servomotor.......................................................95
A-2 Specifications for the y-axis linear motor................................................................95
A-3 Specifications for the y-axis linear encoder.............................................................96
A-4 Specifications for the x- and y-axis hydrostatic guide way.....................................96
A-5 Specifications for the x- and z-axis amplifier..........................................................96
A-6 Specifications for the y-axis amplifier.....................................................................96
B-1 Mass of linearly moving components in the x-axis..................................................97
B-2 Moment of inertia of rotational components in the x-axis.......................................97
B-3 Mass of moving components in the y-axis...............................................................98
D-1 Important I variables setup for the traditional CCC implementation.....................103
G-1 Comparison of contouring performance for circular path......................................124
vii
LIST OF FIGURES
Figure page

1-1 Contour error in machining a contour........................................................................1
1-2 Feedback controller for a single axis drive system....................................................2
1-3 Feedforward controller for a single axis drive system...............................................3
1-4 Axial and contour errors for different cutter locations...............................................4
1-5 Cross coupling controller for a biaxial drive system..................................................5
2-1 High-speed milling machine (HSM2)........................................................................9
2-2 Guideways for (a) x-axis, (b) y-axis and (c) z-axis..................................................12
2-3 Schematic diagram of electrical components for the HSM2....................................13
2-4 Interface modules for (a) x- and z-axis and (b) y-axis.............................................14
2-5 Amplifiers for (a) x- and z-axis and (b) y-axis.........................................................14
3-1 Simplified system block diagram of the HSM2.......................................................15
3-2 Block diagram of the Turbo PMAC2 servo loop.....................................................16
3-3 Block diagram of the Turbo PMAC2 current loop..................................................17
3-4 Block diagram of the x-axis electromechanical feed drive system..........................18
3-5 Block diagram of the y-axis electromechanical feed drive system..........................18
3-6 Sample friction measurement on x-axis feed drive..................................................20
3-7 Viscous friction measurement on x-axis feed drive.................................................20
3-8 Sample moment of inertia measurement on x-axis feed drive.................................22
3-9 Comparison of simulation to actual system (x-axis position loop)..........................24
3-10 Sample friction measurement on y-axis feed drive..................................................26
viii
3-11 Viscous friction measurement on y-axis feed drive.................................................26
3-12 Sample mass measurement on y-axis feed drive......................................................27
3-13 Comparison of simulation to actual system (y-axis position loop)..........................29
3-14 Sensitivity of the x-axis viscous friction coefficient................................................31
3-15 Sensitivity of the x-axis equivalent moment of inertia............................................31
3-16 Sensitivity of the y-axis viscous friction coefficient................................................32
3-17 Sensitivity of the y-axis mass...................................................................................32
3-18 The two-dimensional grid encoder set up in HSM 2...............................................33
4-1 Motion command for controller performance evaluation........................................35
4-2 The PID tuned x-axis response to 0.5 m/s motion command...................................38
4-3 The PID tuned y-axis response to 0.5 m/s motion command...................................40
4-4 Contour error before balancing PID controller servos.............................................41
4-5 Contour error after balancing PID controller servos................................................41
5-1 The feedforward scheme in Turbo PMAC2.............................................................44
5-2 The PID and feedforward tuned x-axis response to 0.5 m/s motion command.......46
5-3 The PID and feedforward tuned y-axis response to 0.5 m/s motion command.......48
5-4 Contour error before balancing PID and feedforward controller servos..................50
5-5 Contour error after balancing PID and feedforward controller servos.....................50
6-1 Cross coupling controller for a biaxial drive system................................................51
6-2 Linear contour error.................................................................................................53
6-3 Circular contour error...............................................................................................54
7-1 Time-varying coordinate frame................................................................................58
7-2 The 2-D plane curve parameterization.....................................................................67
8-1 Square path on the x-y plane....................................................................................70
8-2 Diamond path on the x-y plane................................................................................71
ix
8-3 Circular path on the x-y plane..................................................................................71
8-4 Comparison between motor encoder data and grid plate data in square path.
(0.2m/s feedrate).......................................................................................................76
8-5 Comparison between motor encoder data and grid plate data in square path.
(0.4m/s feedrate).......................................................................................................77
8-6 Comparison of corner behaviors in square path with 0.2m/s feedrate.....................78
8-7 Comparison of contouring performance in square path with 0.2m/s feedrate.........79
8-8 Comparison of corner behaviors in square path with 0.4m/s feedrate.....................80
8-9 Comparison of contouring performance in square path with 0.4m/s feedrate.........81
8-10 Comparison between motor encoder data and grid plate data in diamond path.
(0.2m/s feedrate).......................................................................................................82
8-11 Comparison between motor encoder data and grid plate data in diamond path.
(0.4m/s feedrate).......................................................................................................83
8-12 Comparison of corner behaviors in diamond path with 0.2m/s feedrate.................84
8-13 Comparison of contouring performance in diamond path with 0.2m/s feedrate......85
8-14 Comparison of corner behaviors in diamond path with 0.4m/s feedrate.................86
8-15 Comparison of contouring performance in diamond path with 0.4m/s feedrate......87
8-16 Comparison between motor encoder data and grid plate data in circular path.
(0.2m/s feedrate).......................................................................................................88
8-17 Comparison between motor encoder data and grid plate data in circular path.
(0.4m/s feedrate).......................................................................................................89
8-18 Comparison of contouring performance in circular path with 0.2m/s feedrate........90
8-19 Comparison of contouring performance in circular path with 0.4m/s feedrate........90
8-20 Comparison of contouring performance in circular path with 0.4m/s feedrate.
(0.06m radius)..........................................................................................................91
C-1 Traditional CCC implementation on HSM2............................................................99
G-1 Comparison of corner behaviors in square path with 0.2m/s feedrate...................115
G-2 Comparison of contouring performance in square path with 0.2m/s feedrate.......116
x